Lesson: Factoring Special Cases

Multiple Select

Do you have your NOTEBOOK OUT?

🙄

• 👍, I have my 📕 out.

• I KNOW I have to take a picture 📸 of my notes 📝at the end to get full 💯credit.

• I DO NOT have a notebook 😖 and understand it means I will get a bad 👎 grade. 😧😞😥

Factoring Special Cases

Objective: Factor special case quadratics​

Match

Match the following binomials with their products.

• (x + 6)(x - 6)

• (x + 6)²

• (x - 6)²

• (x + 9)(x - 4)

• (x - 9)(x + 4)

x² - 36

x² + 12x + 36

x² - 12x + 36

x² + 5x - 36

x² - 5x - 36

• x² - 36

• x² + 12x + 36

• x² - 12x + 36

• x² + 5x - 36

• x² - 5x - 36

​PAST EXAMPLES

​(x + 6)² = (x + 6)(x + 6) = x² + 6x + 6x + 36

​(x + 6)(x - 6) = x² - 6x + 6x - 36

= x² + 12x + 36

= x² - 36

REVIEW Square Roots

1² (means 1×1) = 1

2² (means 2×2) = 4

3² (means 3×3) = 9

4² (means 4×4) = 16

5² (means 5×5) = 25

Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, ...

EXAMPLES ​PERFECT SQUARES

​Factor: x² - 10x + 25

​Factor: x² + 3x + 9

Questions to Ask
1) Are the 1st and 3rd term perfect squares?
2) If YES, multiply them and double it. Is that the middle term?

Math Response

Factor: x² + 12x + 36

Type answer here

Correct Answer: \left(x+6\right)^2

Deg^°

Rad

Multiple Select

Which of the following polynomials is prime?

• x² - 14x + 49

• x² + 4x + 16

EXAMPLES ​PERFECT SQUARES

​Factor: 4x² + 12x + 9

​Factor: 36x² - 48x + 16

Questions to Ask
1) Are the 1st and 3rd term perfect squares?
2) If YES, multiply them and double it. Is that the middle term?

Math Response

Factor: 25x² - 10x + 1

Type answer here

Correct Answer: \left(5x-1\right)^2

Deg^°

Rad

​DIFFERENCE OF SQUARES

​Factor: x² - 81

​Factor: 64x² - 49

​Factor: x² + 9

Math Response

Factor: x² - 121

Type answer here

Correct Answer: \left(x-11\right)\left(x+11\right)

Deg^°

Rad

Math Response

Factor: 49x² - 81

Type answer here

Correct Answer: \left(7x-9\right)\left(7x+9\right)

Deg^°

Rad

Match

Match the following quadratic with its factored form.

• x² - 81

• x² + 81

• x² - 9

• x² - 6x + 9

(x + 9)(x - 9)

Prime

(x + 3)(x - 3)

(x - 3)(x - 3)

• (x + 9)(x - 9)

• Prime

• (x + 3)(x - 3)

• (x - 3)(x - 3)