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Chapter 6: Problem 58

Factor each polynomial using the greatest common binomial factor. $$x(x+7)+10(x+7)$$

Short Answer

Expert verified
The factored form is \( (x+7) \cdot (x + 10)\).

Step by step solution

01

Identify the common binomial factor

From the given equation \(x(x+7) + 10(x+7)\), it can be spotted that \((x+7)\) is a common factor that appears in both terms of the expression.
02

Extract the common binomial factor

The next step in factoring is to pull out the common binomial factor \((x+7)\) from each term. This is done by distributing the common binomial factor across the expression in reverse, leaving only the other factors of each term. In this case, the remaining will be \(x + 10\).
03

Rewriting the expression

Once the common binomial factor has been extracted, the expression can be rewritten as \( (x+7) \cdot (x + 10)\), where \( \cdot \) represents multiplication.

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Most popular questions from this chapter

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$2 y^{5}-128 y^{2}$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$9 x^{4}+18 x^{3}+6 x^{2}$$

Describe a strategy that can be used to factor polynomials.

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$3 x^{4}-9 x^{3} y+3 x^{2} y^{2}$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$9 y^{2}+64$$
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