Uses of Factorization - Examples, Exercises and Solutions

Factorization is the main key to solving more complex exercises than those you have studied up to today.
Factorization helps to solve different exercises, among them, those that have algebraic fractions.
In exercises where the sum or difference of their terms equals zero, factorization allows us to see them as a multiplication of $0$ and thus discover the terms that lead them to this result.

For exercises composed of fractions with expressions that may seem complicated, we can break them down into factors, reduce them, and thus end up with much simpler fractions.

Detailed explanation

Suggested Topics to Practice in Advance

Practice Uses of Factorization

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 uses of factorization

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 uses of factorization

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 uses of factorization

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

Solving Equations by Factoring