Question

Check whether $g\left(y\right)$ is a factor of $f\left(y\right)$ by applying the division algorithm.
$f\left(y\right)=3y^4+5y^3-7y^2+2y+2$
$g\left(y\right)=y^2+3y+1$

• A. Yes
• B. No
• C. Ambiguous
• D. Data insufficient

Answer 1

The correct option is A Yes

Given f(y)=$3y^4+5y^3-7y^2+2y+2$ and (g)=$y^2+3y+1$

Then $y^2+3y+1)3y^4+5y^3-7y^2+2y+2(3y^2-4y+2$

$3y^4+9y^3+3y^2$

- - -

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$-4y^3-10y^2+2y$

$-4y^3-12y^2-4y$

+ + +

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$2y^2+6y+2$

$2y^2+6y+2$

- - -

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0

As remainder is zero. So g(Y) is a factor of f(y).