11.7 Solve by factoring with coefficient not 1 2016 ink.notebook
Lesson Objectives
April 19, 2017
Standards
Lesson page 157
11.7 Solve by
factoring with
a coefficient
not 1
11.7 Solve by Factoring –
With Coefficient not 1
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Lesson Objectives
Standards
Lesson
A.SSE.2
A.SSE.3
A.APR.3
A.REI.4
I will rewrite a trinomial with a coefficient NOT 1 into factored form I will find the factors of a quadratic function and then solve to find the zeros I will factor a quadratic function to determine the zeros I will solve a quadratic equation by factoring first with a trinomial with a coefficient not 1 F.IF.8
I will use factoring to find the zeros of a quadratic function
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Lesson Objectives
Standards
Lesson A.REI.4 Solve quadratic equations in one variable.
b) Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.
A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
a) Factor a quadratic expression to reveal the zeros of the function it defines.
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1
11.7 Solve by factoring with coefficient not 1 2016 ink.notebook
Diamonds with new
top number.
Then grouping to
get factors.
10x2 + 13x - 3 = 0
-30
15
-2
13
10x2 +15x - 2x - 3
Outers make one
factor
5x(2x + 3)-1(2x + 3)
Inners make the
other factor
(5x - 1)(2x + 3) = 0
Remember the "="
sign means you have
to SOLVE each
factor!
x =
1
5
x =
3
2
April 19, 2017
Diamonds with new
10x2 + 13x - 3 = 0
top number.
-30
Put the first
-2
15
coefficient on top of
13
your fraction and your
10 = 5
10 = 2
"diamonds" on the
bottom of each
-2 -1
15 3
fraction.
REDUCE each fraction!
The top # goes in
(2x + 3)(5x - 1) = 0
front of x and the
bottom # is your
constant.
1
3
x =
x =
Remember the "="
5
2
sign means you have
to SOLVE each factor!
Solve each quadratic equation by factoring and applying the Zero­Product Property. 1. 3n2 – 6n + 3 = 0 Solve each quadratic equation by factoring and applying the Zero­Product Property. 2. 4x2 – 5x – 21 = 0
2
11.7 Solve by factoring with coefficient not 1 2016 ink.notebook
Solve each quadratic equation by factoring and applying the Zero­Product Property. 3. 4x2 + 27x – 7 = 0
April 19, 2017
Solve each quadratic equation by factoring and applying the Zero­Product Property. 4. 3x2 – 17x + 20 = 0
On Your
Whiteboards
3
11.7 Solve by factoring with coefficient not 1 2016 ink.notebook
April 19, 2017
On the
Worksheet
Solve each quadratic equation by factoring and applying the Zero­Product Property. 1. 6x2 – 5x – 4 = 0
2. 12x2 – 8x – 7 = 0
Homework
Hint
Homework
Homework
3. 5x2 + 28x – 12 = 0
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
4. 2x2 – 11x – 40 = 0
4
11.7 Solve by factoring with coefficient not 1 2016 ink.notebook
5. 2x2 + 21x – 11 = 0 9. 5x2 + 17x – 12 = 0
6. 8x2 – 14x + 3 = 0
7. 3x2 + 2x – 21 = 0
April 19, 2017
8. 6x2 + 11x – 2 = 0
Solve each equation by factoring first.
10. 6n2 – 24n = 0
11. 81x2 – 25 = 0
5
11.7 Solve by factoring with coefficient not 1 2016 ink.notebook
April 19, 2017
Solve each equation by factoring first.
Solve each equation by factoring first.
13. x2 – 4x + 32 = 0
14. x2 + 14x + 40 = 0
12. 24x – 4x – 30x + 5 = 0
2
Solve each equation by factoring first.
ANSWERS:
15. 3x + 6x – 45 = 0
2
6