factoring lesson 1 (2).notebook
factoring lesson 1 (2).notebook
May 11, 2012
Lesson Objectives: • students will learn how to factor trinomials in the form ax2 + bx + c when a= 1 and when a is not 1
1
factoring lesson 1 (2).notebook
May 11, 2012
Expand and Simplify
Short- cut --- middle term comes from...
last term (constant) comes from...
2
factoring lesson 1 (2).notebook
May 11, 2012
Expand and Simplify:
Recall, factoring a difference of squares:
x2 9 is an equation in Standard form of a quadratic relation which is the graph of the
parabola x2 shifted
units.
The yintercept of this graph is at
Factoring this equation yields the ZEROS or xintercepts.
3
factoring lesson 1 (2).notebook
May 11, 2012
4
factoring lesson 1 (2).notebook
May 11, 2012
The pattern in the product of 2 binomials:
Expand and simplify:
Reflect: For the trinomial x2 + 7x + 12 ,how could you identify the constant terms in the binomial factors
5
factoring lesson 1 (2).notebook
May 11, 2012
Part A: Factoring Trinomials when 'a' = 1 Find the binomial factors of the trinomial:
to get this term, you add the 2 middle x terms
to get this term you multiply the 2 numbers
STEP 2 : of the pairs in step 1, find the pair that adds to 15 (the middle number)
STEP 1: Find all the pairs of numbers that multiply to 36
6 + 6 = 12
6 x 6 = 36
2 + 18 = 20
2 x 18 = 36
1 + 36 = 37
1 x 36 = 36
3 + 12 = 15
3 x 12 = 36
4 + 9 = 13
4 x 9 = 36
with 3 and 12 the 2 conditions are met add to 15 and multiply to 36
The binomial factors are:
check by expanding
6
factoring lesson 1 (2).notebook
May 11, 2012
Your turn: factor the trinomial
7
factoring lesson 1 (2).notebook
May 11, 2012
This is the graph of
notice the yintercept
Notice the ZEROS ∴ it is also the graph of
8
factoring lesson 1 (2).notebook
May 11, 2012
Your turn: factor the trinomial x2 + 7x 18
step 2 : find which of the pairs in step 1, add to +7 remember, one of the numbers is negative.
1 + (18) = 17 1 + 18 = +17 2 + (9) = 7 2 + 9 = + 7 3 + (6) = 3 3 + 6 = +3
step 1: find the pair of numbers that multiplies to 18 NOTE; one of the numbers has to be negative since when you multiply + x =
1 x (18) = 18 1 x 18 = 18 2 x (9) = 18 2 x 9 = 18 3 x (6) = 18 3 x 6 = 18
the factors are ( x 2)(x + 9) check by expanding
FACTORED FORM: gives: a = 1 zeros at +2 and 9
STANDARD FORM; gives: a = 1 yintercept = 18
9
factoring lesson 1 (2).notebook
May 11, 2012
Expand your thinking:
Identify the ZEROS
where is the AXIS OF SYMMETRY?
what are the coordinates of the VERTEX?
write the equation in VERTEX FORM:
10
factoring lesson 1 (2).notebook
May 11, 2012
Assignment: Find the binomial factors of each trinomial.
a)
b)
c)
d)
e)
f)
11
May 11, 2012
Lesson Objectives: • students will learn how to factor trinomials in the form ax2 + bx + c when a= 1 and when a is not 1
1
factoring lesson 1 (2).notebook
May 11, 2012
Expand and Simplify
Short- cut --- middle term comes from...
last term (constant) comes from...
2
factoring lesson 1 (2).notebook
May 11, 2012
Expand and Simplify:
Recall, factoring a difference of squares:
x2 9 is an equation in Standard form of a quadratic relation which is the graph of the
parabola x2 shifted
units.
The yintercept of this graph is at
Factoring this equation yields the ZEROS or xintercepts.
3
factoring lesson 1 (2).notebook
May 11, 2012
4
factoring lesson 1 (2).notebook
May 11, 2012
The pattern in the product of 2 binomials:
Expand and simplify:
Reflect: For the trinomial x2 + 7x + 12 ,how could you identify the constant terms in the binomial factors
5
factoring lesson 1 (2).notebook
May 11, 2012
Part A: Factoring Trinomials when 'a' = 1 Find the binomial factors of the trinomial:
to get this term, you add the 2 middle x terms
to get this term you multiply the 2 numbers
STEP 2 : of the pairs in step 1, find the pair that adds to 15 (the middle number)
STEP 1: Find all the pairs of numbers that multiply to 36
6 + 6 = 12
6 x 6 = 36
2 + 18 = 20
2 x 18 = 36
1 + 36 = 37
1 x 36 = 36
3 + 12 = 15
3 x 12 = 36
4 + 9 = 13
4 x 9 = 36
with 3 and 12 the 2 conditions are met add to 15 and multiply to 36
The binomial factors are:
check by expanding
6
factoring lesson 1 (2).notebook
May 11, 2012
Your turn: factor the trinomial
7
factoring lesson 1 (2).notebook
May 11, 2012
This is the graph of
notice the yintercept
Notice the ZEROS ∴ it is also the graph of
8
factoring lesson 1 (2).notebook
May 11, 2012
Your turn: factor the trinomial x2 + 7x 18
step 2 : find which of the pairs in step 1, add to +7 remember, one of the numbers is negative.
1 + (18) = 17 1 + 18 = +17 2 + (9) = 7 2 + 9 = + 7 3 + (6) = 3 3 + 6 = +3
step 1: find the pair of numbers that multiplies to 18 NOTE; one of the numbers has to be negative since when you multiply + x =
1 x (18) = 18 1 x 18 = 18 2 x (9) = 18 2 x 9 = 18 3 x (6) = 18 3 x 6 = 18
the factors are ( x 2)(x + 9) check by expanding
FACTORED FORM: gives: a = 1 zeros at +2 and 9
STANDARD FORM; gives: a = 1 yintercept = 18
9
factoring lesson 1 (2).notebook
May 11, 2012
Expand your thinking:
Identify the ZEROS
where is the AXIS OF SYMMETRY?
what are the coordinates of the VERTEX?
write the equation in VERTEX FORM:
10
factoring lesson 1 (2).notebook
May 11, 2012
Assignment: Find the binomial factors of each trinomial.
a)
b)
c)
d)
e)
f)
11
