Question
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Part 1
First factor out the greatest common factor from each term. Then factor the remaining polynomial.
5 x squared plus 15 x minus 90
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Part 1
Select the correct choice below and fill in any answer box within your choice.
A.5 x squared plus 15 x minus 90 equals enter your response here
5 x squared plus 15 x minus 90equals
enter your response here
B.
5 x squared plus 15 x minus 90 is prime.
Answers
Answered by
GPT-4o mini
To factor the expression \(5x^2 + 15x - 90\), let's first factor out the greatest common factor (GCF) from each term.
1. Identify the GCF of the coefficients: The coefficients are 5, 15, and -90. The GCF is 5.
2. Factor out the GCF (5) from the expression:
\[
5x^2 + 15x - 90 = 5(x^2 + 3x - 18)
\]
Now, we need to factor the remaining polynomial \(x^2 + 3x - 18\).
To factor \(x^2 + 3x - 18\), we look for two numbers that multiply to -18 (the constant term) and add up to 3 (the coefficient of the middle term).
The numbers that work are 6 and -3, because:
\[
6 \times -3 = -18 \quad \text{and} \quad 6 + (-3) = 3
\]
Thus, we can write:
\[
x^2 + 3x - 18 = (x + 6)(x - 3)
\]
Putting it all together, we have:
\[
5x^2 + 15x - 90 = 5(x + 6)(x - 3)
\]
So, the final factored form of \(5x^2 + 15x - 90\) is:
\[
5(x + 6)(x - 3)
\]
Hence, the answer is:
**A.** \(5x^2 + 15x - 90 = 5(x + 6)(x - 3)\)
1. Identify the GCF of the coefficients: The coefficients are 5, 15, and -90. The GCF is 5.
2. Factor out the GCF (5) from the expression:
\[
5x^2 + 15x - 90 = 5(x^2 + 3x - 18)
\]
Now, we need to factor the remaining polynomial \(x^2 + 3x - 18\).
To factor \(x^2 + 3x - 18\), we look for two numbers that multiply to -18 (the constant term) and add up to 3 (the coefficient of the middle term).
The numbers that work are 6 and -3, because:
\[
6 \times -3 = -18 \quad \text{and} \quad 6 + (-3) = 3
\]
Thus, we can write:
\[
x^2 + 3x - 18 = (x + 6)(x - 3)
\]
Putting it all together, we have:
\[
5x^2 + 15x - 90 = 5(x + 6)(x - 3)
\]
So, the final factored form of \(5x^2 + 15x - 90\) is:
\[
5(x + 6)(x - 3)
\]
Hence, the answer is:
**A.** \(5x^2 + 15x - 90 = 5(x + 6)(x - 3)\)