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Chapter 5: Problem 116

What two binomials must be multiplied using the FOIL method to give a product of \(x^{2}-8 x-20 ?\)

Short Answer

Expert verified
The two binomials are \(( x -10 )\) and \(( x + 2 )\).

Step by step solution

01

Identify the Coefficients

Identify the coefficients for the quadratic trinomial. For \(x^{2}-8 x-20\), \(-8\) and \(-20\) are the coefficients for \(x\) and the constant term, respectively.
02

Find two numbers

Find two numbers such that their sum equals to the coefficient of \(x\) (which is \(-8\)) and their product equals to the constant term (which is \(-20\)). The two numbers that fulfil this are \(-10\) and \(2\), since \(-10 + 2 = -8\) and \(-10 \times 2 = -20\).
03

Write the Factors

Write the quadratic equation as a product of two binomial expressions - i.e., \((x - m)(x - n)\), where \(x\) is the variable, and \(m\) and \(n\) are the numbers found in Step 2. Therefore \(x^{2}-8 x-20\) can be written as \((x - 10)(x + 2) \).

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