Factoring Polynomials

Finding the GCF of a Polynomial

For the partially complete factorization, find the other binomial which will complete the factorization.

a^{2} + 7 a - 18 = (a + 9) (

More examples

Factoring Out Greatest Common Factor (GCF)

Factor the given polynomial by finding the greatest common monomial factor (or the negative of the greatest common monomial factor) and rewrite the expression.

33 + 3 x^{3}

More examples

Identifying the Common Factors

Factorize the polynomial

36 x^{3} y^{2} - 48 x^{2} y^{3} + 60 x^{4} y

More examples

Finding the LCM using GCF

Find the least common multiple (LCM) of the polynomials

4 x^{2} - 9

and

2 x - 3

More examples

Finding the GCF

Find the greatest common factor (GCF) of the polynomials

12 x^{3} y^{2} - 18 x^{2} y^{3} + 24 x^{4} y

More examples

Factoring Trinomials

Question 4 (2 points) Factor:

x^{2} + 7 x + 12

More examples

Trinomial Squares

Factor the trinomial square

x^{2} - 10 x + 25

More examples

Factoring Using Any Method

Short Fall 2023 Question 10, 4.3.39 Part 1 of 2 HW Score:

75 %, 7.5

of 10 points Points: 0 of 1 Factor the polynomial function

f (x)

. Then solve the equation

f (x) = 0

f (x) = x^{3} + 6 x^{2} + 3 x - 10

The factored polynomial function is

f (x) =

(Factor completely)

More examples

Factoring a Difference of Squares

Factorize the following expression:

x^{4} - 256

More examples

Factoring a Sum of Cubes

Factor the expression

x^{3} + 27

More examples

Factoring by Grouping

Factor by grouping (sometimes called the ac-method).

28 x^{2} - x - 2

First, choose a form with appropriate signs. Then, fill in the blanks with numbers to be used for grouping. Finally, show the factorization. Form:

28 x^{2} + ◻ x + ◻ x - 2

28 x^{2} + ◻ x - ◻ x - 2

28 x^{2} - ◻ x + ◻ x - 2

28 x^{2} - ◻ x - ◻ x - 2

Factorization:

More examples

Factoring a Difference of Cubes

Factor the expression

x^{3} - y^{3}

More examples

Determine if an Expression is a Factor

1 point Which expression is a factor of

x^{2} + 3 x - 40 ?

(x - 4)

(x - 5)

(x - 8)

(x - 10)

More examples

Determining if Factor Using Synthetic Division

Use synthetic division to find the quotient and remainder when

9 x^{6} - 5 x^{4} + 5 x^{2} + 6

is divided by

x - 2

. The quotient is The remainder is

More examples

Find the Factors Using the Factor Theorem

Given

f (x) = 6 x^{3} + 5 x^{2} - 12 x + 4

, answer the following. Part: 0 / 2 Part 1 of 2 Factor

f (x)

, given that

\frac{1}{2}

is a zero.

f (x) =

More examples

Determining if the Expression is a Polynomial

Given the expression

5 x^{3} + 2 x^{2} - 3 x + 4

, is it a polynomial? If yes, factorize it.

More examples

Determining if Polynomial is Prime

Exercise 6. Show that the following polynomials are irreducible over

Q

A = x^{4} - 4 x^{3} + 6

B = 4 x^{3} - 15 x^{2} + 60 x + 180

C = 8 x^{3} + 6 x^{2} - 9 x + 24

More examples

Determining if the Polynomial is a Perfect Square

Is the polynomial

x^{4} - 2 x^{2} + 1

a perfect square? If yes, factorize it.

More examples

Expand using the Binomial Theorem

A.Convert from factored form to standard form b.

A (x) = (x - 4) (x + 1)

More examples

Factoring over the Complex Numbers

Factorize the polynomial

x^{3} - 8

over the complex numbers.

More examples

Finding All Integers k Such That the Trinomial Can Be Factored

Form a polynomial whose real zeros and degree are given. Zeros:

- 2, 0, 5

; degree: 3 Type a polynomial with integer coefficients and a leading coefficient of 1.

f (x) = ◻

(Simplify your answer.

)

More examples

Finding the GCF of a Polynomial

Factoring Out Greatest Common Factor (GCF)

Identifying the Common Factors

Finding the LCM using GCF

Finding the GCF

Factoring Trinomials

Trinomial Squares

Factoring Using Any Method

Factoring a Difference of Squares

Factoring a Sum of Cubes

Factoring by Grouping

Factoring a Difference of Cubes

Determine if an Expression is a Factor

Determining if Factor Using Synthetic Division

Find the Factors Using the Factor Theorem

Determining if the Expression is a Polynomial

Determining if Polynomial is Prime

Determining if the Polynomial is a Perfect Square

Expand using the Binomial Theorem

Factoring over the Complex Numbers

Finding All Integers k Such That the Trinomial Can Be Factored

Popular Problems