What does that mean? A trinomial in standard form is represented as y = ax2 + bx + cTo qualify as a trinomial the expression needs A quadratic term (ax2) A linear term (bx) A constant (c) If a (the coefficient in front of x2) is greater or less than 1 try.... How to solve the trinomial where A does not equal one

If neither of these apply we can use the Reverse FOIL Methods demonstrated. There are two different options.

Option 1: Guess and Check Works best when A is a prime number We will use y=3x2+25x+28 as an example

Find the first two terms of the two binomials

(3x+ ) (x+ ) Because 3x and x are the only two terms whose product is 3x2 2. Because all terms are positive the sign are all addition signs 3. Find two factors of 28 which, when FOILed complete the expression 2 and 14 are factors of 28 How to FOIL

Put the numbers into the expression

(3x+2)(x+14)

Find the middle term by multiplying the Inners and outer of FOIL

3x*14 and 2*x

Add them together

2x+42x=44x 44x is not the middle term we are looking for so we need to try again

4 and 7 are factors of 28

Put the numbers into the expression

(3x+4)(x+7)

Find the middle term by multiplying the Inners and outer of FOIL

3x*7 and 4*x

Add them together

21x+4x=25x

This was the term we were looking for, so the answer is,

(3x+4) (x+7)

Additional Example

2x2 -4x -6 Set up two binomials (2x )(x ) Find factors of -6 2 and -3 Put the numbers into the expression (2x-3)(x+2) Find the middle term by multiplying the Inners and outer of FOIL

2x*2 and -3*x

Add them together

-3x+4x=x

That's not what we are looking for, Try again, rearrange the numbers, put them into the equation

(2x+2)(x-3) Find the middle term by multiplying the Inners and outers of FOIL 2x*-3 and 2*x Add them together 2x+-6x=-4x

Everything works! (2x+2)(x-3)

Option 2: Factor by grouping Works best when A is not a prime number We will use 4x2+16x+5 as an example

Multiply a and c

4*15=60

Find all factors of 60 and their sums

Factors

1,60

2,30

3,20

4,15

5,12

6,10

Sums

61

32

23

19

17

16

Look for the numbers whose sum equals the coefficient of the middle term

10 and 6 work

Divide the middle term by the two factors

4x2+6x+10x+15

Separate the first two and last two terms.

(4x2+6x) (10x+15)

Factor out GCF

2x(2x+3) 5(2x+3)

Rewrite the outside numbers as a second binomial

(2x+3) (2x+5)

Additional Problem

Factor 8x2+15x+7

Multiply a and c

8*7=56

Find all factors of 56 and their sums

Factors

1,56

2,28

4,14

7,8

Sums

57

30

18

15

Look for the numbers whose sum equals the coefficient of the middle term

Trinomials where A does not equal 1What does that mean?A trinomial in standard form is represented as y = ax2 + bx + cTo qualify as a trinomial the expression needs

A quadratic term (ax2) A linear term (bx) A constant (c)

If a (the coefficient in front of x2) is greater or less than 1 try....

How to solve the trinomial where A does not equal oneFirst try to solve the trinomial by

Factoring out the Greatest Common Factoror Solve using the Perfect Square Trinomial Method

If neither of these apply we can use the Reverse FOIL Methods demonstrated. There are two different options.

Option 1: Guess and Check

Works best when A is a prime number

We will use

y=3x2+25x+28as an example(3x+ ) (x+ )Because 3x and x are the only two terms whose product is 3x2

2. Because all terms are positive the sign are all addition signs

3. Find two factors of 28 which, when FOILed complete the expression

2 and 14 are factors of 28 How to FOILPut the numbers into the expression

(3x+2)(x+14)Find the middle term by multiplying the Inners and outer of FOIL

3x*14 and 2*x## Add them together

2x+42x=44x44x is not the middle term we are looking for so we need to try again

4 and 7 are factors of 28Put the numbers into the expression

(3x+4)(x+7)Find the middle term by multiplying the Inners and outer of FOIL

## 3x*7 and 4*x

## Add them together

21x+4x=25x(3x+4) (x+7)Additional Example2x2 -4x -6Set up two binomials

(2x )(x )Find factors of -6

2 and -3Put the numbers into the expression

(2x-3)(x+2)Find the middle term by multiplying the Inners and outer of FOIL

2x*2 and -3*x## Add them together

-3x+4x=xThat's not what we are looking for,

Try again, rearrange the numbers, put them into the equation

(2x+2)(x-3)Find the middle term by multiplying the Inners and outers of FOIL

2x*-3 and 2*xAdd them together

2x+-6x=-4xEverything works! (2x+2)(x-3)Option 2: Factor by grouping

Works best when A is not a prime number

We will use

4x2+16x+5as an example4*15=60Factors1,602,303,204,155,126,10Sums61322319171610 and 6 work4x2+6x+10x+15(4x2+6x) (10x+15)2x(2x+3) 5(2x+3)## Rewrite the outside numbers as a second binomial

(2x+3) (2x+5)Additional ProblemFactor 8x2+15x+78*7=56Factors1,562,284,147,8Sums573018157 and 8 work8x2+8x+7x+7(8x2+8x) (7x+7)8x(x+1) 7(x+1)(8x+7) (x+1)LOOK AT THIS COOL VIDEO FROMTEACHER TUBE MATHIS THIS METHOD EASIER?