1.5.6 Polynomials and rational expressions

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Question 70

The internal stress in a structural component is modeled by the cubic polynomial $S(x) = 3x^3 + Ax^2 + Bx - 10$ , where $A$ and $B$ are integer constants and $x$ represents the position along the component.

It is known that:

when $S (x)$ is divided by $(x - 2)$ , the remainder is $R$
when $S (x)$ is divided by $(x + 1)$ , the remainder is $- 2 R$
$R$ is a real constant

Show that $3 A + B = - 5$ .

[4]

Given that the stress is zero at position $\frac{2}{3}$ , such that $(3 x - 2)$ is a factor of $S (x)$ , find the value of $A$ and the value of $B$ .

[3]

Hence determine the quadratic expression $Q (x)$ such that $S (x) = (3 x - 2) Q (x)$ .

[3]

1.5.6 Polynomials and rational expressions Questions

A Level
Maths
1.5.6 Polynomials and rational expressions

A Level
Maths AQA
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