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