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