Product of Linear Factors

 

In mathematics, the term linear function can refer to either of two different but related concepts:
A first-degree polynomial functions of one variable.A map between two vector spaces that preserves vector addition and scalar multiplication.
The term linear function is sometimes used to mean a first-degree polynomial function of one variable. (Source: Wikipedia)Example Problems for Product of Linear Factors
Example problem 1:
Find the product of the given linear factors (x + 13) and (x - 20)
Solution:
Given factors are (x + 13) and (x - 20)
Multiply the each term of the two factors, we get
(x + 13) * (x - 20) = (x * (x - 20)) + (13 * (x - 20))
= x^2 - 20x + 13x - 260
Simplify the above equation, we get
= x^2 - 7x - 260
The product of the given two factors are x^2 - 7x - 260
Answer:
The final answer is x^2 - 7x - 260
Example problem 2:
Find the product of the given linear factors (x - 3) and (x - 17)
Solution:
Given factors are (x - 3) and (x - 17)
Multiply the each term of the two factors, we get
(x - 3) * (x - 17) = (x * (x - 17)) - (3 * (x - 17))
= x^2 - 17x - 3x + 51
Simplify the above equation, we get
= x^2 - 20x + 51
The product of the given two factors are x^2 - 20x + 51
Answer:
The final answer is x^2 - 20x + 51
Example problem 3:
Find the product of the given linear factors (x + 15) and (x + 10)
Solution:
Given factors are (x + 15) and (x + 10)
Multiply the each term of the two factors, we get
(x + 15) * (x + 10) = (x * (x + 10)) + (15 * (x + 10))
= x^2 + 10x + 15x + 150
Simplify the above equation, we get
= x^2 + 25x + 150
The product of the given two factors are x^2 + 25x + 150
Answer:
The final answer is x^2 + 25x + 150Practice Problems for Product of Linear Factors
Practice problem 1:
Find the product of the given linear factors (x + 12) and (x + 2)
Answer:
The final answer is x^2 + 14x + 24
Practice problem 2:
Find the product of the given linear factors (x - 2) and (x + 23)
Answer:
The final answer is x^2 + 21x - 46
Practice problem 3:
Find the product of the given linear factors (x - 10) and (x - 14)
Answer:
The final answer is x^2 - 24x + 140