# Practice factoring binomials

## Factoring Binomials - Difference of Squares

Related Topics: More Algebra Lessons
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Objective: I can factor binomials that are difference of squares.

A difference of squares is a binomial of the form:

a2b2

Take note that the first term and the last term are both perfect squares.

When we factor a difference of two squares, we will get

a2b2 = (a + b)(a – b)

This is because (a + b)(a – b) = a2ab + ab – b2 = a2b2

Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!

Factoring Binomials Calculator
Type in the binomial and select factor.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Sours: https://www.onlinemathlearning.com/factoring-binomials.html
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### Section 1-5 : Factoring Polynomials

For problems 1 – 4 factor out the greatest common factor from each polynomial.

1. $$6{x^7} + 3{x^4} - 9{x^3}$$ Solution
2. $${a^3}{b^8} - 7{a^{10}}{b^4} + 2{a^5}{b^2}$$ Solution
3. $$2x{\left( {{x^2} + 1} \right)^3} - 16{\left( {{x^2} + 1} \right)^5}$$ Solution
4. $${x^2}\left( {2 - 6x} \right) + 4x\left( {4 - 12x} \right)$$ Solution

For problems 5 & 6 factor each of the following by grouping.

1. $$7x + 7{x^3} + {x^4} + {x^6}$$ Solution
2. $$18x + 33 - 6{x^4} - 11{x^3}$$ Solution

For problems 7 – 15 factor each of the following.

1. $${x^2} - 2x - 8$$ Solution
2. $${z^2} - 10z + 21$$ Solution
3. $${y^2} + 16y + 60$$ Solution
4. $$5{x^2} + 14x - 3$$ Solution
5. $$6{t^2} - 19t - 7$$ Solution
6. $$4{z^2} + 19z + 12$$ Solution
7. $${x^2} + 14x + 49$$ Solution
8. $$4{w^2} - 25$$ Solution
9. $$81{x^2} - 36x + 4$$ Solution

For problems 16 – 18 factor each of the following.

1. $${x^6} + 3{x^3} - 4$$ Solution
2. $$3{z^5} - 17{z^4} - 28{z^3}$$ Solution
3. $$2{x^{14}} - 512{x^6}$$ Solution
Sours: https://tutorial.math.lamar.edu/problems/alg/factoring.aspx

## Factoring practice

Factor the following polynomials (as fully as possible).
1. x2 + 3 x - 10
2. x2+ 2 x - 24
3. x2- 9 x + 18
4. 2 x2 - 5 x - 12
5. x2+ 4 x + 6
6. 3 x2+ 5 x + 2
7. x2 + 1.5 x - 10
8. x2- x + 9
9. 8 x2- 62 x + 99
10. 24 x2- 22 x - 35
11. 2x3+ 3 x2- 17 x - 30
12. x3- 3 x2- x + 3
13. x3+ 4 x2- 7 x + 2
14. 18 x3- 57 x2- 85 x + 100

1. (x - 2) (x + 5)
2. (x - 4) (x + 6)
3. (x - 3) (x - 6)
4. (x - 4) (2 x + 3)
5. It is as factored as it gets.
6. (3 x + 2) (x + 1)
7. (2 x + 5) (0.5 x - 2)
8. It is as factored as it gets.
9. (4 x - 9) (2 x - 11)
10. (4 x - 7) (6 x + 5)
11. (x - 3) (2 x + 5) (x + 2)
12. (x - 1) (x + 1) (x - 3)
13. (x - 1) (x2 + 5 x - 2) is as factored as it gets.
14. (x - 4) (3 x + 5) (6 x - 5)
Sours: http://webspace.ship.edu/deensley/m100/ws5.html
Factoring Binomials - Step by Step - Part 2

## Worksheet on Factoring Binomials

Practice the worksheet on factoring binomials to know how to find the common factor from the binomials. For factoring the binomials we need to find the common factor in each term so that we can find out the common factor.

Note: To practice factoring binomials recall the reverse method of distributive law means in short nu-distributing the factor.

1. Factorize the following binomials:

(i) 3a + 21

(ii) 7m – 14

(iii) y3+ 3y

(iv) 20x + 5x2

(v) – 16x + 20x3

(vi) 5x2y + 15xy2

(vii) 9a2+ 5a

(viii) 19a – 57b

(ix) 25a2b2c3– 15ab3c

2. Factor each of the following algebraic expression:

(i) 13n + 39

(ii) 19y - 57z

(iii) 21xy + 49xyz

(iv) – 16p + 20p3

(v) 12x2y – 42xyz

(vi) 27a3b3+ 36a4b2

Answers for the worksheet on factoring binomials are given below to check the exact answers of the simple factors.

1. (i) 3(a + 7)

(ii) 7(m - 2)

(iii) y(y + 3)

(iv) 5x(4 + x)

(v) 4x(-4 + 5x2)

(vi) 5xy(x + y)

(vii) a(9a + 5)

(viii) 19(a – 3b)

(ix) 5ab2c(5ac2– 3b)

2. (i) 13(n + 3)

(ii) 19(y - 3z)

(iii) 7xy(3 - 7z)

(iv) 4p(-4 + 5p2)

(v) 6xy(2x – 7z)

(vi) 9a3b2(3b + 4a)

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## Factoring binomials practice

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Factoring Trinomials The Easy Fast Way

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