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Chapter 1: Problem 9

Solve each equation in Exercises \(1-14\) by factoring. $$3 x^{2}+12 x=0$$

Short Answer

Expert verified
The solutions to the given equation are \(x = 0, -4\).

Step by step solution

01

Factor out the Greatest Common Factor (GCF)

The first step in factoring is to always check if there is a Greatest Common Factor (GCF) that can be factored out. Looking at the terms of the equation \(3x^2\) and \(12x\), the GCF is \(3x\). Factoring this GCF out of the equation gives us \(3x(x + 4) = 0\).
02

Set Each Factor Equal to Zero

A fundamental principle of solving equations is that if the product of several quantities equals zero, then at least one of the quantities must be zero. Based on this, set each factor equal to zero gives us two possible solutions: \(3x = 0\) and \(x + 4 = 0\).
03

Solve for x

Solve each of these equations for x. The first equation \(3x = 0\) gives \(x = 0 / 3 = 0\). The second equation \(x + 4 = 0\) gives \(x = 0 - 4 = -4\).

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Most popular questions from this chapter

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-2 x+1>0 $$

Solve each inequality by first rewriting each one as an equivalent inequality without absolute value bars. Graph the solution set on a number line. Express the solution set using interval notation. $$3|x-1|+2 \geq 8$$

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$4(x+1)+2 \geq 3 x+6$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \left|x^{2}+6 x+1\right|>8 $$

Explain why \(|x|<-4\) has no solution.
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