Question

check using division if
$2y + 3 \: is \: a \: factor \: of \: 4y ^{2} + 12y + 9$
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Answer 1

Answer:

Yes

Note:

★ Factor theorem : If the remainder obtained on dividing the polynomial p(x) by another polynomial g(x) is zero , then g(x) is a factor of p(x) .

★ If g(x) is a factor of the polynomial p(x) , then the remainder obtained on dividing the polynomial p(x) by g(x) is zero .

Explaination:

• For division of 4y² + 12y + 9 by 2y + 3 , please refer to the attachment .

• Here, the remainder obtained on dividing the polynomial 4y² + 12y + 9 by 2y + 3 is zero , thus 2y + 3 is a factor of the polynomial 4y² + 12y + 9 .