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Algebra 1 Factoring Quadratic Equations Worksheet

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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.


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

    How about :

    = 2×2 2x + 7x 7= 2×2 + 5x 7

    OK, how about :

    = 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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    Factorising Quadratic Equation Worksheets

    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.

    Answers By Expert Tutors

    Algebra 1 Factoring By Grouping Worksheet


    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:


    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!

    Recommended Reading: Kuta Software Geometry Answer Key

    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 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.

    Teachers can use math worksheets as tests, practice assignments or teaching tools . Parents can work with their children to give them extra practice, to help them learn a new math skill or to keep their skills fresh over school breaks. Students can use math worksheets to master a math skill through practice, in a study group or for peer tutoring.

    Use the buttons below to print, open, or download the PDF version of the Factoring Quadratic Expressions with Positive ‘a’ Coefficients of 1 math worksheet. The size of the PDF file is 34255 bytes. Preview images of the first and second pages are shown. If there are more versions of this worksheet, the other versions will be available below the preview images. For more like this, use the search bar to look for some or all of these keywords: math, algebra, quadratics, factoring.

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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 .

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    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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