Question

$P(x)=2x {?}^{2} -3x +1$
Write a first degree polynomial which is a factor of p(x)​

Answer 1

Step-by-step explanation:

(a) If (x+1) is a factor of p(x)=6x

3

+3x

2

, then p(−1)=0

P(−1)=6(−1)

3

+3(−1)

2

=−6+3=−3



=0

Hence, (x+1) is not a factor of p(x)=6x

3

+3x

2

(b) Let f(x) be the required polynomial.

p(x)=6x

3

+3x

2

Let the first degree polynomial to be added to ax+b.

f(x)=p(x)+ax+b

If x

2

−1 is a factor of the f(x), then f(−1)=0 and f(1)=0

f(−1)=p(−1)+a(−1)+b

⇒0=6(−1)

3

+3(−1)

2

1. −a+b

⇒0=−6+3−a+b

⇒a−b=−3....(i)

Also, f(1)=p(1)+a(1)+b

⇒0=6(1)

3

+3(1)

2

+a+b

⇒a+b=−9....(ii)

Solving (i) and (ii), we get

a=−6,b=−3

∴ The polynomial is (−6x−3)