Question Video: Factoring a Linear Algebraic Expression | Nagwa Question Video: Factoring a Linear Algebraic Expression | Nagwa

Question Video: Factoring a Linear Algebraic Expression Mathematics • Second Year of Preparatory School

Factorize 12𝑥 + 9 + 𝑥(4𝑥 + 3) fully.

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Video Transcript

Factorize 12𝑥 plus nine plus 𝑥 multiplied by four 𝑥 plus three fully.

In this question, we are asked to fully factor an algebraic expression. We might be tempted to start by distributing the factor of 𝑥 over the parentheses. However, we should always check for shared factors first.

In this case, we can see that the first two terms share a factor of three. If we take this out, we might be able to factor the expression by using factoring by grouping. Taking out the factor of three from the first two terms gives us three multiplied by four 𝑥 plus three plus 𝑥 multiplied by four 𝑥 plus three.

We can then see that there is a shared factor of four 𝑥 plus three that we can take out. Taking out this factor gives us four 𝑥 plus three times three plus 𝑥.

Finally, we recall that we write expressions in descending powers of 𝑥. So we reorder the two terms in the final factor. We also note that these are linear factors with no shared factors in the terms. So we cannot factor further.

Hence, our answer is four 𝑥 plus three times 𝑥 plus three.

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