Download Sec 9.6 Page 9.6 Factor x2 + bx + c and ax² + bx + c WARM

9.6 Factor x2 + bx + c and ax² + bx + c
WARM-UP: Factor polynomials in the form x2 + bx + c:
1. x² - 4x - 77
2. y² + 26y +88
3. x² - 30x + 225
4. x² + 20x + 100
5. y² + 2y - 120
6. y² - 21y + 108
Factoring ax² + bx + c (when the leading coefficient is not “1”).
Example 1 - Factor using the guess and check method:
Factor 6x 2 + 26x + 20
Example 2 – Factor by grouping, a.k.a. split term factoring (the box method…sort of)
Step 1: Multiply and rewrite the polynomial.
Multiply the first term by the third term. “Separate” the product into a sum which adds up to the
middle term:
Step 2: Factor a common monomial out of the first two terms and the last two terms.
Step 3: Factor out the common binomial. Rewrite as a product of two binomials.
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2a) 6x 2 + 26x + 20
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2b) 6n² - 7n - 20
NOW YOU TRY IT!
1. 5n 2 + 2n – 3
2. 3y 2 + 10y + 3
3. 6z² - 5z – 6
Example 3 - Always factor out a -1 first if the leading coefficient is negative!
Factor –4x 2 - 15x - 9
NOW YOU TRY!
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4. Factor –2y 2 – 11y – 5
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Example 4 - Factor out a common factor first if possible!
Factor -4x² - 8x - 4
NOW YOU TRY!
5. Factor –2y 2 – 11y – 5
6. Factor 5y² + 20y + 15
Example 5 - Write and solve a polynomial equation
John dives off of a cliff when his center of gravity is 80 feet above the water level. His initial vertical
velocity, as he leaves the cliff is 64 feet per second.
a. Write an equation that gives the height (in feet) of John as a function of the time (in seconds)
since he left the cliff.
h = –16t 2 + vt + s
v=
s=
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b. After how many seconds will John hit the water?
Sec 9.6
NOW YOU TRY!
7. A cricket jumps from the ground into the air with an initial vertical velocity of 2 feet per second.
a. Write an equation that gives the cricket’s height (in feet) as a function of the time (in seconds)
since it left the ground.
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b. After how many seconds will the cricket land?
Sec 9.6