Question

Check whether (x+2) is a factor of the polynomial 2x3+3x2–5x+1

Answer 1

Answer:

To check that x−2 is the factor of x

3

−2x

2

−5x+4:

The value of x−2=0 ⟹ x=2.

So, put x=2 in expression, we get,

f(x)=x

3

−2x

2

−5x+4

f(2)=(2)

3

−2(2)

2

−5(2)+4

⇒f(2)=8−2×4−5×2+4

⇒f(2)=8−8−10+4

⇒f(2)=−6.

Remainder is not 0, when x−2 divides the polynomial x

3

−2x

2

−5x+4.

Thus x−2 is not a factor of polynomial x

3

−2x

2

−5x+4.