sat problem of the day. 5.3 factoring quadratic expressions 5.3 factoring quadratic expressions...
DESCRIPTION
5.3 Factoring Quadratic Expressions 5.3 Factoring Quadratic Expressions Objectives: Factor a quadratic expression Use factoring to solve a quadratic equation and find the zeros of a quadratic functionTRANSCRIPT
SAT Problem of the Day
SAT Problem of the Day
5.3 Factoring Quadratic Expressions5.3 Factoring Quadratic ExpressionsObjectives: •Factor a quadratic expression•Use factoring to solve a quadratic equation and find the zeros of a quadratic function
Example 1Factor each quadratic expression.
a) 27x2 – 18x9
factor out the GCF for all terms(3x – 2)
27 18x2 xx
b) 5x(2x + 1) – 2(2x + 1)
factor out the GCF for all terms
(2x + 1)(2x + 1)
( )5x - 2
(2x + 1)
Factor a quadratic expression
Factoring x2 + bx + cTo factor an expression of the form ax2 + bx + c, where a = 1, look for integers r and s such that r s = c and r + s = b. Then factor the expression.
x2 + bx + c =
(x + r)(x + s)
Factor a quadratic expression
Example 2Factor x2 + 12x + 27.
( ) ( ) x x +
+
3 9
Factor a quadratic expression
Example 3Factor x2 - 15x - 54.
( ) ( )
x x +
- 3 18
Factor a quadratic expression
Example 4Factor 5x2 + 14x + 8.
( ) ( ) 5x x +
+
4 2
Factor a quadratic expression
Practice
1) 5x2 + 15x Factor.
2) (2x – 1)4 + (2x – 1)x
3) x2 + 9x + 20 4) x2 – 7x - 30
5) 3x2 + 11x - 20
Factor a quadratic expression
Special ProductsFactoring the Difference of Two Squares
a2 – b2 = (a + b)(a – b)
Factoring Perfect-Square Trinomials
a2 + 2ab + b2 = (a + b)(a + b)a2 - 2ab + b2 = (a - b)(a - b)
Factor a quadratic expression
Example 5Factor x2 - 16.
( ) ( ) x x +
- 4 4
Factor a quadratic expression
x2
Example 6Factor x4 - 81.
( ) ( )
x2 +
- 9 9 ( )
(x2 + 9)
( )
x x +
- 3 3
Factor a quadratic expression
x - 6
Example 7Factor 2x2 – 24x + 72.2 2
4 72
2 ( ) x2 – 12x + 36 2( )( ) x - 6
Factor a quadratic expression
Zero-Product Property
If pq = 0, then p = 0 or q = 0.
Find the zeros of a quadratic function
Example 8Solve .5x2 + 7x = 0
x(5x + 7) = 0x = 0 5x + 7 = 0or
5x = -77x 5
CHECK: 5x2 + 7x = 05(0)2 + 7(0) = 0
0 + 0 = 0
CHECK: 5x2 + 7x = 027 75 7 05 5
49 495 025 5
Find the zeros of a quadratic function
Example 9Find the zeroes of the functionf(x) = x2 – 5x + 6
x2 – 5x + 6 = 0
x -3 = 0 x - 2 = 0orx = 2
CHECK: x2 – 4x = x - 632 – 4(3) = 3 - 6
9 – 12 = -3
CHECK: x2 – 4x = x - 6
(x – 3)(x – 2) = 0
x = 3
-3 = -3
22 – 4(2) = 2 - 64 – 8 = -4
-4 = -4
The zeroes are located at x = 2 and x = 3.Find the zeros of a quadratic function
PracticeFind the zeroes of each function.
1) h(x) = 3x2 + 12x
2) j(x) = x2 + 4x - 21
Find the zeros of a quadratic function
Collins Type 2
What do you know about the factors of x2+bx+c when c is positive? When c is negative? What information does the sign of b give you in each case?
Factor a quadratic expression
Homework
Do the problems listed on page 5 of today's packet ("Finding zeros of quadratic functions using factoring"). Some of these are exercises from Lesson 5.3 of the textbook.
Find the zeros of a quadratic functionFactor a quadratic expression