Please help me this is for my exam and i need to pass this or i won’t graduate. please

C. -3 must be a root of the polynomial 2·x² + 9·x + 9

Step-by-step explanation:

Given that the remainder when (2·x² + 9·x + 9) is divided by (x + 3) equals zero, then (x + 3) is a factor of 2·x² + 9·x + 9 and -3 is a root of the polynomial

Explaining by using the long division of the polynomial is presented as follows;

2·x + 3

(2·x² + 9·x + 9)/(x + 3)

- (2·x² + 6·x)

3·x + 9

-(3·x + 9)

0

Therefore, (2·x + 3) × (x + 3) = 2·x² + 9·x + 9

The solution of the 2·x² + 9·x + 9 = 0 gives the root of the polynomial

The root is given by, 2·x² + 9·x + 9 = (2·x + 3) × (x + 3) = 0

Therefore, the roots are;

2·x = -3 or x = -3/2 and x = -3

Therefore;

-3 must be a root of the polynomial 2·x² + 9·x + 9.

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