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Chapter 6: Problem 61

Factor each polynomial using the greatest common binomial factor. $$x(y+6)-7(y+6)$$

Short Answer

Expert verified
The factored form of the polynomial \(x(y+6)-7(y+6)\) is \((y+6)(x-7)\).

Step by step solution

01

Identify Common Binomial Factor

In the given polynomial \(x(y+6)-7(y+6)\) the common binomial to both terms is \((y+6)\).
02

Factor out the common binomial factor

Factoring out a common binomial factor involves using the distributive property, which states that in the expression \(a(b + c)\) it equals to \(ab + ac\). If we apply this rule in reverse to the exercise, we will get the factored form by taking \((y + 6)\) as a common factor. The expression \(x(y+6)-7(y+6)\) then becomes \((y+6)(x-7)\).

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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. $$2 r^{3}+30 r^{2}-68 r$$

Use the \([\mathrm{GRAPH}]\) or \([\mathrm { TABLE }]\) feature of a graphing utility to determine if the polynomial on the left side of each equation has been correctly factored. If not, factor the polynomial correctly and then use your graphing utility to verify the factorization. $$\begin{aligned}&3 x^{3}-12 x^{2}-15 x=3 x(x+5)(x-1) ;[-5,7,1] \text { by }\\\ &[-80,80,10] \end{aligned}$$

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. $$27 x^{2}+75$$

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. $$y^{3}+2 y^{2}-y-2$$

Factor completely. $$3 x^{5}-21 x^{3}-54 x$$
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