Factoring

Factoring

By Juan Montano

Common factor and Difference of Squares

Multiple Choice

Factor:

6m + 2n - 14

• 2(3m + n - 7)

• 2m(1 + n - 7)

• 2(3m + n + 7)

• 2m(1 + n + 7)

Math Response

Factor:

60x²y - 3xy

Type answer here

Correct Answer: 3xy\left(20x-1\right)

Deg^°

Rad

Math Response

Factor:

8x² + 10x + 16xy

Type answer here

Correct Answer: 2x\left(4x+5+8y\right)

Deg^°

Rad

Multiple Choice

Factor the following completely.

$$9n^4-16$$  

• $$\left(3n-4\right)\left(3n+4\right)$$  

• $$n^2\left(3n+4\right)\left(3n-4\right)$$  

• $$\left(3n^2-4\right)\left(3n^2+4\right)$$  

• $$prime$$  

Math Response

Factor the following completely.

$$81x^2-100$$

Type answer here

Correct Answer: \left(9x-10\right)\left(9x+10\right)

Deg^°

Rad

Math Response

Factor the following completely.

$$64x^4-1$$  

Type answer here

Correct Answer: \left(8x^2-1\right)\left(8x^2+1\right)

Deg^°

Rad

For 4, 6, 8, ... terms

1. Get the common factor ​for each pair

2. Get the common factor one more time of all the terms

Factoring By Grouping​

Factoring By Grouping​

Multiple Choice

Factor by grouping:

$$4p^3+8p^2+3p+6$$  

• $$\left(2p^2+3\right)\left(p+2\right)$$  

• $$\left(2p^2+6\right)\left(p+4\right)$$  

• $$\left(4p^2+3\right)\left(p+2\right)$$  

• $$\left(4p^2+8p\right)\left(3p+6\right)$$  

Multiple Choice

What is the factored form of $$5n^3-10n^2+3n-6$$  ?

• $$\left(5n^2+3\right)\left(n-2\right)$$  

• $$\left(5n^2-3\right)\left(n-2\right)$$  

• $$\left(5n^3+3\right)\left(n-2\right)$$  

• $$10n\left(n^2-6\right)$$  

Multiple Choice

Factor by grouping: $$20p^3-25p^2+4p-5$$  

• $$\left(5p^2-1\right)\left(4p-5\right)$$  

• $$\left(5p^2+1\right)\left(4p+5\right)$$  

• $$\left(5p^2+1\right)\left(4p-5\right)$$  

• $$\left(5p^2-1\right)\left(4p+5\right)$$  

Math Response

Factor by grouping: $$x^3-4x^2-4x+16$$  

Type answer here

Correct Answer: \left(x-4\right)\left(x^2-4\right)

Deg^°

Rad

1. ​Look for two numbers whos product is -15 and its addition is -2

2. Construct your binomials using those numbers​

Trinomial x²+bx+c

Multiple Choice

Select two numbers that fullfil the following conditions

a) its product is -5

b) its addition is -4

• 1, 5

• -1, 5

• 1, -5

• 3, -2

Multiple Choice

Select two numbers that fullfil the following conditions

a) its product is -12

b) its addition is -4

• 3, 4

• -4, 3

• -6, 2

• 6, -2

Multiple Choice

Select two numbers that fullfil the following conditions

a) its product is -27

b) its addition is 6

• -9, -3

• -9, 3

• 9, -3

• 9, 3

Math Response

Factor
x² - 2x - 24

Type answer here

Correct Answer: \left(x-6\right)\left(x+4\right)

Deg^°

Rad

Math Response

Factor
y² + 16y + 63

Type answer here

Correct Answer: \left(y+9\right)\left(y+7\right)

Deg^°

Rad

Math Response

Factor Completely $$x^2+11x+28$$  

Type answer here

Correct Answer: \left(x+7\right)\left(x+4\right)

Deg^°

Rad

Math Response

Factor
x² + 9x - 36

Type answer here

Correct Answer: \left(x+12\right)\left(x-3\right)

Deg^°

Rad

Math Response

Factor completely: 
3x² + 18x +15
Hint: Factor GCF first.

Type answer here

Correct Answer: 3\left(x+1\right)\left(x+5\right)

Deg^°

Rad

1. ​Multiply leading coefficient by constant term (2 by -1 is -2)

2. Look for two numbers whos product is -2 and whos addition is the coefficient of the linear term (x-term +1)

3. Copy the leading term, write down two new terms with the numbers found and copy the constant term

4. Use grouping to factor it

​

Trinomials ax²+bx+c

Trinomials ax²+bx+c

Math Response

Factor completely:
$$3x^2+5x-12$$

Type answer here

Correct Answer: \left(3x-4\right)\left(x+3\right)

Deg^°

Rad

Math Response

A rectangle has an area of $$2x^2-19x+45$$ ft². Write the product of the dimensions of the rectangle

Type answer here

Correct Answer: \left(2x-9\right)\left(x-5\right)

Deg^°

Rad

Math Response

Factor completely:
$$2x^2+17x+21$$

Type answer here

Correct Answer: \left(2x+3\right)\left(x+7\right)

Deg^°

Rad

Math Response

Factor completely:
$$3x^2+14x-5$$

Type answer here

Correct Answer: \left(3x-1\right)\left(x+5\right)

Deg^°

Rad

Difference or addition of cubes

1. ​Get the cubic root of each term

2. Write them in the binomial part

3. Create the special trinomial following the rule

Difference/Addition of Cubes

Some text here about the topic of discussion

Math Response

Factor the following expression

$$x^3-1$$  

Type answer here

Correct Answer: \left(x-1\right)\left(x^2+x+1\right)

Deg^°

Rad

Math Response

Factor the following expression

$$8x^3+27$$  

Type answer here

Correct Answer: \left(2x+3\right)\left(4x^2-6x+9\right)

Deg^°

Rad

Math Response

Factor completely the following expression

$$2x^3-16$$  

Type answer here

Correct Answer: 2\left(x-2\right)\left(x^2+2x+4\right)

Deg^°

Rad

Perfect Square Trinomial

Perfect Square Trinomial

Math Response

Factor completely the following expression

$$9x^2+6x+1$$  

Type answer here

Correct Answer: \left(3x+1\right)^2

Deg^°

Rad

Math Response

Factor completely the following expression

$$49x^2-28x+4$$  

Type answer here

Correct Answer: \left(7x-2\right)^2

Deg^°

Rad