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.