Question

if ax3+x2-bx-4 has x+2 as a factor and leaves a remainder -15 when divided by x-1, find the values of a and b. hence factorise the polynomial completely

Answer 1

Step-by-step explanation:

Given

X+ 2 = 0

X = -2

on putting in polynomial

-8a +2b= 0

- 8a = 2b

b = -4a

Now

when divided by x - 1 give remainder -15

so

x - 1 = -15

x = -14

on putting in polynomial

-2744a + 198 + 14b - 4 = -14

-2744a + 56a = - 208

-2688a = -208

a = 168/13

Now

b = 672/13

Answer 2

Let f(x) = ax3 + bx2 - 5x + 2

Since x+2 is a factor of f(x), f(-2) = 0

So, -8a + 4b + 12 = 0

Since the remainder is 12 when f(x) is divided by x-2, f(2) = 12

So, 8a + 4b - 8 = 12

We have the system of equations: -8a + 4b = -12

8a + 4b = 20

Add the equations to obtain 8b = 8

b = 1

Since b = 1 and 8a + 4b = 20, 8a + 4 = 20

8a = 16

a = 2