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Chapter 0: Problem 125

Explain how to factor \(3 x^{2}+10 x+8\)

Short Answer

Expert verified
The factored form of \(3x^{2}+10x+8\) is \((3x+4)(x+2)\).

Step by step solution

01

Find factors of 24

First, find two numbers that multiply to \(3 * 8 = 24\) and add up to 10. The numbers are 6 and 4.
02

Rewrite middle term

Re-write the original quadratic by splitting the middle term using the numbers found in Step 1. This becomes \(3x^{2} + 6x + 4x + 8\). Note that you haven't modified the equation, just expressed it differently.
03

Group terms and factor

Then break the four-term polynomial into two groups and factor out the Greatest Common Factor (GCF) of each group:\((3x^{2} + 6x) + (4x + 8)\) becomes \(3x(x + 2) + 4(x + 2)\). 'x+2' is a common factor.
04

Complete factoring

Finally, you write the answer as \((x + 2)\) times \((3x + 4)\). So, the factored form of the quadratic equation \(3x^{2}+10x+8\) is \((3x+4)(x+2)\).

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. A. Find \(\sqrt{16} \cdot \sqrt{4}\) B. Find \(\sqrt{16 \cdot 4}\) C. Based on your answers to parts (a) and (b), what can you conclude?

What is a perfect square trinomial and how is it factored?

Simplify by reducing the index of the radical. $$ \sqrt[9]{x^{6} y^{3}} $$

Factor Completely. $$y^{7}+y$$

Determine whether each statement is trueor false. If the statement is false, make the necessary change(s) toproduce a true statement. $$x^{3}-64=(x+4)\left(x^{2}+4 x-16\right)$$
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