Which is the factorised form of (x^2+17x+72)?
Correct answer: A
Here (8+9=17) and (8\cdot9=72). In exams choose factors of the constant whose sum is the middle coefficient.
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Factorisation
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Expert · Level 69 · factorisation,trinomial,split middle
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- ((x+8)(x+9))
- ((x+6)(x+12))
- ((x-8)(x-9))
- ((x+4)(x+18))
Expert · Level 69 · factorisation,negative factors,trinomial
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- ((x+9)(x+10))
- ((x-9)(x-10))
- ((x-5)(x-18))
- ((x-6)(x-15))
Expert · Level 69 · factorisation, algebraic identities, perfect square trinomial, binomial square, class 9 mathematics
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- \(x^2+10x+25\)
- \(x^2+10x+24\)
- \(x^2-25\)
- \(x^2+5x+25\)
Expert · Level 69 · factorisation,signed quadratic,expert
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- ((3x-1)(x+5))
- ((3x+5)(x-1))
- ((3x-5)(x+1))
- ((3x+1)(x-5))
Expert · Level 69 · perfect square,identity,factorisation
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- ((2a-3b)^2)
- ((2a+3b)^2)
- ((4a-9b)^2)
- ((2a-9b)(2a-b))
Expert · Level 69 · factorisation, algebraic identities, perfect square trinomial, class 9 mathematics, polynomial factorisation
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- \(x^2+10x+25\)
- \(x^2+10x+20\)
- \(x^2-25\)
- \(x^2+25\)
Expert · Level 69 · factorisation, algebraic identities, middle term, sign error, quadratic expressions
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- \((3m+2n)(4m-5n)\)
- \((3m-2n)(4m+5n)\)
- \((3m-5n)(4m+2n)\)
- \((6m+5n)(2m-2n)\)
Expert · Level 69 · grouping,common binomial,factorisation
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- ((a-5)(b-2))
- ((a+5)(b-2))
- ((a-5)(b+10))
- ((a-5)(b+2))
Expert · Level 69 · factorisation, algebraic identities, perfect square trinomial, class 9 mathematics
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- \(4p^2-12pq+9q^2\)
- \(4p^2-12pq-9q^2\)
- \(4p^2+12pq+6q^2\)
- \(4p^2-6pq+9q^2\)
Expert · Level 69 · sum of cubes,factorisation,identity
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- ((3a+4b)(9a^2-12ab+16b^2))
- ((3a-4b)(9a^2+12ab+16b^2))
- ((27a+64b)(a^2-b^2))
- ((3a+4b)(9a^2+12ab+16b^2))
Expert · Level 69 · algebraic identities, factorisation, perfect square trinomial, class 9 mathematics
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- \((p+q)^2\)
- \((p-q)^2\)
- \((p+q)(p-q)\)
- \(p^2+q^2\)
Expert · Level 69 · perfect cube,negative cube,factorisation
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- ((x+2)^3)
- ((x-4)^3)
- ((x-2)^3)
- ((x-2)(x^2+4))
Expert · Level 69 · common factor,trinomial,factorisation
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- (2y(x^2+3x+2))
- (2y(x+1)(x+2))
- (y(2x+2)(x+2))
- (2xy(x+3+2))
Expert · Level 69 · perfect square,factorisation,identity
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- ((2x+5)^2)
- ((4x-5)^2)
- ((2x-10)(2x-5))
- ((2x-5)^2)
Expert · Level 69 · perfect square,negative middle,factorisation
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- ((3p-4q)^2)
- ((3p+4q)^2)
- ((9p-16q)^2)
- ((3p-8q)(3p-2q))
Expert · Level 69 · grouping,difference of squares,factorisation
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- ((x-y-z)(x-y+z))
- ((x+y-z)(x+y+z))
- ((x-y)^2-z^2)
- ((x-y-z)^2)
Expert · Level 69 · factorisation,grouping,identity
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- ((a+b+c)(a+b-c))
- ((a-b+c)(a-b-c))
- ((a+b)^2-c^2)
- ((a+c)(b-c))
Expert · Level 69 · complete factorisation,difference of squares,expert
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- ((x^2-4)(x^2+4))
- ((x-2)(x+2)(x^2+4))
- ((x-4)(x+4))
- ((x^2-2)(x^2+8))
Expert · Level 69 · difference of squares,complete factorisation,expert
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- ((4x^2-9y^2)(4x^2+9y^2))
- ((2x-3y)(2x+3y)(4x^2+9y^2))
- ((4x-9y)(4x+9y))
- ((2x-3y)^2(2x+3y)^2)
Expert · Level 69 · algebraic identities, factorisation, difference of squares, class 9 mathematics, perfect squares
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- \(49p^2-36q^2\)
- \(49p^2+36q^2\)
- \(49p^2-12pq+36q^2\)
- \(49p^2+12pq+36q^2\)
Factorise (x^2-19x+90).
Correct answer: B
Here (-9+(-10)=-19) and ((-9)(-10)=90). In exams use two negative signs when the constant is positive and the middle term is negative.
