Solution of equations using factoring - Examples, Exercises and Solutions

To solve equations through factorization, we must transpose all the elements to one side of the equation and leave 0 0 on the other side.
Why? Because after factoring, we will have 0 0 as the product.

Let's remember the following property

The product of two numbers equals 0 0 when, at least, one of them is 0 0 .
If  x×y=0x\times y=0
then
either: x=0x=0
or: y=0y=0
or both are equal to 0 0 .

Steps to carry out to solve equations through factorization

  • Let's move all the elements to one side of the equation and leave 0 0 on the other.
  • Let's factor using one of the methods we have learned: by taking out the common factor, with shortcut multiplication formulas, or with trinomials.
  • Let's find out when the elements achieve a product equivalent to 0 0 .

Suggested Topics to Practice in Advance

  1. Factoring using contracted multiplication
  2. Factorization
  3. Extracting the common factor in parentheses
  4. Factorization: Common factor extraction
  5. Factoring Trinomials
  6. Algebraic Fractions
  7. Simplifying Algebraic Fractions
  8. Factoring Algebraic Fractions
  9. Addition and Subtraction of Algebraic Fractions
  10. Multiplication and Division of Algebraic Fractions

Practice Solution of equations using factoring

Exercise #1

Find the value of the parameter x.

2x27x+5=0 2x^2-7x+5=0

Video Solution

Answer

x=1,x=2.5 x=1,x=2.5

Exercise #2

Find the value of the parameter x.

x27x12=0 -x^2-7x-12=0

Video Solution

Answer

x=3,x=4 x=-3,x=-4

Exercise #3

Find the value of the parameter x.

(x5)2=0 (x-5)^2=0

Video Solution

Answer

x=5 x=5

Exercise #4

Find the value of the parameter x.

x225=0 x^2-25=0

Video Solution

Answer

x=5,x=5 x=5,x=-5

Exercise #5

Find the value of the parameter x.

12x39x23x=0 12x^3-9x^2-3x=0

Video Solution

Answer

x=0,x=1,x=14 x=0,x=1,x=-\frac{1}{4}

Exercise #1

Find the value of the parameter x.

2x(3x)+(x3)2=9 -2x(3-x)+(x-3)^2=9

Video Solution

Answer

x=0,x=4 x=0,x=4

Exercise #2

Find the value of the parameter x.

(x4)2+x(x12)=16 (x-4)^2+x(x-12)=16

Video Solution

Answer

x=0,x=10 x=0,x=10

Exercise #3

Find the value of the parameter x.

(x+5)2=0 (x+5)^2=0

Video Solution

Answer

x=5 x=-5

Exercise #4

A right triangle is shown below.

x>1


Calculate the lengths of the sides of the triangle.

x+9x+9x+9x+2x+2x+2x+10x+10x+10

Video Solution

Answer

5,12,13 5,12,13

Exercise #5

A right triangle is shown below.

x>1

Find the lengths of the sides of the triangle.

x+2x+2x+2xxxx+4x+4x+4

Video Solution

Answer

6,8,10 6,8,10

Exercise #1

In front of you is a square.

The expressions listed next to the sides describe their length.

( x>-2 length measurements in cm).

Since the area of the square is 16.

Find the lengths of the sides of the square.

161616x+2x+2x+2

Video Solution

Answer

4

Exercise #2

In front of you is a square.

The expressions listed next to the sides describe their length.

( x>-4 length measurements in cm).

Since the area of the square is 36.

Find the lengths of the sides of the square.

363636x+4x+4x+4

Video Solution

Answer

6

Exercise #3

In front of you is an isosceles right triangle.

The expressions listed next to the sides describe their length.

( x>-5 length measurements in cm).

Since the area of the triangle is 12.5.

Find the lengths of the sides of the triangle.

12.512.512.5x+5x+5x+5

Video Solution

Answer

5,5,52 5,5,5\sqrt{2}

Exercise #4

In front of you is an isosceles right triangle.

The expressions listed next to the sides describe their length.

( x>-8 length measurements in cm).

Since the area of the triangle is 32.

Find the lengths of the sides of the triangle.

323232x+8x+8x+8

Video Solution

Answer

8,8,82 8,8,8\sqrt{2}

Topics learned in later sections

  1. Uses of Factorization