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

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

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)

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)