What is the value of (x^2-5x+6) when (x=2)?
Correct answer: A
Substitution gives (2^2-5\cdot2+6=0). In exams do powers first, then multiplication, then addition or subtraction.
View question detailsMathematics
Quadratic expressions
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Hard · Level 72 · quadratic expressions,evaluation,substitution
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- (0) / correct value
- (2) / substitution error
- (4) / square only
- (6) / constant only
Hard · Level 72 · quadratic expressions, algebraic identities, polynomial degree, class 9 mathematics, expression classification
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- \((x+1)(x-1)+1\)
- \((x+1)^2-x(x+2)\)
- \((x^2+1)(x+1)\)
- \(\frac{x^2}{x}+1\)
Hard · Level 72 · quadratic expressions,perfect square,unknown coefficient
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- (4) / square root only
- (8) / correct middle coefficient
- (16) / constant term
- (32) / doubled twice
Hard · Level 72 · quadratic expressions,complete square,unknown constant
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- (14) / middle coefficient
- (7) / half coefficient
- (49) / square of half coefficient
- (196) / square of middle coefficient
Hard · Level 72 · quadratic expressions,unknown coefficient,factorisation
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- (3) / one factor only
- (7) / one factor only
- (10) / sum of constants
- (21) / product of constants
Hard · Level 72 · quadratic expressions, algebraic identities, coefficients, polynomials, class 9 mathematics
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- 3x² + 5x + 8
- 2x² + 7x + 10
- 4x² - 3x + 1
- 5x² + 2x + 6
Hard · Level 72 · quadratic expressions,algebraic identities,binomial multiplication,polynomial expansion,distributive property
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- \(x^2-2x-8\)
- \(x^2+6x-8\)
- \(x^2-6x-8\)
- \(x^2+2x+8\)
Hard · Level 72 · quadratic expressions,expansion,cross terms
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- (2x^2+7x-15) / correct expansion
- (2x^2+10x-15) / one cross term missed
- (2x^2-13x-15) / sign error
- (2x^2+7x+15) / constant sign wrong
Hard · Level 72 · quadratic expressions,common factor,perfect square
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- (x^2-4x+4) / correct inside expression
- (5x^2-4x+4) / common factor incomplete
- (x^2+4x+4) / sign error
- (x^2-20x+20) / not simplified
Hard · Level 72 · quadratic expressions,complete factorisation,difference of squares
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- (3(x-3)(x+3)) / correct complete form
- (3(x^2-27)) / wrong common factor
- (3(x-9)(x+9)) / wrong square root
- (3(x-3)^2) / wrong identity
Hard · Level 72 · quadratic expressions,unknown constant,perfect square
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- (3) / half of (6)
- (9) / correct constant
- (12) / middle coefficient
- (36) / square of (6)
Hard · Level 72 · quadratic expressions,perfect square,unknown coefficient
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- (30) / positive middle
- (-30) / correct middle
- (15) / half middle
- (-15) / half value
Hard · Level 72 · algebraic identities, quadratic expressions, perfect square trinomial, binomial square, class 9 mathematics
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- \(9a^2-24ab+16b^2\)
- \(9a^2-12ab+16b^2\)
- \(9a^2+24ab-16b^2\)
- \(9a^2-16b^2\)
Hard · Level 72 · quadratic expressions, algebraic identities, perfect square trinomial, factorisation, class 9 mathematics
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- \(9p^2-24pq+16q^2\)
- \(9p^2-24pq+15q^2\)
- \(9p^2+24pq+15q^2\)
- \(9p^2-16q^2\)
Hard · Level 72 · quadratic expressions,cross terms,factorisation
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- ((3p-q)(2p+q)) / correct factors
- ((3p+q)(2p-q)) / middle sign wrong
- ((6p-q)(p+q)) / middle term wrong
- ((2p-q)(3p-q)) / constant sign wrong
Hard · Level 72 · quadratic expressions,algebraic identities,perfect square trinomial,factorisation,class 9 mathematics
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- \(9x^2+12x+4\)
- \(9x^2+12x+2\)
- \(9x^2+6x+4\)
- \(9x^2-12x+4\)
Hard · Level 72 · quadratic expressions,grouping,difference of squares
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- ((x+2-y)(x+2+y)) / correct form
- ((x-2-y)(x-2+y)) / sign error
- ((x+2)^2-y^2) / partial form
- ((x+y+2)^2) / wrong square
Hard · Level 72 · quadratic expressions,perfect square,difference of squares
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- ((x-3-z)(x-3+z)) / correct form
- ((x+3-z)(x+3+z)) / sign error
- ((x-3)^2-z^2) / partial form
- ((x-3-z)^2) / wrong square
Hard · Level 72 · quadratic expressions, factorisation, algebraic identities, binomial factors, class 9 mathematics
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- The sum of p and q is 7 and their product is 12
- The sum of p and q is -7 and their product is 12
- The sum of p and q is 12 and their product is 7
- The sum of p and q is 7 and their product is -12
Hard · Level 72 · quadratic expressions,unknown coefficient,negative middle
View options
- (3) / one constant
- (6) / one constant
- (9) / correct value
- (18) / product
Which of the following expressions remains a quadratic expression in x after simplification?
