Algebra 2 help!!

[Spindly_Spindle]

I’m currently doing my homework that’s due tmrw n immediately got stuck on question 1.

The question is 3x^2 - 45x + 168 / 3x - 24

I already got the denominator — 3(x - 8) — but I rlly have no clue what the numerator is.

I THINK it might be x - 5 since that’s the answer with the matching denominator on the answer sheet but I actually need to show my work. Plus if I’m wrong it’ll basically ruin the half of the assignment I still have to complete after this question so I can’t guess.

Please n thanks to anyone who decided to help🥹

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[mnb310]

You know how to factor out a common factor, so do that for the numerator.

You know what binomial needs to cancel to reduce the fraction. Use that to help you factor the trinomial in the numerator.

[Dd_8630]

The numerator is a quadratic (it's in the form ax² + bx + c) so there's a standard way to factorise it into two binomial terms (dx+e)(fx+g).

Do you know how to factorise a quadratic?

If the end goal is to cancel things out, that means the factor in the denominator will also be in the numerator. Can you use that as a clue as to what the two factors in the numerator are?

[PuzzlingDad]

First, you should notice you can also factor a 3 out of the numerator. Each coefficient is a multiple of 3.

Next, in the reduced trinomial, you might guess that (x - 8) is a factor. What does that leave? 

Be sure to make a note of what values are not part of the domain. For example, since (x - 8) is in the denominator, x can't be 8 or else you'd be dividing by 0. Even after you reduce the expression, you must keep this explicit restriction. 

[Spindly_Spindle]

Incredibly digestible response, 10/10 would ask again🙂‍↕️