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Chapter 0: Problem 103

Factor completely. $$10 x^{2}(x+1)-7 x(x+1)-6(x+1)$$

Short Answer

Expert verified
The completely factored form of \(10 x^{2}(x+1)-7 x(x+1)-6(x+1)\) is \((x+1)(5x - 6)(2x + 1)\).

Step by step solution

01

Identify the Common Factor

First, determine the common factor for each term of the expression. For this equation, the common factor for all three terms is \((x+1)\). The expression can be rewritten as: \(10x^2*(x+1) - 7x*(x+1) - 6*(x+1)\).
02

Factor Out the Common Factor

The common factor \((x+1)\) can be factored out from each term of the expression: \((x+1)*(10x^2 - 7x - 6)\).
03

Factorize the Quadratic Equation

Now factorize the quadratic part that is still intact. For the quadratic \(10x^2 - 7x - 6\), look for two numbers that multiply to \(-60\) (which is the result of the product of \(10\) and \(-6\)) and add up to \(-7\). Those numbers are \(-12\) and \(5\). The quadratic factorizes to \((5x - 6)(2x + 1)\).
04

Write the Final Factored Form

Now, incorporate this back into the expression to have the fully factored form: \((x+1)(5x - 6)(2x + 1)\).

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Most popular questions from this chapter

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