Question

Check where did the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial is x+2,2x^2+3x+1

Answer 1

Step-by-step explanation:

Given :-

x+2 and 2x²+3x+1

To find :-

Check where did the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial ?

Solution :-

Let P(x) = 2x²+3x+1

Let g(x) = x+2

On dividing P(x) by g(x) then

x+2) 2x²+3x+1 ( 2x-1

2x²+4x

(-) (-)

_________

-x+1

-x-2

(+) (+)

__________

3

___________

Quotient q(x) = 2x-1

Remainder r(x) = 3

Since the remainder is not zero so g(x) is not a factor of P(x) .

Answer:-

x+2 is not a factor of 2x²+3x+1

Alternative Method :-

We know that

Factor Theorem

If x-a is a factor of P(x) then P(a) = 0

P(x) = 2x²+3x+1

g(x) = x+2

P(-2) = 2(-2)²+3(-2)+1

=> P(-2) = 2(4)-6+1

=> P(-2) = 8-6+1

=> P(-2) = 9-6

=> P(-2) = 3

Since, P(-2) is not equal to zero then x+2 is not a factor of 2x²+3x+1.