Combining the GCF and the simple diamond method (A=1)

Presentation

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Mathematics

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9th - 12th Grade

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Dianna Johnson

Used 9+ times

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12 Slides • 16 Questions

Combining the GCF and the simple diamond method (A=1

Hey there! Recall that we have TWO magic factoring tools in our tool belt so far.

-We know we can use the method where we “pull” the greatest common factor to the front and factor it out

-And we know the method where we use the solutions of out factor diamond to factor out two binomials.

To use the GCF method: Pull out whatever number divides out of all three terms to the front

Multiple Choice

Factor
4b⁵+4b³+16b²

4b³(b⁴+b²+4b)

4b³(b⁴+4b+5)

4(b⁵+b³+4b²)

4b²(b³+b+4)

Multiple Choice

What is the factored form of 2a³-2a²

2a²(a)

2a(2a²-a)

2a²(a-1)

2a²(a+1)

Multiple Choice

Factor (GCF)
10x² + 15x - 5

25 (10x³ + 45x -15)

5 (2x³ + 3x² - x)

x (10x³ + 15x - 5)

5 (2x² + 3x - 1)

Multiple Choice

Factor out the GCF

3x³ + 9x

3x (x²+ 3)

3x ( x³ + 9)

x (3x² + 9)

3x (x³ + 3x)

In order to understand and use the simple diamond method of factoring you need to be able to use standard form of a quadratic. Ax²+Bx+C

A is the number in front of x²

B is the number in front of x

C is your plain number (AKA the constant)

In the equation 6x²+2x+1

A=6 B=2 C=1

In the equation x²-2x+4

A=1 B=-2 C=4

In the equation -x²+20

A=-1 B=0 C=20

Fill in the Blanks

For the equation x²+3x-4, what does A =?

Type answer...

Fill in the Blanks

For the equation x²+3x-4, what does B=?

Type answer...

Fill in the Blanks

For the equation x²+3x-4, what does C=?

Type answer...

We can ONLY use the simple diamond method when A=1

SO I cannot use the simple diamond method to factor 5x²+x+3 (Because A=5)
BUT I can use it to factor x²+12x-28 (Because A=1)

Multiple Choice

Factor: x² - 16x + 24

(x + 2)(x - 14)

(x - 2)(x - 14)

(x + 14)(x - 2)

(x - 4)(x - 6)

Multiple Choice

Factor the expression: x² + 21x + 38

(x + 1)(x + 38)

(x + 2)(x + 19)

(x - 1)(x - 38)

(x - 2)(x - 19)

Multiple Choice

Factor the Trinomial:
x² - 8x + 15

(x + 5) ( x + 3)

(x - 5) (x - 3)

(x + 15) (x - 1)

(x - 7) (x - 8)

Multiple Choice

Factor x² + 7x + 12

(x + 2)(x + 10)

(x + 3)(x + 4)

(x + 4)(x + 5)

(x + 4)(x + 6)

Fill in the Blanks

Factor completely. Write your answer with no spaces: for example (x+1)(x+2). If not factorable, write not factorable.
BE SURE TO USE THE LETTER n like the problem does when typing your answer
$n^2-4n-21$

Type answer...

Fill in the Blanks

Factor completely. Write your answer with no spaces: for example (x+1)(x+2). If not factorable, write not factorable.
BE SURE TO USE THE LETTER k like the problem does when typing your answer
$k^2-16k+48$

Type answer...

For SOME problems, you can use both these methods to FULLY factor it.

Always check for this! If you have an equation where factoring out the GCF makes A=1 you may be able to use both the GCF and the diamond method.
EX: 4x²+20x+24 can be factored using both!

Multiple Choice

Factor of 6x²-24x+24

6(x-4)(x+2)

6(x-2)(x+6)

6(x-2)²

6(x+3)(x+1)

Multiple Choice

Factor 5x²+40x+75

5(x+3)(x+5)

5(x+15)(x+1)

5(x+4)(x+10)

5(x+25)(x+3)

Multiple Choice

Factor 2x²+20x+32

2(x+4)²

2(x+2)(x+8)

2(x+16)(x-2)

2(x+10)(x+16)

Combining the GCF and the simple diamond method (A=1

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