Factoring Quadratics: a = 1 SA 22-23

Factoring Quadratics: a = 1

How to break down standard form expressions

How to use this videos in this lesson:

• There are obviously videos. They start at different times; do not go backwards in the videos, only watch the part that is represented.

• This way, you don't have to watch a 20-30 minute video, just the part that matters most, usually just a 5-6 minute chunk.

• I have trimmed the parts so let it play as the slide comes up. When it stops you're done, even if the video didn't finish according to the time.

A quick checkpoint

Before we begin, let me give you some questions on the GCF from yesterday.

Multiple Choice

Factor:
56a³-8a

• 8a²(56a³-8a)
• 8a(7a²-1)
• 8a(7a³-a)
• 8a²(35a²-a)

Multiple Choice

Factor
12x + 9

• 3(4x + 3)
• x(12+9)
• 3(4x - 3)
• not factorable

Multiple Choice

What is the prime factorization of the number 60?

• 4 x 3 x 5

• 2 x 2 x 3 x 5

• 2 x 3 x 3 x 5

• 2 x 3 x 1 0

Multiple Choice

Factor:
2n³+16n+12

• 2n(n³+24n+6)
• 2(n³+8n+6)
• 2n(n³+8n+6)
• 3(n³+8n+6)

Factor - to break down into simpler parts

• Write down this example!

• Notice we go from standard polynomial form to factored form (x + a)(x + b).

• The KEY is to find two numbers that multiply to get the constant, and add to get the middle coefficient (5 in this problem).

Take notes on the following videos

The better your notes, the better help you'll get when answering the questions. Plus...you're gonna turn in your notes!

Time for practice!

• Look at your notes

• The timer is turned off

• Remember, we are splitting up the polynomial into two parenthesis of the form: (x + a)(x + b).

Fill in the Blank

To factor the expression below, we need to determine two numbers that multiply to get what?

 $x^2-8x-20$  

Fill in the Blank

To factor the expression below, we need to find two numbers that multiply to get -20, but add up to get what?

 $x^2+8x-20$  

Multiple Choice

Factor
n² + 16n + 63

• (n-7)(n+4)
• (n+7)(n-9)
• (n-3)(n-10)
• (n+7)(n+9)

Multiple Choice

Factor
x² + 9x - 36

• (x + 12)(x - 3)
• (x + 9)(x - 4)
• (x - 12)(x + 3)
• (x - 9)(x - 4)

Multiple Choice

Factor
d² - 10d + 25

• (d + 5) (d - 5)
• (d - 15) (d + 10)
• (d + 5) (d - 20)
• (d - 5) (d - 5)

Multiple Choice

Factor
n² - 13n + 40

• (n-5)(n-8)
• (n+5)(n-8)
• (n-5)(n+8)
• (n+6)(n+1)

Multiple Choice

Factor
k² - 2k - 24

• (k+4)(k-6)
• (k+4)(k+6)
• (k+6)(k-1)
• (k-4)(k+6)