Question
Factor the polynomial: \( x^{2}+5 x-14=(x+2) \)
Ask by Schultz Garza. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The factored form is \((x-2)(x+7)\).
Solution
Factor the expression \( x^{2}+5x-14 \).
Factor the expression by following steps:
- step0: Factor:
\(x^{2}+5x-14\)
- step1: Rewrite the expression:
\(x^{2}+\left(7-2\right)x-14\)
- step2: Calculate:
\(x^{2}+7x-2x-14\)
- step3: Rewrite the expression:
\(x\times x+x\times 7-2x-2\times 7\)
- step4: Factor the expression:
\(x\left(x+7\right)-2\left(x+7\right)\)
- step5: Factor the expression:
\(\left(x-2\right)\left(x+7\right)\)
The factored form of the polynomial \(x^{2}+5x-14\) is \((x-2)(x+7)\).
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Simplify this solution Mind Expander
To factor the polynomial \( x^{2} + 5x - 14 \), we need to find two numbers that multiply to \(-14\) (the constant term) and add up to \(5\) (the coefficient of the \(x\) term). These two numbers are \(7\) and \(-2\). Hence, we can rewrite the polynomial as: \[ x^{2} + 5x - 14 = (x + 7)(x - 2) \] Now you have factored it correctly! But, be sure to double-check your factors! It's always helpful to expand the factors back to see if they match the original polynomial. Happy factoring!
