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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 \(3 x^{2}+10 x+8\) is \((3x+4)(x+2)\)

Step by step solution

01

Identify the coefficients

Identify the coefficients 'a', 'b', and 'c' in the given quadratic equation which is in the form \(ax^2 + bx + c\). Here, a=3, b=10, and c=8
02

Find two numbers

Find two numbers that multiply to give ac (which is a* c = 3*8 = 24) and add up to b which is 10. The two numbers that satisfy this condition are 6 and 4 as 6*4 =24 and 6 + 4 = 10
03

Rewrite the equation

Rewrite the equation breaking down the middle term using the two identified numbers. The given equation becomes \(3x^2+ 6x + 4x + 8\)
04

Factor by grouping

Factor by grouping. First, factor out the greatest common factor (GCF) from the first two terms, and then from the last two terms. This would give us \(3x(x+2) + 4(x+2)\)
05

Write the final result

As \(x+2\) is common to both terms, you can factor it out. This gives us our final result of \((3x+4)(x+2)\)

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