What is obtained by taking out the common factor from (12p^2q-8pq^2)?
Correct answer: B
The greatest common factor is (4pq). Exam tip: find common variables and numbers in every term.
View question detailsMathematics
Factorisation
TOPIC PRACTICE
Quiz this set
Up to 20 questions from this page. Select your focus, then start.
20 questions
Choose questions
Easy · Level 75 · monomial factor,greatest common factor,factorisation
View options
- (2pq(6p-4q))
- (4pq(3p-2q))
- (8pq(12p-q))
- (4p(3pq-2q^2))
Easy · Level 75 · minus square,perfect square,factorisation
View options
- ((z+2)^2)
- (z(z-4)+4)
- ((z-2)^2)
- ((z-4)(z+1))
Easy · Level 75 · algebraic identities, factorisation, perfect square trinomial, binomial square, class 9 mathematics
View options
- \(25p^2-20p+4\)
- \(25p^2-4\)
- \(25p^2-10p+4\)
- \(25p^2+20p+4\)
Easy · Level 75 · trinomial factorisation,easy quadratic,algebra
View options
- ((a+2)(a+3))
- ((a+1)(a+6))
- ((a-2)(a-3))
- ((a+5)(a+6))
Easy · Level 75 · factorisation,difference of squares,algebraic identities,quadratic expressions,class 9 mathematics
View options
- \((4n-5)(4n+5)\)
- \((4n-5)^2\)
- \((16n-5)(16n+5)\)
- \((n-5)(n+5)\)
Easy · Level 75 · greatest common factor,simple factorisation,linear
View options
- (2(4x+6))
- (8(x+12))
- (4(2x+3))
- (12(8x+1))
Easy · Level 75 · perfect square,coefficient,binomial
View options
- ((9x+1)^2)
- ((3x-1)^2)
- ((x+3)^2)
- ((3x+1)^2)
Easy · Level 75 · algebraic identities,factorisation,perfect square trinomial,binomial square,class 9 mathematics
View options
- \(x^2+6x+9\)
- \(x^2+6x+8\)
- \(x^2-9\)
- \(x^2+9\)
Easy · Level 75 · factorisation, algebraic identities, perfect square trinomial, class 9 mathematics, polynomial coefficients
View options
- 6
- 12
- 18
- 36
Easy · Level 75 · factorisation, common factor, algebraic expressions, class 9 mathematics, algebraic identities
View options
- \(7x^2+21x\)
- \(14x+7\)
- \(7x^2+14\)
- \(21x^2+7\)
Easy · Level 75 · factorisation, algebraic identities, perfect square trinomial, quadratic trinomial, class 9 mathematics
View options
- x^2+10x+25
- x^2+10x+20
- x^2+8x+25
- x^2+5x+10
Easy · Level 75 · factorisation, algebraic identities, distributive property, common factor, class 9 mathematics
View options
- \(5(3a-4)=15a-20\)
- \(5(3a-4)=15a-4\)
- \(5(3a-4)=15a-25\)
- \(5(3a-4)=8a-20\)
Easy · Level 75 · algebraic identities,factorisation,perfect square trinomial,class 9 mathematics,binomial square
View options
- \((m-n)^2\)
- \(m(m+2n)\)
- \((m+n)(m-n)\)
- \((m+n)^2\)
Easy · Level 75 · signed trinomial,factorisation,quadratic
View options
- ((c-2)(c-4))
- ((c+2)(c+4))
- ((c-1)(c-8))
- ((c+2)(c-4))
Easy · Level 75 · greatest common factor,two terms,factorisation
View options
- (3y(6x-8))
- (6y(3x-4))
- (18y(x-24))
- (24y(18x-1))
Easy · Level 75 · difference of squares,basic factorisation,identity
View options
- (x(x-1))
- ((x-1)^2)
- ((x-1)(x+1))
- ((x+1)^2)
Easy · Level 75 · algebraic identities, factorisation, perfect square trinomial, class 9 mathematics
View options
- \(x^2+14x+49\)
- \(x^2+14x+36\)
- \(x^2+7x+49\)
- \(x^2+14x+42\)
Easy · Level 75 · trinomial,sum product,factorisation
View options
- ((q+2)(q+3))
- ((q-1)(q-5))
- ((q+1)(q+5))
- ((q+6)(q+5))
Easy · Level 75 · difference of squares,two variables,factorisation
View options
- ((36p-49q)(36p+49q))
- ((6p-7q)^2)
- ((6p-q)(6p+49q))
- ((6p-7q)(6p+7q))
Easy · Level 75 · common factor,two variables,factorisation
View options
- (5xy(3x+4y))
- (5x(3xy+4y^2))
- (15xy(x+20y))
- (20xy(15x+1))
What is the factorised form of (z^2-4z+4)?
Correct answer: C
(4=2^2) and (-4z=-2\times z\times2), so it is ((z-2)^2). Exam tip: identify subtraction perfect squares.
View question detailsReena claims that \(25p^2-20p+4\) factorises as \((5p-2)^2\). Which is the correct expansion of \((5p-2)^2\) to verify her claim?
