Three binomials and non-monic factorisation

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 4 marks
Factorise each expression.
(a) Factorise $2x^2 + 7x + 3$ (2)
(b) Factorise $6x^2 - x - 2$ (2)
Question 2Non-calculator · 4 marks
Consider $(2x+3)(x-4)$ .
(a) Expand and simplify. (2)
(b) Now multiply your result by (x + 1) and expand. (2)
Question 3Non-calculator · 4 marks
Consider $6x^2+38x+56$ .
(a) Factorise fully. (2)
(b) Solve the equation obtained by setting the expression equal to zero. (2)

Answers and marks

(a) $(2x + 1)(x + 3)$

M1 Splitting to $2x^2 + 6x + x + 3$ , or brackets $(2x \pm a)(x \pm b)$ with $ab = 3$ .
A1 $(2x + 1)(x + 3)$ .

(b) $(3x - 2)(2x + 1)$

M1 Splitting the middle term as $-4x + 3x$ , or a pair of brackets with the right $x^2$ and constant terms.
A1 $(3x - 2)(2x + 1)$ .

(a) $2x^{2}-5x-12$

(b) $2x^{3}-3x^{2}-17x-12$

(a) $2(x+4)(3x+7)$

(b) $-4, -7/3$

Three binomials and non-monic factorisation

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