Nice Add. Maths. Qn

wee_ws SG

Hi,

Students can give this question a try:

When a polynomial h(x) is divided by (x - 1) and (x + 3) the remainder is -2 and 10 respectively. Find the remainder when h(x) is divided by (x - 1)(x + 3).

Thanks.

Cheers,
Wen Shih

AmuletxHeart SG

Ok. Just trying, might not be correct.

h(1) = -2

h(-3)= 10

h(1 times -3)= -2 times 10

= -20

SBS261P SG

is the answer 2?

wee_ws SG

Hi,

The answer is a linear expression.

Please take note of the following points:

1. When a polynomial is divided by a linear factor, the remainder is a constant.

2. When a polynomial is divided by a quadratic factor, the remainder is a linear expression.

To convince yourself about point 2, consider (x^3 + 1) / (x^2 - 2x). Thanks.

Cheers,
Wen Shih

wee_ws SG

Hi,

The steps to solving the question are given below as reference:

Let h(x) / {(x - 1)(x + 3)} = Q(x) + A / (x - 1) + B / (x + 3), where Q(x) is some polynomial.

Then h(x) = (x - 1)(x + 3)Q(x) + A(x + 3) + B(x -1). Note that the last 2 terms form the remainder of h(x) when it is divided by (x - 1)(x + 3).

Since h(1) = -2, we can solve for A.

Since h(-3) = 10, we can find the value of B.

Thanks.

Cheers,
Wen Shih