Correct answer: A
Using \((a-b)^2=a^2-2ab+b^2\), take \(a=5p\) and \(b=2\). The middle term is \(-2\times5p\times2=-20p\), so the expansion is \(25p^2-20p+4\). Exam tip: always check the sign of the middle term.
View question detailsWhat are the factors of (a^2+5a+6)?
Correct answer: A
(2+3=5) and (2\times3=6), so the factors are correct. Exam tip: check factors of the last term.
View question detailsWhat will be the factorised form of (16n^2-25)?
Correct answer: A
This expression is a difference of squares: \(16n^2=(4n)^2\) and \(25=5^2\). Using \(a^2-b^2=(a-b)(a+b)\), we get \(16n^2-25=(4n-5)(4n+5)\). Expanding \((16n-5)(16n+5)\) gives \(256n^2-25\), so it is not correct. Exam tip: identify the square roots of both terms before applying the difference-of-squares formula.
View question detailsWhich is the simplest factorised form of (8x+12)?
Correct answer: C
The greatest common factor of (8x) and (12) is (4). Exam tip: take the greatest factor for the simplest form.
View question detailsWhose square is (9x^2+6x+1)?
Correct answer: D
(9x^2=(3x)^2), (1=1^2), and (6x=2\times3x\times1). Exam tip: match the perfect square pattern.
View question detailsWhich of the following expressions can be factorised as the square of a binomial?
Correct answer: A
In \(x^2+6x+9\), the first and last terms are \(x^2\) and \(3^2\), while the middle term is \(2\times x\times3=6x\). Hence it is \((x+3)^2\). In \(x^2+6x+8\), the constant term is not \(3^2\). Exam tip: check whether the middle term equals \(2ab\).
View question detailsFor which value of \(b\) will the polynomial \(x^2+bx+36\) be a perfect-square trinomial?
Correct answer: B
Since \(36=6^2\), the required form is \((x+6)^2=x^2+2\times6x+36=x^2+12x+36\). Hence, \(b=12\). For \(b=6\), the middle term is not twice the square root of 36. Exam tip: double the square root of the constant term.
View question detailsIn which of the following expressions is \(7x\) a common factor of both terms?
Correct answer: A
Both terms of \(7x^2+21x\) are divisible by \(7x\): \(7x^2\div7x=x\) and \(21x\div7x=3\). Hence it factorises as \(7x(x+3)\). In B, the constant term 7 has no \(x\). Exam tip: check every term.
View question detailsWhich of the following quadratic trinomials is a perfect-square trinomial?
Correct answer: A
A perfect-square trinomial has the form \(a^2+2ab+b^2\). Here, \(x^2+10x+25=x^2+2\cdot x\cdot5+5^2=(x+5)^2\). In option B, the constant term would need to be \(25\). Exam tip: check whether the middle term equals twice the product of the square roots of the first and last terms.
View question detailsRima factorised the expression \(15a-20\) as \(5(3a-4)\). Which of the following expansions correctly verifies her answer?
Correct answer: A
Using the distributive property, multiply 5 by both terms: \(5\times3a=15a\) and \(5\times(-4)=-20\). Hence \(5(3a-4)=15a-20\). Exam tip: expand the bracket to check a factorisation.
View question detailsWhich is the factorised form of (m^2+2mn+n^2)?
Correct answer: D
Using \(a^2+2ab+b^2=(a+b)^2\), put \(a=m\) and \(b=n\). Thus, \(m^2+2mn+n^2=(m+n)^2\). Expanding \((m-n)^2\) gives the middle term \(-2mn\), so it is not correct. Exam tip: use the sign of the middle term to distinguish \((a+b)^2\) from \((a-b)^2\).
View question detailsWhat are the factors of (c^2-6c+8)?
Correct answer: A
(-2-4=-6) and ((-2)\times(-4)=8). Exam tip: for positive last term and negative middle term, take both signs negative.
View question detailsWhat is obtained by taking out the greatest common factor from (18xy-24y)?
Correct answer: B
The greatest common factor of (18xy) and (24y) is (6y). Exam tip: check numbers and variables together.
View question detailsChoose the factorised form of (x^2-1).
Correct answer: C
Since (1=1^2), (x^2-1) is a difference of squares. Exam tip: apply small identities carefully.
View question detailsWhich of the following expressions can be factorised using the identity \(a^2+2ab+b^2\)?
Correct answer: A
In \(x^2+14x+49\), \(49=7^2\) and the middle term is \(2\times x\times7=14x\). Hence it is \((x+7)^2\). In exams, check whether the middle term matches \(2ab\).
View question detailsWhat are the factors of (q^2+6q+5)?
Correct answer: C
(1+5=6) and (1\times5=5), so the correct pair is (1) and (5). Exam tip: match sum and product.
View question detailsWhat is the factorised form of (36p^2-49q^2)?
Correct answer: D
(36p^2=(6p)^2) and (49q^2=(7q)^2). Exam tip: form factors from square roots of both squares.
View question detailsWhich is the correct factorised form of (15x^2y+20xy^2)?
Correct answer: A
The greatest common factor in both terms is (5xy). Exam tip: keep the inside terms simplified.
View question detailsQUIZ COMPLETE