Factor Polynomials Completely

In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Factorization (also factorisation in British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. (Source: Wikipedia)

Example problems for factor polynomials completely

Factor polynomials completely example problem 1:

Factorize the given polynomial equation completely 4x^2 - 45x + 11

Solution:

Given polynomial equation is 4x^2 - 45x + 11

First factorize the given equation, we get

(4x^2 - 45x + 11) = (4x^2 - 44x - x + 11)

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

= (4x^2 - 44x) - (x - 11)

= 4x (x - 11) - 1 (x - 11)

= (x - 11) (4x - 1)


The factors of the given polynomial equation is (x - 11) and (4x - 1)

Answer:

The final answer is (x - 11) and (4x - 1)

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Factor polynomials completely example problem 2:

Factorize the given polynomial expression 7x^2 + 33x + 36

Solution:

Given polynomial expression is 7x^2 + 33x + 36

First factorize the given expression, we get

(7x^2 + 33x + 36) = (7x^2 + 21x + 12x + 36)

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

= (7x^2 + 21x) + (12x + 36)

= 7x (x + 3) + 12 (x + 3)

= (x + 3) (7x + 12)


The factors of the given polynomial expression is (x + 3) and (7x + 12)

Answer:

The final answer is (x + 3) and (7x + 12)

Factor polynomials completely example problem 3:

Factorize the given polynomial expression x^2 + 48x - 49

Solution:

Given polynomial expression is x^2 + 48x - 49

First factorize the given expression, we get

(x^2 + 48x - 49) = (x^2 + 49x - x - 49)

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

= (x^2 + 49x) + (- x - 49)

= x (x + 49) - 1 (x + 49)

= (x + 49) (x - 1)


The factors of the given polynomial expression is (x + 49) and (x - 1)

Answer:

The final answer is (x + 49) and (x - 1)

Practice problems for factor polynomials completely

Factor polynomials completely practice problem 1:

Factorize the given polynomial expression 3x^2 - 18x + 24

Answer:

The final answer is (x - 4) and (3x - 6)
Factor polynomials completely practice problem 2:

Factorize the given polynomial expression 10x^2 - 25x + 10

Answer:

The final answer is (x - 2) and (10x - 5)