Thursday, August 1, 2024

# Algebra 1 Factoring Quadratic Equations Worksheet

## Example: And Are Factors Of X2 + 3x 4

KutaSoftware: Algebra 1- Solving Quadratics By Factoring Part 1

Let us “expand” and to be sure:

Yes, and are definitely factors of x2 + 3x 4

Did you see that Expanding and Factoring are opposites?

Expanding is usually easy, but Factoring can often be tricky.

It is like trying to find which ingredientswent into a cake to make it so delicious.It can be hard to figure out!

OK, let’s try an example where we don’t know the factors yet:

## Definition Of A Quadratic Equation

A quadratic equation is an equation involving the square of a number which is the highest power in the equation.

It is usually in the standard form:

ax2 + bx + c = 0

where a, b and c are numbers, and x is an unknown. The variable a cannot be 0

Note that the operations can be ‘+’ or ‘-‘.

It is also sometimes called a second degree polynomial equation.

Examples

The following ARE quadratic equations in standard form:

• x2 + 7x + 4 = 0
• 4a 2 – ½ a + 15 = 0

The following ARE quadratic equations but not yet in standard form:

• can be rewritten as x2 + 6x – 4 = 0
• can be rewritten as 3n2 – 6n – 10 = 0
• The following are NOT quadratic equations:

• x3 + 7x + 4 = 0
• 4a5 – ½ a + 15 = 0

## Example: What Are The Factors Of 6×2 2x = 0

6 and 2 have a common factor of 2:

2 = 0

Let’s guess :

= 2×2 + 2x + 3x + 3= 2×2 + 5x + 3

= 2×2 2x + 7x 7= 2×2 + 5x 7

= 2×2 2x + 9x 9= 2×2 + 7x 9

We could be guessing for a long time before we get lucky.

That is not a very good method. So let us try something else.

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The sheets are arranged in order of difficulty to help introduce you into more complicated examples gradually.

• Sheets 1 & 2 – positive values inside each bracket only
• Sheet 3 – negative values inside each bracket only
• Sheet 4 – one positive and one negative value in the brackets.
• Sheets 5 to 8 – mixed quadratic equations with one x2, gradually getting harder.
• Sheet 9 – mixed quadratic equations with 2×2, either both brackets positive or both negative
• Sheets 10 to 11 – mixed quadratic equations with more than one x2

Section 1: Beginning Section

Take a look at some more of our worksheets similar to these.

Hey!

In order to solve any quadratic for the x-intercepts you must set the entire equation equal to zero.

Remember, before factoring using FOIl or any similar method, always check for a GCF!

The GCF is 16x. Pulling this in front, we have:

16x.

We know we need two roots, since the equation has a degree of two. One is in parentheses, the other is on the outside. Set both equal to zero, solve and you have:

x=3 and x=0.

Hope this helped!

## Factoring Quadratic Expressions With Positive ‘a’ Coefficients Of 1

Welcome to The Factoring Quadratic Expressions with Positive ‘a’ Coefficients of 1 Math Worksheet from the Algebra Worksheets Page at Math-Drills.com. This math worksheet was created on 2019-11-15 and has been viewed 36 times this week and 3,051 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

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## How To Solve A Quadratic Equation

There are 2 main methods to use when solving a quadratic equation:

1) The factoring method – this is used for paticular cases when the solution involves integers or fractions

2) The formula method – this can be used for any quadratic equation

The worksheets on this page are designed to be solved using the factoring method .

## A Method For Simple Cases

There is a method for simple cases.

With the quadratic equation in this form:

Step 1: Find two numbers that multiply to give ac , and add to give b.

Example: 2×2 + 7x + 3

ac is 2×3 = 6 and b is 7

So we want two numbers that multiply together to make 6, and add up to 7

In fact 6 and 1 do that

How do we find 6 and 1?

It helps to list the factors of ac=6, and then try adding some to get b=7.

Factors of 6 include 1, 2, 3 and 6.

Aha! 1 and 6 add to 7, and 6×1=6.

Step 2: Rewrite the middle with those numbers:

Rewrite 7x with 6x and 1x:

2×2 + 6x + x + 3

Step 3: Factor the first two and last two terms separately:

The first two terms 2×2 + 6x factor into 2x

The last two terms x+3 don’t actually change in this case

So we get:

2x +

Step 4: If we’ve done this correctly, our two new terms should have a clearly visible common factor.

In this case we can see that is common to both terms, so we can go:

Check: = 2×2 + 6x + x + 3 = 2×2 + 7x + 3

Let’s see Steps 1 to 4 again, in one go:

 2×2 + 7x + 3

Check: = 6×2 4x + 9x 6 = 6×2 + 5x 6

## Algebra 1 Factoring Quadratic Equations Worksheet

KutaSoftware: Algebra 1- Solving Quadratics By Factoring Part 2

Algebra 1 Factoring Quadratic Equations Worksheet Expressions and Equations Worksheets are designed to help children learn faster and more efficiently. These worksheets contain interactive exercises as well as problems built around the order that operations are carried out. These worksheets make it simple for children to grasp complicated concepts and simple concepts quickly. It is possible to download these free documents in PDF format. They will aid your child in learning and practice math-related equations. These resources are beneficial for students between 5th and 8th Grades.

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