Factoring

Question 1

“Expanding”

Answer 1

Using the Distributive Law to expand certain algebraic expressions.

Question 2

“Factoring”

Answer 2

Using the Distributive Law to factor certain algebraic expressions as the product of a simpler one by extracting common factors within an expression.

Question 3

Describe how to factor a quadratic of the form x^2 + bx + c

Answer 3

x^2 + bx + c

(x + r)(x + s) = x^2 + (r + s)x + rs; Choose values for r and s so that r + s = b and rs = c.

Question 4

Factor: a^2 - b^2

Answer 4

a^2 - b^2 = (a - b)(a + b)

Question 5

What is the analogous formula for a difference of cubes?

Answer 5

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Question 6

What is the analogous formula for a sum of cubes?

Answer 6

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Question 7

What is the Factor Theorem?

Answer 7

If P is a polynomial and P(b) = 0, then x - b is a factor of P(x)