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)
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)
