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Chapter 6: Problem 6

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}+13 x+12$$

Short Answer

Expert verified
The factorization of \(x^{2}+13x+12\) is \((x + 1)(x + 12)\).

Step by step solution

01

Factor the trinomial

The trinomial can be factored as \(x^{2} + 13x + 12 = (x + 1)(x + 12)\). Here, the numbers 1 and 12 have been found such that they add up to 13 and their product gives 12.
02

Apply FOIL Method

We can check the factorization by re-multiplying the factors using the FOIL method. \n\n - First terms multiplication: x * x = \(x^{2}\) \n - Outer terms multiplication: x * 12 = 12x \n - Inner terms multiplication: 1 * x = x \n - Last terms multiplication: 1 * 12 = 12 \n\nAdding these together, we have: \(x^{2}\) + 12x + x + 12 = \(x^{2}\) + 13x + 12
03

Confirm Factorization

The expression obtained after applying FOIL method matches with the original trinomial, thus confirming that our factorization is correct.

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Most popular questions from this chapter

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$72 a^{3} b^{2}+12 a^{2}-24 a^{4} b^{2}$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$20 a^{4}-45 a^{2}$$

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$16 a^{3} b^{2}-4 a b^{2}$$

Determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. When a factorization requires two factoring techniques, I'm less likely to make errors if I show one technique at a time rather than combining the two factorizations into one step.

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$3 x^{4}-9 x^{3} y+3 x^{2} y^{2}$$
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