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Chapter 1: Problem 78

Exercises \(78-80\) will help you prepare for the material covered in the next section. Factor: \(2 x^{2}+7 x-4\)

Short Answer

Expert verified
The factored form of the quadratic equation \(2x^{2}+7x-4\) is \(2(x+2)(x-2)\).

Step by step solution

01

Identifying the Coefficients

Identify the coefficients for the quadratic equation. In this case, a = 2, b = 7, and c = -4.
02

Finding two numbers

Find two numbers such that they add up to b (which is 7) and their product is equal to the product of a and c (which is -8). The numbers in this case are 4 and -2.
03

Split the Middle Term

Split the middle term of the quadratic equation using the two numbers found above. It then becomes: \(2x^{2}+4x-2x-4\).
04

Group the Terms

Group the terms and factor by grouping. This will result in \(2x(x+2)-2(x+2)\).
05

Factoring

Finally, we can factor out the common binomial term to obtain the factorized form of the quadratic equation. The factors are: \(2(x+2)(x-2)\).

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