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Chapter 0: Problem 21

Factor each trinomial, or state that the trinomial is prime. $$x^{2}-8 x+15$$

Short Answer

Expert verified
The factored form of the trinomial \(x^{2}-8 x+15\) is \((x-5)(x-3)\).

Step by step solution

01

Identifying factor pairs of the constant term

Firstly, identify the pairs of factors of the constant term, which is 15 in this case. The pairs are (1,15) and (3,5). Both the pairs multiply to give 15.
02

Identifying the correct factor pair

Next, find the pair of factors that can add or subtract to give the coefficient of the second term, which is -8. Here, you see that (3,5) can subtract to give -8 if 5 is considered negative but not the pair (1,15). So, (3,-5) is the correct pair.
03

Factoring the trinomial

Now, replace the middle term (which is -8x) with -3x and -5x and factor by grouping, which would give \((x-5)(x-3)\).

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