Question

Factor the trinomial if possible. $$x^{2}-10 x+24$$

Short answer

The factored form of the trinomial \(x^{2}-10x+24\) is \((x-4)(x-6)\).

Step-by-step solution

Find the numbers

First, we need to find two numbers which multiply to give 24 (since `a`*`c`=1*24=24) and when added together they give -10 (which is our 'b'). After some trials, we find these numbers to be -4 and -6. We can check this: (-4)*(-6)=24 and -4+-6=-10.

Rewrite the trinomial

Next, we rewrite the trinomial, but we split up the -10x term into the two terms we found in the previous step. This gives us the expression \(x^{2}-4x-6x+24\).

Factor by grouping

Now, we factorise the expression by grouping. We group the first two terms together and the last two terms together and factor out the greatest common factor (GCF) from each group. This gives us: \(x(x-4)-6(x-4)\).

Factoring out the common binomial

Finally, we factor out the common binomial term \((x-4)\) from each group to get our final factored form. So, \(x^{2}-10x+24\) factors to \((x-4)(x-6)\).