Factorising Solutions
Question 1
(a) 5(x + 5)
(e) 3xy(3xy + 1)
(b) 3x(x − 3)
(f ) x(1 + x + x2 )
(c) 4x(y + 10x)
(g) Can’t be factorised
(d) y(7x2 z − 8)
(h) y(16x2 y − 8x2 + 9)
Question 2 (Simple Factorisation)
(a) (x + 1)(x + 2)
(h) (x + 5)(x − 2)
(b) (x + 2)(x + 3)
(i) (x + 5)(x − 1)
(c) (x + 7)(x + 3)
(j) (x − 2)(x − 1)
(d) (x + 4)2
(k) (x − 5)(x − 2)
(e) (x + 2)2
(l) (x − 6)(x + 1)
(f ) (x + 4)(x + 5)
(m) (x − 2)2
(g) (x + 10)(x + 3)
(n) (x − 8)(x − 3)
Question 3 (More Factorisation)
(a) 3(x + 1)(x + 2)
(h) 11(x + 5)(x − 2)
(b) 4(x + 2)(x + 3)
(i) x(x + 1)(x + 2)
(c) 5(x + 2)(x + 5)
(j) x(x + 2)(x + 3)
(d) 7(x + 4)2
(k) 2x(x + 3)(x + 4)
(e) 2(x + 1)(x + 7)
(l) 3x2 (x + 5)(x + 1)
(f ) 3(x + 1)(x + 5)
(m) x5 (x − 2)2
(g) 5(x + 10)(x + 3)
(n) 4x8 (x + 2)(x + 3)
Question 4 (The Difference of Two Squares)
(a) (x − 2)(x + 2)
(e) (x − 10)(x + 10)
(i) (7 − x)(7 + x)
(b) (x − 3)(x + 3)
(f ) (2x − 3)(2x + 3)
(j) (3 − x)(3 + x)
(c) (x − 5)(x + 5)
(g) (8x − 4)(8x + 4)
(k) (2 − 5x)(2 + 5x)
(d) (x − 1)(x + 1)
(h) (9x − 6)(9x + 6)
(l) (7x − 4)(7x + 4)
Question 5 (More Differences of Two Squares)
(a) 3(x − 3)(x + 3)
(e) 3(x − 10)(x + 10)
(i) 2(5 − x)(5 + x)
(b) 2(x − 3)(x + 3)
(f ) 13(x − 2)(x + 2)
(j) 2(6 − x)(6 + x)
(c) 7(x − 2)(x + 2)
(g) 32(2x − 1)(2x + 1)
(k) 10(2 − 5x)(2 + 5x)
(d) 2(x − 1)(x + 1)
(h) 9(3x − 2)(3x + 2)
(l) 3(7x − 4)(7x + 4)
Polynomials Questions
Question 6 (Warming Up)
(a) x5 + x3 + x2 + x
(f ) −9x7 − x2 − 17
(b) x5 + 2x4 + 3x2
(g) −10x + 5
(c) 2x3 + 2x2 − 4x
(h) −13x10 − 7x5 + x2 + 14x
(d) 6x2 + 6x − 4
(i) −7x5 + 4x2 − 12x
(e) 7x5 − 6x2 − 6x + 5
Question 7 (Coefficients)
(a) 1
(d) 6
(g) 0
(b) 3
(e) −6
(h) 1
(c) 2
(f ) −1
(i) 4
Question 8 (Adding and Subtracting Polynomials)
(a) 7x3 + 8x2 + 7x + 11
(d) 6x3 + 6x2 + 2x − 9
(b) 11x2 + x + 1
(e) 2x2 + 9x + 2
(c) 5x2 − x − 20
(f ) 6x3 − 3x2 + 7x + 1
(g) −2x4 − 5x2 + 9x
(l) 7x2 + 2x + 6
(h) 15x3 + 13x + 1
(m) −3x2 − 48x + 42
(i) 8x2 + 16x + 21
(n) −2x3 + 85x2 − 13x + 89
(j) 15x2 + 15x + 51
(o) −10x4 + 3x3 − 15x2 + 48x − 14
(k) 31x3 + 38x2 + 52x + 44
Question 9 (Multiplying Polynomials)
(a) 10x2 + 34x + 28
(h) −50x6 − 85x4 − 36x
(b) 12x2 + 2x − 2
(i) 10x3 + 16x2 + 31x + 15
(c) 20x2 − 88x + 96
(j) 3x3 + 24x2 + 24x + 21
(d) 2x4 + 7x2 + 3
(k) 7x4 + 61x3 + 47x2 + 26x + 15
(e) 8x4 + 24x3 + 8x2 + 24x
(l) 3x4 + 9x3 + 16x2 + 14x + 8
(f ) 15x3 − x2 − 6x
(m) x4 + 5x3 − 15x2 + 38x − 20
(g) 35x8 − 21x6 − 25x5 + 15x3
(n) −x6 −5x5 +55x4 +x3 +121x2 −47x+
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