Correct answer: A
In option A, \((x+1)(x-1)+1=x^2-1+1=x^2\), whose highest power is 2, so it is quadratic. In option B, all variable terms cancel and only 1 remains. Exam tip: check the highest power after simplifying.
View question detailsIf (x^2+kx+16) is a perfect square and (k) is positive, what is the value of (k)?
Correct answer: B
(16=4^2), and in a perfect square the middle term is (2\cdot x\cdot4=8x). In exams double the root of the constant term.
View question detailsIf (x^2-14x+c) is a perfect square, what is (c)?
Correct answer: C
(-14x=-2\cdot x\cdot7), so (c=7^2=49). In exams take half of the middle coefficient and square it.
View question detailsThe factors of (x^2+px+21) are ((x+3)(x+7)). What is the value of (p)?
Correct answer: C
((x+3)(x+7)=x^2+10x+21), so (p=10). In exams the middle term comes from the sum of the constants.
View question detailsIn which quadratic expression is the constant term equal to the sum of the coefficients of its other two terms?
Correct answer: A
In 3x² + 5x + 8, the coefficients of x² and x are 3 and 5. Their sum is 3 + 5 = 8, which equals the constant term. In option B, 2 + 7 = 9, not 10. Exam tip: include signs while adding coefficients.
View question detailsWhich quadratic expression is obtained from ((x-4)(x+2))?
Correct answer: A
Use the distributive property: \((x-4)(x+2)=x(x+2)-4(x+2)=x^2+2x-4x-8=x^2-2x-8\). Therefore, the correct expression is \(x^2-2x-8\). In \(x^2+6x-8\), the negative sign of \(-4x\) has been handled incorrectly. Exam tip: write all four products first, then combine like terms.
View question detailsWhat is the expansion of ((2x-3)(x+5))?
Correct answer: A
(2x\cdot5=10x) and (-3\cdot x=-3x), so the middle term is (7x). In exams write all four products.
View question detailsAfter taking the common factor from (5x^2-20x+20), which quadratic expression remains inside?
Correct answer: A
Taking common (5) gives (5(x^2-4x+4)). In exams first take the common factor and then apply identities.
View question detailsWhat is the complete factorised form of (3x^2-27)?
Correct answer: A
First take out (3), and (x^2-9) is a difference of squares. In exams factorise the inside expression too.
View question detailsIf (4x^2+12x+k) is a perfect square, what is (k)?
Correct answer: B
(4x^2=(2x)^2) and (12x=2\cdot2x\cdot3), so (k=9). In exams identify the second part using (2ab).
View question detailsIf (9x^2+kx+25) is a perfect square and (k) is negative, what is (k)?
Correct answer: B
(9x^2=(3x)^2), (25=5^2), so the middle term is (-2\cdot3x\cdot5=-30x). In exams follow the given sign.
View question detailsWhich of the following expressions can be identified as a perfect square of a binomial?
Correct answer: A
Here, \(9a^2=(3a)^2\) and \(16b^2=(4b)^2\). The middle term is \(-2\times3a\times4b=-24ab\), so the expression is \((3a-4b)^2\). Exam tip: always verify the middle coefficient.
View question detailsWhich of the following quadratic expressions is a perfect square of a binomial?
Correct answer: A
A perfect-square trinomial has the form \(a^2\pm2ab+b^2\). Here, \(9p^2=(3p)^2\) and \(16q^2=(4q)^2\), while \(-2(3p)(4q)=-24pq\). Therefore, \(9p^2-24pq+16q^2=(3p-4q)^2\), so option A is correct. In option B, the last term is \(15q^2\) instead of \(16q^2\), so it is not a perfect square. Exam tip: take the square roots of the first and last terms, then check whether the middle term equals \(\pm2ab\).
View question detailsChoose the correct factorised form of (6p^2+5pq-q^2).
Correct answer: A
Actually ((3p-q)(2p+q)) gives (6p^2+pq-q^2). Check the cross terms carefully in exams.
View question detailsWhich of the following quadratic trinomials is the expansion of a perfect square?
Correct answer: A
\(9x^2+12x+4=(3x)^2+2(3x)(2)+2^2=(3x+2)^2\), so A is a perfect-square trinomial. D is also a square form, but it has a negative middle term: \((3x-2)^2\). Exam tip: compare the middle term with \(2ab\).
View question detailsWhat is the complete factorised form of (x^2+4x+4-y^2)?
Correct answer: A
First (x^2+4x+4=(x+2)^2), then apply difference of squares. In exams do not stop at the partial form.
View question detailsFactorise (x^2-6x+9-z^2).
Correct answer: A
First (x^2-6x+9=(x-3)^2), then use the (a^2-b^2) identity. In exams identify the perfect-square group.
View question detailsWhen the quadratic expression y^2 - 7y + 12 = (y-p)(y-q) is factorised, which statement about p and q is correct?
Correct answer: A
(y-p)(y-q)=y^2-(p+q)y+pq
. Comparing it with
y^2-7y+12
gives p+q=7 and pq=12. A sum of -7 would produce +7y. Exam tip: expand the signs once to verify the middle term.
The factors of (x^2-bx+18) are ((x-3)(x-6)). What is (b)?
Correct answer: C
((x-3)(x-6)=x^2-9x+18), so (b=9). In exams (b) remains positive because the expression has (-bx).
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