Lesson on Root Form of Polynomial

How many roots does this quadratic equation have?

This polynomial must have an exponent that is at least to what power?

Polynomial #1 continued: What are my roots or solutions for x?

1 Factor the polynomial: 4(x-5)(x-6)

2 Set each factor to zero and solve for the variable

x-5=0 and x-6=0.

Solve for x by adding the needed number to both sides.

Can we factor this?

Polynomial #3:

x² + 4x + 4 = (x + 2)(x + 2)

We set it to zero: (x + 2)(x + 2)= 0. Then we set each parentheses (or factor) equal to zero. What are the roots?

Polynomial #4: Find the roots or zeros of x² + 9x + 18

Hint: Factor it. Then set each factor in parentheses = 0 and solve for x.

Polynomial #5:

What are the roots of 6x³ + 6x² - 36 = 6x (x - 2)(x + 3)?

Polynomial #6: What are the roots of x² + 10x + 24?

Hint: Factor the polynomial and then set each factor equal to zero.

Polynomial #7:

If our roots are -4 and 2 then x=-4 and x=2.

Now add to both sides so that the number is on the same side of the equation. x+4=0 and x-2=0. What are the factors of this polynomial?

CHECK FOR UNDERSTANDING

a. The roots of a polynomial are where the graph of the polynomial crosses which axis?

b. The roots or zeros of a polynomial is where what equals zero?

c. Polynomial #8:

What is the polynomial with roots of 0, -3?

d. Which is true?