Questions: Factor. 3z^2 + 20z - 7

Factor. 3z^2 + 20z - 7
Transcript text: Factor. \[ 3 z^{2}+20 z-7 \]
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Solution

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Solution Steps

Step 1: Identify the Polynomial

We start with the polynomial \( 3z^{2} + 20z - 7 \).

Step 2: Factor the Polynomial

To factor the polynomial, we look for two binomials that multiply to give the original polynomial. The factorization results in: \[ (3z - 1)(z + 7) \]

Step 3: Verify the Factorization

To ensure the factorization is correct, we can expand the factors: \[ (3z - 1)(z + 7) = 3z^2 + 21z - z - 7 = 3z^2 + 20z - 7 \] This confirms that the factorization is accurate.

Final Answer

\(\boxed{(3z - 1)(z + 7)}\)

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