4: Algebra

Question 1

What is a factor of a quadratic equation where you can factor out an x

Answer 1

If you have a quadratic expression equal to zero, and you can factor an x out of the expression, then x=0 is a solution of the equation.

Question 2

Special Product 1: x^2-y^2

Answer 2

x^2-y^2 = (x+y)(x-y)

Question 3

Special Product 2: x^2 + 2xy + y^2

Answer 3

(x^2 +2xy + y^2) = (x+y)(x+y) = (x+y)^2

Question 4

Special Product 3: x^2 - 2xy + y^2

Answer 4

(x^2 - 2xy + y^2) = (x-y)(x-y) = (x-y)^2

Question 5

xy>0

Answer 5

x and y are both positive or both negative

Question 6

xy<0

Answer 6

x and y have different signs (one positive, one negative)

Question 7

x^2 - x < 0

x^2 < x

Answer 7

These are two different versions of the same inequality. Both mean that 0 < x < 1

Question 8

What do you do when you multiply or divide an inequality by a negative number?

Answer 8

Flip the sign