Factors and Product in Math

Introduction to factors in math:
Divisor, an integer which evenly divides a number without leaving a remainder
Factorization, the decomposition of an object into a product of other objects
Integer factorization, the process of breaking down a composite number into smaller non-trivial divisors
A coefficient, a multiplicative factor in an expression, usually a number
A von Neumann algebra with a trivial center
Factor (graph theory), a spanning sub graph
(Source: Wikipedia)

Example Problem for Factors and Product in Math

Factors and product in math example problem 1:

Find the factors of the given quadratic equation  x2 - 11x - 180

Solution:

Given quadratic equation is x2 - 11x - 180

First factorize the given equation, we get

(x2 - 11x - 180) = (x2 - 20x + 9x - 180)

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

= (x2 - 20x) + (9x - 180)

= x (x - 20) + 9 (x - 20)

= (x - 20) (x + 9)


The factors of the given quadratic equation is (x - 20) and (x + 9)

Answer:

The final answer is (x - 20) and (x + 9)

Factors and product in math example problem 2:

Find the factors of the given quadratic equation  x2 + 13x + 42

Solution:

Given quadratic equation is x2 + 13x + 42

First factorize the given equation, we get

(x2 + 13x + 42) = (x2 + 7x + 6x + 42)

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

= (x2 + 7x) + (6x + 42)

= x (x + 7) + 6 (x + 7)

= (x + 6) (x + 7)


The factors of the given quadratic equation is (x + 6) and (x + 7)

Answer:

The final answer is (x + 6) and (x + 7)

Factors and product in math example problem 3:

Find the product of the given two factors (x - 2) and (x + 3)

Solution:

Given two factors are (x - 2) and (x + 3)

Multiply the each term of the two factors together, we get

(x - 2) * (x + 3) = (x * (x + 3)) - (2 * (x + 3))

= x2 + 3x - 2x - 6

= x2 + x - 6

The product of the two factors are x2 + x - 6

Answer:

The final answer is x2 + x - 6

Factors and product in math example problem 4:

Find the product of the given two factors (x - 4) and (x + 6)

Solution:

Given two factors are (x - 4) and (x + 6)

Multiply the each term of the two factors together, we get

(x - 4) * (x + 6) = (x * (x + 6)) - (4 * (x + 6))

= x2 + 6x - 4x - 24

= x2 + 2x - 24

The product of the two factors are x2 + 2x - 24

Answer:

The final answer is x2 + 2x - 24

Practice Problems for Factors and Product in Math

Factors and product in math practice problem 1:

Find the factors of the given quadratic equation  x2 - 31x - 360

Answer:

The final answer is (x - 40) (x + 9)

Factors and product in math practice problem 2:

Find the product of the given two factors (x + 4) and (x + 3)

Answer:

The product of the two factors are x2 + 7x + 12