Solving Polynomial Equations in Factored Form

Introduction to polynomial equations in factored form:
In mathematics, a polynomial is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents. (Source: Wikipedia)

Generally polynomial equations can be written as, x^2 - 3x + 9. Polynomial equations in factored form can be written as

(x - 2) (x - 3).

Example Problems for Solving Polynomial Equations in Factored Form
Solving polynomial equations in factored form example problem 1:

Write the given polynomial expression x^2 - 17x + 16 in factored form.

Solution:

Given polynomial expression is x^2 - 17x + 16

First factorize the given expression, we get

(x^2 - 17x + 16) = (x^2 - 16x - x + 16)

Grouping the first two terms and second two terms, we get

= (x^2 - 16x) - (x - 16)

= x (x - 16) - 1 (x - 16)

= (x - 16) (x - 1)


The factors of the given polynomial expression is (x - 16) and (x - 1)

Answer:

The final answer is (x - 16) and (x - 1)

Solving polynomial equations in factored form example problem 2:

Write the given polynomial expression x^2 + 27x + 140 in factored form.

Solution:

Given polynomial expression is x^2 + 27x + 140

First factorize the given expression, we get

(x^2 + 27x + 140) = (x^2 + 20x + 7x + 140)

Grouping the first two terms and second two terms, we get

= (x^2 + 20x) + (7x + 140)

= x (x + 20) + 7 (x + 20)

= (x + 20) (x + 7)


The factors of the given polynomial expression is (x + 20) and (x + 7)

Answer:

The final answer is (x + 20) and (x + 7)

Solving polynomial equations in factored form example problem 3:

Write the given polynomial expression x^2 + 17x - 434 in factored form.

Solution:

Given polynomial expression is x^2 + 17x - 434

First factorize the given expression, we get

(x^2 + 17x - 434) = (x^2 + 31x - 14x - 434)

Grouping the first two terms and second two terms, we get

= (x^2 + 31x) - (14x + 434)

= x (x + 31) - 14 (x + 31)

= (x + 31) (x - 14)


The factors of the given polynomial expression is (x + 31) and (x - 14)

Answer:

The final answer is (x + 31) and (x - 14)

Algebra is widely used in day to day activities watch out for my forthcoming posts on what does algebraic expression mean and algebraic expression examples. I am sure they will be helpful.

Practice Problems for Solving Polynomial Equations in Factored Form
Solving polynomial equations in factored form practice problem 1:

Write the given polynomial expression x^2 + 4x - 32 in factored form.

Answer:

The final answer is (x + 8) and (x - 4)

Solving polynomial equations in factored form practice problem 2:

Write the given polynomial expression x^2 - 7x - 260 in factored form.

Answer:

The final answer is (x - 20) and (x + 13)

Solving polynomial equations in factored form practice problem 3:

Write the given polynomial expression x^2 + 21x + 110 in factored form.

Answer:

The final answer is (x + 10) and (x + 11)