Question

Find the remainder when x^4+x^3-8x^2+5x-8 is divided by x+2

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Answer 1

Answer:

Let us first divide the given polynomial x

4

+x

3

+8x

2

+ax+b by (x

2

+1) as shown in the above image:

From the division, we observe that the quotient is x

2

+x+7 and the remainder is (a−1)x+(b−7).

Since it is given that x

4

+x

3

+8x

2

+ax+b is exactly divisible by x

2

+1, therefore, the remainder must be equal to 0 that is:

(a−1)x+(b−7)=0

⇒(a−1)x+(b−7)=0⋅x+0

⇒(a−1)=0,(b−7)=0(Bycomparingcoefficients)

⇒a=1,b=7

Hence, a=1 and b=7.

Step-by-step explanation:

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