Related Topics:

More Lessons for Algebra, Math Worksheets

There are several techniques that can be used to factor quadratic equations.

In this lesson, we will learn how to factor quadratic equations, where the coefficient of*x*^{2 }is 1, using the trial and error method. In this method, we will need to try out different possibilities to get the
right factors for the given quadratic equation.

We also have another technique that does not need require guessing or trial and error.

### If the Coefficient Of *x*^{2} Is 1

**Examples of solving quadratic equations**

Examples:

1. Solve x^{2} + 6x + 8 = 0

2. Solve 2x^{2} + 20x + 50 = 0

3. Solve x^{2} - x - 30 = 0

**Factoring Quadratic Expressions**

coefficient of*x*^{2} = −1

Examples:

1. Factor x^{2} + 10x + 9

2. Factor x^{2} - 11x + 24

3. Factor x^{2} - x - 56

3. Factor -x^{2} - 5x + 24

3. Factor -x^{2} + 18x - 72

**Solve quadratic equation by factoring**

Example:

Solve x^{2} - 3x = 4

**How to factor quadratics?**

Examples:

1) x^{2} - 3x - 18

2) x^{2} - 6x - 16

Related Topics:

Factoring Out Common Factors (GCF).

Factoring Quadratic Equations using Perfect Square Trinomial (Square of a Sum or Square of a Difference) or Difference of Two Squares.

Factoring Quadratic Equations where the coefficient of*x*^{2} is greater than 1

Factoring Quadratic Equations by Completing the Square

Factoring Quadratic Equations using the Quadratic Formula.

More Lessons for Algebra, Math Worksheets

There are several techniques that can be used to factor quadratic equations.

In this lesson, we will learn how to factor quadratic equations, where the coefficient of

We also have another technique that does not need require guessing or trial and error.

To factorize quadratic equations of the form: *x*^{2} + *bx + c*, you will need to find two numbers whose product is *c* and whose sum is *b*.

Example 1:* (b and c are both positive) *

Solve the quadratic equation:

x^{2}+ 7x+ 10 = 0

Step 1: List out the factors of 10:

1 × 10, 2 × 5

Step 2: Find the factors whose sum is 7:

1 + 10 ≠ 7

2 + 5 = 7

Step 3: Write out the factors and check using the distributive property.

(

x+ 2) (x+ 5) =x^{2}+ 5x+ 2x+ 10 =x^{2}+ 7x+ 10

The factors are (x+ 2) (x+ 5)

Step 4: Going back to the original quadratic equation

x^{2}+ 7x+ 10 = 0 Factorize the left side of the quadratic equation

(x+ 2) (x+ 5) = 0We get two values for

x.

Answer: *x* = – 2, *x* = – 5

Example 2:* (b is positive and c is negative) *

Get the values of

xfor the equation:x^{2}+ 4x– 5 = 0

Step 1: List out the factors of – 5:

1 × –5, –1 × 5

Step 2: Find the factors whose sum is 4:

1 – 5 ≠ 4

–1 + 5 = 4

Step 3: Write out the factors and check using the distributive property.

(

x– 1)(x+ 5)=x^{2}+ 5x–x– 5 =x^{2}+ 4x– 5

Step 4: Going back to the original quadratic equation

x^{2}+ 4x– 5 = 0 Factorize the left hand side of the equation

(x– 1)(x+ 5) = 0We get two values for

x.

Answer: *x* = 1, *x* = – 5

Example 3:* (b and c are both negative) *

Get the values of

xfor the equation:x^{2}– 5x– 6

Step 1: List out the factors of – 6:

1 × –6, –1 × 6, 2 × –3, –2 × 3

Step 2: Find the factors whose sum is –5:

1 + ( –6) = –5

Step 3: Write out the factors and check using the distributive property.

(

x+ 1) (x– 6) =x^{2}– 6x+x– 6 =x^{2}– 5x– 6

Step 4: Going back to the original quadratic equation

x^{2}– 5x– 6 = 0 Factorize the left hand side of the equation

(x+ 1) (x– 6) = 0We get two values for

x.

Answer:* x* = –1, *x* = 6

Example 4:* (b is negative and c is positive)*

Get the values of

xfor the equation:x^{2}– 6x+ 8 = 0

Step 1: List out the factors of 8:

We need to get the negative factors of 8 to get a negative sum.

–1 × – 8, –2 × –4

Step 2: Find the factors whose sum is – 6:

–1 + ( –8) ≠ –6

–2 + ( –4) = –6

Step 3: Write out the factors and check using the distributive property.

(

x– 2) (x– 4) =x^{2}– 4x– 2x+ 8 =x^{2}– 6x+ 8

Step 4: Going back to the original quadratic equation

x^{2}– 6x+ 8 = 0 Factorize the left hand side of the equation

(x– 2) (x– 4) = 0We get two values for

x.

Answer:* x* = 2, *x* = 4

Examples:

1. Solve x

2. Solve 2x

3. Solve x

coefficient of

Examples:

1. Factor x

2. Factor x

3. Factor x

3. Factor -x

3. Factor -x

Example:

Solve x

Examples:

1) x

2) x

Related Topics:

Factoring Out Common Factors (GCF).

Factoring Quadratic Equations using Perfect Square Trinomial (Square of a Sum or Square of a Difference) or Difference of Two Squares.

Factoring Quadratic Equations where the coefficient of

Factoring Quadratic Equations by Completing the Square

Factoring Quadratic Equations using the Quadratic Formula.

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