Question
Question 1 of 10, Step 1 of 1 Factor the given trinomial. If the trinomial cannot be factored, indicate "Not Factorable". Answer How to enter your answer (opens in new window) Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answ \( x^{2}-3 x-18 \) Not Factorable
Ask by Erickson Thornton. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x^{2}-3x-18 \) factors to \( (x-6)(x+3) \).
Solution
Factor the expression by following steps:
- step0: Factor:
\(x^{2}-3x-18\)
- step1: Rewrite the expression:
\(x^{2}+\left(3-6\right)x-18\)
- step2: Calculate:
\(x^{2}+3x-6x-18\)
- step3: Rewrite the expression:
\(x\times x+x\times 3-6x-6\times 3\)
- step4: Factor the expression:
\(x\left(x+3\right)-6\left(x+3\right)\)
- step5: Factor the expression:
\(\left(x-6\right)\left(x+3\right)\)
The trinomial \( x^{2}-3x-18 \) can be factored as:
\[
(x-6)(x+3)
\]
So, the answer is \( (x-6)(x+3) \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
The trinomial \( x^2 - 3x - 18 \) can actually be factored! It can be rewritten as \( (x - 6)(x + 3) \). To find the correct factors, look for two numbers that multiply to -18 (the constant term) and add to -3 (the coefficient of the linear term). In this case, -6 and +3 work perfectly! To double-check your factors, you can simply distribute \( (x - 6)(x + 3) \) back out to ensure you return to the original trinomial. This beautiful process of factoring not only shows how algebra works but also brings a satisfaction in simplifying equations, like cracking a code!
