Factoring Cubics

Factoring Polynomials

Four types of Factoring

1. Greatest Common Factor

2. Difference of Cubes

3. Sum of Cubes

4. Factoring by Grouping

Factor out a common number and/or letter of the problem.

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Greatest Common Factor

Multiple Choice

Factor this Polynomial.

$$12x^3+18x^2-9x$$

• $$6x\left(2x^2+3x-3\right)$$

• $$3\left(4x^3+6x^2-3x\right)$$

• $$9x\left(3x^2+2x-1\right)$$

• $$3x\left(4x^2+6x-3\right)$$

Rule:

a³-b³=(a-b)(a²+ab+b²)

The first term will always be a³ and the second term b³.

Difference of Cubes

Multiple Choice

Use the difference of Cubes to Factor this polynomial.

$$64-y^3$$

• $$\left(4-y\right)\left(8+4y+y^2\right)$$

• $$\left(4-y\right)\left(16+4y+y^2\right)$$

• $$\left(y-4\right)\left(y^2+4y+16\right)$$

• $$\left(y-4\right)\left(y^2+4y+8\right)$$

Rule:

a³+b³=(a+b)(a²-ab+b²)

Sum of Cubes

Multiple Choice

Use the Sum of Cubes to Factor this Polynomial.

$$x^3+27y^3$$

• $$\left(x+3y\right)\left(x^2-3xy+9y^2\right)$$

• $$\left(x+3y\right)\left(x^2-3xy+6y^2\right)$$

• $$\left(x+3y\right)\left(x^2-3xy+9y\right)$$

• $$\left(x+3y\right)\left(x^2-3xy+6y\right)$$

Use the rules in your foldable to guide you through the example problem.

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Factor by Grouping

Multiple Choice

Use grouping to factor this Polynomial.

• $$\left(3n^2-4\right)\left(2n-1\right)$$

• $$\left(3n^2+4\right)\left(3n^2-1\right)$$

• $$2\left(n+2\right)\left(3n^2-1\right)$$

• $$\left(3n^2+4\right)\left(2n-1\right)$$

Mix and Match

Mix and Match

Multiple Choice

What Factoring rule would apply to this binomial: $$\left(x^3+8\right)$$ ?

• Sum of Cubes

• Difference of Cubes

• Grouping

• Difference of Sqaures

Multiple Choice

Use the Sum of Cubes to Factor $$\left(x^3+8\right)$$ .

• $$\left(x+8\right)\left(x^2-8x+4\right)$$

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

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

• $$\left(x-6\right)\left(x^2+2x-8\right)$$

Congrats! 🥳

​You have completed the Warm-Up!

You can now go finish the Factoring Polynomial Practice on your own with more confidence in your skills.