Polynomials, Exponents and Factoring

What is the first step in factoring common monomials?

• Divide the given polynomials to the GCF.

• Find the GCF of the coefficient and variable.

• Multiply the exponents.

• Add the coefficient and exponents.

Factor: x⁴-5x²-36

• (x²-9)(x²+4)

• (x²-9)(x²-4)

• (x²+9)(x²+4)

• (x²+9)(x²-4)

Factor: 8x³ - 1

• (2x - 1)(4x² + 2x + 1)

• (2x + 1)(4x² - 2x + 1)

• (2x - 1)(4x² - 2x - 1)

• (2x + 1)(4x² +2x + 1)

x⁴ + 7x² - 30=0

What indicates what factoring method to use between sum/difference of cubes, factor by grouping, and quadratic form?

• The number of terms

• Powers of Descending Order

• The highest exponent

• Does it have a GCF

When using the quadratic form to factor higher-order polynomials, what do we need?

• A constant, the first exponent is even, and the second exponent is half of the first.

• No constant and whole number exponents.

• A constant, whole number exponents, and four terms.

• Perfect cubes or perfect squares

x³-5x²+5x-25

• (x²-5)(x-5)

• (x²+5)(x-5)

• (x²+5)(x+5)

• (x²-1)(x-25)

Factor:

Identify if the expression can be factored as sum or difference of cubes:

3x³ + 24

• No

• Yes

• Yes, getting GCF first

• It is a sum of squares

Complete the formula

a³+b³=

• (a-b)(a²+ab+b²)

• (a+b)(a²-ab+b²)

• (a-b)(a²-ab+b²)

• (a+b)(a²+ab+b²)