# Solve The Quadratic Equation By Factoring Worksheet

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Solving the quadratic equation by factoring means breaking down the equation $$ax^2 + bx + c = 0$$ into simpler factors that multiply to give the original equation. Once factored, set each factor equal to zero and solve for $$x$$. This method helps find the solutions where the quadratic equation equals zero, making it easier to understand and solve.

Algebra 2

## How Will This Worksheet on “Solve the Quadratic Equation by Factoring” Benefit Your Student's Learning?

• Reinforces factoring skills.
• Enhances problem-solving abilities.
• Improves algebraic manipulation.
• Clarifies the zero product property.
• Provides ample practice opportunities.
• Builds confidence in solving equations.
• Prepares for tests and assessments.
• Encourages independent learning.

## How to Solve the Quadratic Equation by Factoring?

• Ensure the equation is in the form $$ax^2 + bx + c = 0$$.
• Factor the quadratic expression into two binomials such that their product equals zero.
• Set each binomial factor equal to zero.
• Solve each resulting linear equation for $$x$$.

## Solved Example

Q. Solve for $u$. $\newline$$u^2 + 8u + 16 = 0$$\newline$Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $\newline$$u = \_\_$
Solution:
1. Identify Quadratic Equation: Identify the quadratic equation to solve for $u$. The given equation is $u^2 + 8u + 16 = 0$. We need to find values of $u$ that satisfy this equation.
2. Factorization Check: Determine if the quadratic can be factored.$\newline$We are looking for two numbers that multiply to $16$ and add up to $8$.$\newline$The numbers $4$ and $4$ satisfy these conditions because $4 \times 4 = 16$ and $4 + 4 = 8$.
3. Write Factored Form: Write the factored form of the quadratic equation.$\newline$Since both numbers are $4$, the equation can be written as $(u + 4)(u + 4) = 0$.$\newline$This is also known as a perfect square trinomial.
4. Solve for $u$: Set each factor equal to zero and solve for $u$.$\newline$First, set $u + 4 = 0$.$\newline$Subtract $4$ from both sides to solve for $u$.$\newline$$u + 4 - 4 = 0 - 4$$\newline$$u = -4$
5. Final Solution: Since both factors are the same, we only get one solution for $u$. The solution is $u = -4$. There is no need to solve the second factor because it is identical to the first.

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