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Factoring: c Negative

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Factoring: c Negative

Study Guide

Key Definition

Factoring a trinomial of the form $ax^2 + bx + c$ when $c$ is negative involves finding two numbers that multiply to $c$ and add to $b$.

Important Notes

When $c$ is negative, the factors must have opposite signs.
Look for pairs of numbers that multiply to $c$ and add to $b$.
The expression $x^2 + 5x - 6$ can be factored to $(x + 6)(x - 1)$.
Use the distributive property to check your factors.
Practice makes perfect!

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Understanding the relationship between multiplication and addition in factoring helps break down the trinomial into its binomial factors.

Remember

To factor trinomials successfully, always consider the signs of $b$ and $c$.

Quick Reference

Factoring Formula:$(x + m)(x + n)$ where $m$ and $n$ are the factors of $c$; if $c$ is negative, one of $m$ or $n$ is negative.

Understanding Factoring: c Negative

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Video explanation of this concept

Beginner

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Beginner Explanation

Factoring trinomials with negative $c$ involves finding two numbers that add to $b$ and multiply to $c$. For example, to factor $x^2 + 5x - 6$, find $6$ and $-1$ because $6 + (-1) = 5$ and $6 \times -1 = -6$, so the factors are $(x + 6)(x - 1)$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What are the factors of $x^2 + 5x - 6$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine if you have a function $y = x^2 - 4x - 5$. How can you factor it to find the zero points?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given the equation $x^2 - 7x - 8 = 0$, think about how you would factor it.

Challenge Quiz

Single Choice Quiz

Advanced

Find the factors of $x^2 + x - 12$.

Recap

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Review key concepts and takeaways