Factors of Polynomials Structured Questions | Cambridge O Level Additional Mathematics

Question 1 of 3 · 9 marks

Factors of Polynomials · Remainder & Factor Theorems

3 parts

Additional Mathematics 4037 · Question 1Paper 2 · Calculator[9 marks]

The polynomial $P(x)$ is given by $P(x) = 2x^3 + ax^2 + bx - 12$ , where $a$ and $b$ are constants. It is given that $(x - 2)$ is a factor of $P(x)$ , and that when $P(x)$ is divided by $(x + 1)$ , the remainder is $-3$ .

(a)

Form a pair of simultaneous equations in $a$ and $b$ , and show that $a = 3$ and $b = -8$ .

[4]

(b)

Using $a = 3$ and $b = -8$ , find the remainder when $P(x)$ is divided by $(2x + 1)$ .

[2]

(c)

Factorise $P(x)$ completely into three linear factors, and solve $P(x) = 0$ .

[3]