Problem 58
Question
Factor each polynomial using the greatest common binomial factor. $$x(x+7)+10(x+7)$$
Step-by-Step Solution
Verified Answer
The factored form is \( (x+7) \cdot (x + 10)\).
1Step 1: 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.
2Step 2: 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 \(x + 10\).
3Step 3: 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.
Other exercises in this chapter
Problem 58
Factor completely. $$y^{4}-12 y^{3}+35 y^{2}$$
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Solve each equation and check your solutions. $$(x-5)\left(x^{2}-3 x+2\right)=0$
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Factor any perfect square trinomials, or state that the polynomial is prime. $$x^{2}-7 x+49$$
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Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$12 x^{2}+7 x
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