Question

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factor the common factor out of each expression.

1. $15n^2 + 35$
2. $-27x^2 + 63x$
3. $5 + 15b^3$
4. $12r^{11} + 9r^{10}$
5. $5a^4 - 4a^2 + 7a$
6. $35v^3 + 14v + 35$

Explanation:

Problem 1: \(15n^2 + 35\)

Step 1: Find the GCF of 15 and 35

The factors of 15 are \(1, 3, 5, 15\), and the factors of 35 are \(1, 5, 7, 35\). The greatest common factor (GCF) is 5.

Step 2: Factor out the GCF

Factor 5 out of each term: \(15n^2 + 35 = 5(3n^2 + 7)\)

Step 1: Find the GCF of -27 and 63, and the common variable factor

The GCF of 27 and 63 is 9, and since the first term is negative, we can factor out -9. The common variable factor is \(x\) (the lowest power of \(x\) is 1). So the GCF is \(-9x\).

Step 2: Factor out the GCF

\(-27x^3 + 63x=-9x(3x^2 - 7)\)

Step 1: Find the GCF of 5 and 15

The GCF of 5 and 15 is 5.

Step 2: Factor out the GCF

Factor 5 out of each term: \(5 + 15b^3=5(1 + 3b^3)\)

Answer:

\(5(3n^2 + 7)\)

Problem 2: \(-27x^3 + 63x\)