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Chapter 5: Problem 29

Factor completely. If the polynomial cannot be factored, write prime. \(m^{2}+m-20\)

Short Answer

Expert verified
(m + 5)(m - 4)

Step by step solution

01

Identify the polynomial

The given polynomial is a quadratic trinomial: \(m^{2} + m - 20\).
02

Write in standard form

The polynomial is already in standard form as \(am^{2} + bm + c\), where \(a = 1\), \(b = 1\), and \(c = -20\).
03

Find factors of the constant term

Find two numbers that multiply to the constant term \(c = -20\), and add up to the coefficient \(b = 1\).
04

Identify the factors

The numbers 5 and -4 multiply to -20 and add up to 1:\(5 \times -4 = -20\)\(5 + (-4) = 1\).
05

Write the factors

The polynomial \(m^2 + m - 20\) can be factored into: \((m + 5)(m - 4)\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

quadratic trinomial
A quadratic trinomial is a polynomial with three terms and the highest exponent is 2. In simpler words, it's like having a math expression with one squared term. An example would be:
standard form
The standard form of a quadratic trinomial helps us understand & easily work with the expression. Our exercise shows us the standard form with the polynomial as : m^2 + m - 20: . This guide below helps: understand to the format better.

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