Question

If a polynomial x4-3x3-6x2+kx-16is exactly divisible by x2-3x+2,then find the valu of k

Answer 1

Step-by-step explanation:

Use remainder and factor theorem

x2-3x+2=0

Then factorise this

x2-2x-x+2=0

x(x-2)-1(x-2)=0

(x-2)(x-1)=0

x=2 or 1

Now put the value in the polynomial

For x=2

x4-3x3-6x2+kx-16=0

16-24-12+2k-16=0

2k=36

k=18

For x= 1

x4-3x3-6x2+kx-16=0

1-3-6+k-16=0

k=24

Hope u understood

Answer 2

Step-by-step explanation:

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