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 $0$ on the other side.
Why? Because after factoring, we will have $0$ as the product.

Let's remember the following property

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

Steps to carry out to solve equations through factorization

Let's move all the elements to one side of the equation and leave $0$ 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 $0$ .

Detailed explanation

Suggested Topics to Practice in Advance

Practice Solution of equations using factoring

Question 1

Find the value of the parameter x.

$\( (x-5)^2=0 \)$

Question 2

Find the value of the parameter x.

$\( x^2-25=0 \)$

Question 3

Find the value of the parameter x.

$\( 2x^2-7x+5=0 \)$

Question 4

Find the value of the parameter x.

$\( -x^2-7x-12=0 \)$

Question 5

Find the value of the parameter x.

$\( -2x(3-x)+(x-3)^2=9 \)$

examples with solutions for solution of equations using factoring

Exercise #1

Find the value of the parameter x.

$(x-5)^2=0$

Video Solution

Answer

$x=5$

Exercise #2

Find the value of the parameter x.

$x^2-25=0$

Video Solution

Answer

$x=5,x=-5$

Exercise #3

Find the value of the parameter x.

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

Video Solution

Answer

$x=1,x=2.5$

Exercise #4

Find the value of the parameter x.

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

Video Solution

Answer

$x=-3,x=-4$

Exercise #5

Find the value of the parameter x.

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

Video Solution

Answer

$x=0,x=4$

Question 1

Find the value of the parameter x.

$\( (x-4)^2+x(x-12)=16 \)$

Question 2

Find the value of the parameter x.

$\( 12x^3-9x^2-3x=0 \)$

Question 3

Find the value of the parameter x.

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

Question 4

A right triangle is shown below.

$\( x>1 \)$

Calculate the lengths of the sides of the triangle.

Question 5

A right triangle is shown below.

$\( x>1 \)$

Find the lengths of the sides of the triangle.

examples with solutions for solution of equations using factoring

Exercise #1

Find the value of the parameter x.

$(x-4)^2+x(x-12)=16$

Video Solution

Answer

$x=0,x=10$

Exercise #2

Find the value of the parameter x.

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

Video Solution

Answer

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

Exercise #3

Find the value of the parameter x.

$(x+5)^2=0$

Video Solution

Answer

$x=-5$

Exercise #4

A right triangle is shown below.

$x>1$

Calculate the lengths of the sides of the triangle.

Video Solution

Answer

$5,12,13$

Exercise #5

A right triangle is shown below.

$x>1$

Find the lengths of the sides of the triangle.

Video Solution

Answer

$6,8,10$

Question 1

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.

Question 2

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.

Question 3

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.

Question 4

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.

examples with solutions for solution of equations using factoring

Exercise #1

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.

Video Solution

Answer

6

Exercise #2

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.

Video Solution

Answer

4

Exercise #3

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.

Video Solution

Answer

$8,8,8\sqrt{2}$

Exercise #4

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.

Video Solution

Answer

$5,5,5\sqrt{2}$

Topics learned in later sections

Uses of Factorization