View question detailsWhich of the following polynomials can be factorised as the perfect square of a binomial?
Correct answer: A
\(x^2+10x+25=x^2+2\cdot x\cdot5+5^2=(x+5)^2\), so it is a perfect-square binomial. In option B, the constant should be 25. Exam tip: match the middle term with \(2ab\).
View question detailsWhat are the factors of (3x^2-14x-5)?
Correct answer: D
((3x+1)(x-5)=3x^2-14x-5). In exams look for factors with opposite signs when the constant is negative.
View question detailsWhat will be the factorised form of (4a^2-12ab+9b^2)?
Correct answer: A
(4a^2=(2a)^2), (9b^2=(3b)^2), and the middle term is (-12ab). In exams the sign of the middle term is decisive in a perfect square.
View question detailsWhich of the following expressions is a perfect-square trinomial that can be factorised as the product of two identical binomials?
Correct answer: A
\(x^2+10x+25=x^2+2\cdot x\cdot5+5^2=(x+5)^2\). Hence, it is the product of two identical binomials, \((x+5)(x+5)\). In option B, the middle term \(10x\) requires \(5\), so the constant term should be \(25\), not \(20\). Exam tip: use the identity \(a^2+2ab+b^2=(a+b)^2\).
View question detailsA student factorised \(12m^2-7mn-10n^2\) as \((3m-2n)(4m+5n)\). Which is the correct factorisation after checking the sign of the middle term?
Correct answer: A
In \((3m+2n)(4m-5n)\), the cross-products are \(-15mn\) and \(+8mn\), giving \(-7mn\). Option B gives \(+7mn\), so its middle-term sign is wrong. Exam tip: always add the cross-products to verify factorisation.
View question detailsFactorise (ab+2a-5b-10) by grouping.
Correct answer: D
The grouping gives (a(b+2)-5(b+2)). In exams you may need to take a negative factor from the second group.
View question detailsWhich of the following expressions is a perfect-square trinomial and can be factorised using an identity?
Correct answer: A
Here, \(4p^2=(2p)^2\) and \(9q^2=(3q)^2\). The middle term is \(-2(2p)(3q)=-12pq\), so A is \((2p-3q)^2\). In exams, always check the sign of the middle term.
View question detailsWhat is the factorised form of (27a^3+64b^3)?
Correct answer: A
It is ((3a)^3+(4b)^3). In exams the middle term in the second bracket is negative for sum of cubes.
View question detailsIn a trinomial, the first and last terms are \(p^2\) and \(q^2\) respectively, and the middle term is \(2pq\). What is its factorised form?
Correct answer: A
The identity \(p^2+2pq+q^2=(p+q)^2\) applies, so A is correct. In \((p-q)^2\), the middle term is \(-2pq\). Exam tip: check the middle-term sign first.
View question detailsFactorise (x^3-6x^2+12x-8).
Correct answer: C
It is ((x-2)^3) because the expansion gives (x^3-6x^2+12x-8). In exams match the signs of a perfect cube in order.
View question detailsWhat is the complete factorised form of (2x^2y+6xy+4y)?
Correct answer: B
First take out (2y), then (x^2+3x+2=(x+1)(x+2)). In exams check the trinomial after taking the common factor.
View question detailsWhat will be the factorised form of (4x^2-20x+25)?
Correct answer: D
(4x^2=(2x)^2), (25=5^2), and (-20x=-2\cdot2x\cdot5). In exams decide the sign from the middle term.
View question detailsChoose the correct factorised form of (9p^2-24pq+16q^2).
Correct answer: A
The two square terms come from (3p) and (4q), and the middle term is negative. In exams match all three terms of the perfect square.
View question detailsFactorise (x^2-2xy+y^2-z^2).
Correct answer: A
First (x^2-2xy+y^2=(x-y)^2), then apply difference of squares. In exams group first and apply the identity.
View question detailsWhat is the complete factorised form of (a^2+2ab+b^2-c^2)?
Correct answer: A
First (a^2+2ab+b^2=(a+b)^2), then apply difference of squares. In exams treat the perfect-square group as one term.
View question detailsCompletely factorise (x^4-16).
Correct answer: B
(x^4-16=(x^2-4)(x^2+4)) and (x^2-4=(x-2)(x+2)). In exams do not stop at partial factorisation.
View question detailsWhich is the complete factorised form of (16x^4-81y^4)?
Correct answer: B
It is ((4x^2)^2-(9y^2)^2), and (4x^2-9y^2) factors again. In exams check difference of squares repeatedly.
View question detailsWhich of the following expressions is a difference of two squares and can therefore be factorised using the identity \(a^2-b^2=(a-b)(a+b)\)?
Correct answer: A
\(49p^2=(7p)^2\) and \(36q^2=(6q)^2\), with a minus sign between them. Thus A becomes \((7p-6q)(7p+6q)\). In exams, check for two perfect squares separated by subtraction.
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