Factoring Trinomials Notebook

Factoring Trinomials Notebook

By Mr. Resch

Multiple Choice

Simplify This Polynomial

(Use FOIL)

$$\left(x+1\right)\left(x+5\right)$$  

• $$x^2+6x+5$$  

• $$x^2+4x+5$$  

• $$x^2+5x+5$$  

• $$X^2+5$$  

Multiple Choice

Simplify This Polynomial

(Use FOIL)

$$\left(m-4\right)\left(m+6\right)$$  

• $$m^2+2m-24$$  

• $$m^2+10x+24$$  

• $$m^2+6m-24$$  

• $$m^2-2m-24$$  

Multiple Choice

Simplify This Polynomial

(Use FOIL)

$$\left(k-7\right)\left(k-3\right)$$  

• $$k^2-7k+21$$  

• $$k^2+10k+21$$  

• $$k^2+10k-21$$  

• $$k^2-10k-21$$  

Trinomials Can be Factored back into Binomials!

• x²​+6x+5 -----> (x+1)(x+5)​

• m²​+2m-24 ------> (m-4)(m+6)

• k²​-10k-21 -------> (k-7)(k-3)

Fill in the Blanks

To factor a trinomial of the form $x^2+bx+c$  

you must find two integers that 1 and 2 .

(Fill in Answer 1)

Fill in the Blanks

To factor a trinomial of the form $x^2+bx+c$  

you must find two integers that add together for "b" and 2 .

(Fill in Answer 2)

Multiple Select

What two integers (Numbers) have

- A Product (b x c) of 12

- A Sum (b + c) of 7

• 3

• 2

• 6

• 4

• 7

Draw

Write two Binomials using the integers 3 & 4

Multiple Select

Factor the Trinomial

$$n^2+9n+20$$  

Pick the correct binomials below

• (n+4)

• (n+9)

• (n+10)

• (n+5)

• (n+2)

Multiple Select

Factor the Trinomial

$$w^2+9w+18$$  

Pick the correct binomials below

• (w+9)

• (w+3)

• (w+6)

• $$\left(w+9\right)^2$$  

• (w+2)

Multiple Select

Factor the Trinomial

$$n^2+3n-18$$  

Pick the correct binomials below

• (n+9)

• (n+3)

• (n+6)

• (n-3)

• (n-6)

Multiple Select

Factor the Trinomial

$$x^2+2x-8$$  

Pick the correct binomials below

• (x+4)

• (x+2)

• (x-2)

• (x-4)

• (x+8)

Multiple Select

Factor the Trinomial

$$x^2-7x-30$$  

Pick the correct binomials below

• (x-10)

• (x+3)

• (x-3)

• (x+10)

• (x+6)

Multiple Select

Factor the Trinomial

$$b^2-2b-63$$  

Pick the correct binomials below

• (b-7)

• (b+9)

• (b+7)

• (b-9)

• (b+18)

Multiple Select

Factor the Trinomial

$$x^2-14x+49$$  

Pick the correct binomials below

• $$\left(x+7\right)^2$$  

• $$\left(x-3\right)$$  

• $$\left(x-11\right)$$  

• $$\left(x-7\right)^2$$  

Multiple Select

Factor the Trinomial

$$x^2+12x+36$$  

Pick the correct binomials below

• $$\left(x-6\right)^2$$  

• $$\left(x+3\right)$$  

• $$\left(x+4\right)$$  

• $$\left(x+6\right)^2$$  

​Factoring Trinomials + GCF

​If you can remove a Greatest Common Factor, do that before factoring a trinomial into it's binomial form

Multiple Choice

Factoring a Trinomial + GCF

$$2b^2+10b+12$$  

Part 1: What is the GCF?

• $$2\left(b^2-5b+6\right)$$  

• $$2\left(b^2+5b+6\right)$$

• $$\left(b+3\right)\left(b-2\right)$$  

• $$\left(b+3\right)\left(b-2\right)$$  

Multiple Choice

Factoring a Trinomial + GCF

Original : $$2b^2+10b+12$$  

Part 1: $$2\left(b^2+5b+6\right)$$  

What is the remaining factor?

• $$2\left(b+3\right)\left(b+2\right)$$   

• $$3\left(b+3\right)\left(b+2\right)$$  

• $$2\left(b-3\right)\left(b-2\right)$$   

• $$2\left(b-3\right)\left(b+2\right)$$   

Multiple Choice

Factoring a Trinomial + GCF

$$5x^2y-15xy-140y$$  

Part 1: What is the GCF?

• $$5\left(x^2y-3xy-28y\right)$$  

• $$5y\left(x^2-3x+-28\right)$$

• $$5x\left(xy-3y-28y\right)$$  

• $$5y\left(x^2y-3x-28\right)$$  

Multiple Choice

Factoring a Trinomial + GCF

Original : $$5x^2y-15xy-140y$$  

Part 1: $$5y\left(x^2-3x-28\right)$$  

What is the remaining factor?

• $$5y\left(x-7\right)\left(x+4\right)$$   

• $$5y\left(x+7\right)\left(x-4\right)$$  

• $$5y\left(x+7\right)\left(b+4\right)$$   

• $$5y\left(x-7\right)\left(x-4\right)$$