Download 10.5 Factoring x2+bx+c

10.5 Factoring x²+bx+c
10.5 Factoring Trinomials With a Lead Coefficient of 1 to Solve

Factoring a Quadratic Trinomial
 Remember!!!! To factor a quadratic expression means
to write it as the product of two linear (degree or
exponent of 1) expressions
 In this section you will learn how to factor quadratic
(degree or exponent of 2) trinomials (3 terms) that
have a leading coefficient of 1
Factoring to solve…
 a quadratic expression can be solved by factoring
and then using the zero-product property.
Solve: x2 + 10x + 21 = 0
…and whose sum is 10.
Find two numbers whose product is 21...
(x + 7)(x + 3) = 0
x = -7 and -3 They should check out!
Figuring out the signs!
• Frame it with the signs. x2 + bx + c = 0
(x +
)(x +
)=0
• Frame it with the signs. x2 – bx + c = 0
(x)(x)=0
• Frame it with the signs. x2 – bx – c = 0
(x )(x +
)=0
The larger # goes here.
• Frame it with the signs. x2 + bx – c = 0
(x )(x+
)=0
The larger # goes here.
Methods
Method 1: List out all the factors of the constant in the
List factors of -36
trinomial.
Factor. x2 + 5x – 36 = 0
Frame it.
Solve.
(x + 9 )(x - 4 ) = 0
-12 and 3
-18 and 2
12 and -3
18 and -2
9 and -4
36 and -1
-9 and 4
-36 and 1
Which set of factors add to +5?
x = 4 and -9
Method 2: Do this process in your head!!!
Factor. x2 – 14x = -48
x2 – 14x + 48 = 0
Put in standard form.
Frame it with signs.
(x - 6 )(x- 8 ) = 0
Solve.
x = 6 and 8
6 and -6
Solve.
x2 – 15x – 7 = -61
+ 61 +61
Put in standard form!
x2 – 15x + 54 = 0
(x - 9 )(x - 6) = 0
x = 9 and 6
Solve.
1) x2 + 3x – 18 = 0
(x – 3)(x + 6) = 0
2) m2 + 11m = -10
m2 + 11m + 10 = 0
(m + 10)(m + 1) = 0
3) x2 – 2x – 40 = 8
x2 – 2x – 48 = 0
(x + 6)(x – 8) = 0
x = -6 and 8
4) a2 – 33a = 280
a2 – 33a – 280 = 0
(a – 40)(a + 7) = 0
a = 40 and -7
x = 3 and -6
m = -10 and -1
Solve.
5) x2 + 3x = 6
x2 + 3x – 6 = 0
(x – )(x + ) = 0
Then how do you solve the equation?
x = -3 +√33
2
x = -3 - √33
2
If you think the quadratic equation cannot be factored, check the discriminant.
If the discriminant is a perfect square: The equation can be factored.
If the discriminant is not a perfect square: The equation cannot be factored.
b2 – 4ac
32 – 4(1)(-6)
9 + 24
33 Not a perfect square,
the trinomial cannot be factored.
HW
 P. 607-609 #12-44 EVEN