Question

In a polynomial P(x)=2x³-7x²+kx+20. It P(2)=P(3).
a) find the value of k. then write polynomial
b) then find P(-2)​

Answer 1

The given polynomial is p(x)=x

4

−2x

3

+3x

2

−ax+3a−7

Given that, the polynomial p(x) when divided by (x+1) leaves remainder 19

Therefore, p(−1)=19 (By Remainder theorem)

=>(−1)

4

−2×(−1)

3

+3(−1)

2

−(−1)a+3a−7=19

=>1+2+3+a+3a−7=19

=>4a−1=19

=>4a=20

=>a=5

The value of a is 5

Now,

p(x)=x

4

−2x

3

+3x

2

−5x+3×5−7

=x

4

−2x

3

+3x

2

−5x+15−7

=x

4

−2x

3

+3x

2

−5x+8

Remainder when the polynomial is divided by (x+2)

=p(−2) (By Remainder Theorem)

=−2

4

−2(−2)

3

+3(−2)

2

−5(−2)+8

=16+16+12+10+8

=62

Thus, the remainder of the polynomial p(x) when divided by (x+2) is 62