Question

Find the remainder when -8x^3+4x^2-2x+7 is divided by (a) x+1 (b) 2x-1

Answer 1

Concept used to solve :

Remainder theorem

Answer :

p(x)= -8x³ + 4x² - 2x +7

When divided by x+1, x = -1

p(-1) = -8× (-1)³ + 4× (-1)² -2 × -1 + 7

       = -8 ×-1 + 4 × 1 +2 +7

       = 8+4+2+7 = 21

Remainder when p(x) = -8x³ + 4x² - 2x + 7 is divided by x+1 is 21.

b) p(x) = -8x³ + 4x² -2x + 7 ,

2x -1, x = 1/2

p($\frac{1}{2}$) = $-8 * (\frac{1}{2})^{3} + 4* (\frac{1}{2})^{2} - 2 * \frac{1}{2}+ 7$

       = $-8*\frac{1}{8} + 4* \frac{1}{4} - 2*\frac{1}{2} +7$

        = -1+1-1+7

       = 6

The remainder left is 6 when p(x) = -8x³ +4x² - 2x + 7 is divided by 2x-1.

Final Answer :

a) 21

b) 6