SECTION 10.4 SECTION 10.4 Solving Polynomials Equations in Factored Form
DAILY WARM-UPDAILY WARM-UP
Directions: Find the product.
1. (5x² – 3x)²
2. (x – 3)(3x2 + 9 – 7x)
24x24x44 – 30x – 30x33 + + 9x9x22
3x3x33 – 16x – 16x22 + 30x – + 30x – 2727
10.4 – SOLVING POLYNOMIAL 10.4 – SOLVING POLYNOMIAL EQUATIONS IN FACTORED FORMEQUATIONS IN FACTORED FORM
Objectives:1. Solve a polynomial equation in factored
form.2. Understand the difference between
factors, solutions, and zeros.
VOCABULARYVOCABULARY
A polynomial in factored form is written as a product of two or
more linear factors.A clue to look for is if there are
multiple sets of parenthesis.
Example: The factored form of x² +4x + 4 is:
(x + 2)(x + 2).
ZERO-PRODUCT PROPERTYZERO-PRODUCT PROPERTY
Let a and b be real numbers. If (a)(b) = 0, then a = 0 or b = 0.
HOW TO GUIDE: USING THE ZERO-HOW TO GUIDE: USING THE ZERO-PRODUCT PROPERTY PRODUCT PROPERTY
Solve the equation (x – 4)(x + 1) = 0 by
the zero-product property:
1. (x – 4)(x + 1) = 0
2. (x – 4) = 0 (x + 1) = 0
3. x = 4 and x = -1
1. Set each piece equal to zero. Hint: Pieces are separated by ( ) .
2. Solve each equation for x.
3. Check your solutions.
Example Explanation
+ 4 +4
-1 -1
USING THE ZERO-PRODUCT USING THE ZERO-PRODUCT PROPERTYPROPERTY
Solve (x – 9)(x + 8) = 0
Solve (2z – 6)(z + ¾) = 0
Example: Example:
x = 9x = 9x = -8x = -8
z = 3z = 3z = -3/4z = -3/4
USING THE ZERO-PRODUCT USING THE ZERO-PRODUCT PROPERTYPROPERTY
Solve (w – 14)² = 0 Solve x(2x + 8)(x – 32)=0
Example: Example:
w = 14w = 14x = 0x = 0x = -4x = -4x = 32x = 32
Brain BreakBrain BreakUSE THIS TIME TO STRETCH OUT OR …
Try these Rebus Puzzles…
Too funny for words
The wrong end of the stick
FACTORS, SOLUTIONS, AND X-FACTORS, SOLUTIONS, AND X-INTERCEPTSINTERCEPTS
For any quadratic polynomial ax² + bx + c, if one statement is true, then all 3 statements are true.
1. (x – 4) and (x + 4) are factors of x² -162. x = 4 and x = -4 are solutions of x² - 16 = 03. 4 and -4 are x-intercepts of y = x² - 16
FIND THE FACTORS, SOLUTIONS, AND X-FIND THE FACTORS, SOLUTIONS, AND X-INTERCEPTS OFINTERCEPTS OF
Y = (X – 3)(X + 1)
x = 3x = 3x = -1x = -1
FIND THE FACTORS, SOLUTIONS, AND X-FIND THE FACTORS, SOLUTIONS, AND X-INTERCEPTS OFINTERCEPTS OF
Y = (X + 4)(X - 2)
x = -4x = -4x = 2x = 2
ROW RELAYS ROW RELAYS
Each member of your row has a different task.
Once you finish your role, pass your team’s worksheet back.
The first correct row gets 2 points.
Each other correct row gets 1 point.
1st: Set each factor equal to zero.
2nd: Solve each equation for the variable.
3rd: Check the work! 4th: List the factors,
solutions, and x-intercepts.
5th: Plot the x-intercepts.
Directions Your Starring Role
ROW RELAYS: ROUND 1ROW RELAYS: ROUND 1
(x – 1)(x + 2) = 0 1st: Set each factor equal to zero.
2nd: Solve each equation for the variable.
3rd: Check the work! 4th: List the factors,
solutions, and x-intercepts.
5th: Plot the x-intercepts.
Problem Your Starring Role
x = 1x = 1x = -2x = -2
ROW RELAYS: ROUND 2ROW RELAYS: ROUND 2
(x – 5)² = 0 1st: Set each factor equal to zero.
2nd: Solve each equation for the variable.
3rd: Check the work! 4th: List the factors,
solutions, and x-intercepts.
5th: Plot the x-intercepts.
Debacle Your Starring Role
x = 5x = 5
ROW RELAYS: ROUND 3ROW RELAYS: ROUND 3
(3z + 9)(2z – 2) = 0 1st: Set each factor equal to zero.
2nd: Solve each equation for the variable.
3rd: Check the work! 4th: List the factors,
solutions, and x-intercepts.
5th: Plot the x-intercepts.
Predicament Your Starring Role
z = -3z = -3z = 1z = 1
ROW RELAYS: ROUND 4ROW RELAYS: ROUND 4
(6b – 18)(2b + 4)(2b + 8) = 0
1st: Set each factor equal to zero.
2nd: Solve each equation for the variable.
3rd: Check the work! 4th: List the factors,
solutions, and x-intercepts.
5th: Plot the x-intercepts.
Dilemma Your Starring Role
b = 3b = 3b = -2b = -2b = -4b = -4
ROW RELAYS: ROUND 5ROW RELAYS: ROUND 5
n(9n + 27)(6n – 24) = 0
1st: Set each factor equal to zero.
2nd: Solve each equation for the variable.
3rd: Check the work! 4th: List the factors,
solutions, and x-intercepts.
5th: Plot the x-intercepts.
Quandary Your Starring Role
n = 0n = 0n = -3n = -3n = 4n = 4
HOMEWORKHOMEWORKpgs. 600-601 #19-24, #37-39,
#44-46
BONUS EXAMPLES: SOLVE THE BONUS EXAMPLES: SOLVE THE FOLLOWING EQUATIONSFOLLOWING EQUATIONS
Solve (x + 8)² = 0
Solve (x – 4)(x + 3) = 0
Solve x(x+3)(2x – 3) = 0
(3x – 2)(4x + 3)(x + 4) = 0
-8
4, -3
0, -3, 3/2
2/3, -3/4, -4