Download 8-7 Solving ax2 +bx +c =0.notebook

8­7 Solving ax2 +bx +c =0.notebook
8­7 Solving ax2 +bx +c =0
January 25, 2015
Factor: 2x2+5x+3
Goals:
1. Factor trinomials of the form ax2 +bx +c =0
2. Solve equations of the form ax2 +bx +c =0
Notice that there now is a number other than 1 in the "a" position of the trinomial.
Bustin' the "b" in ax2 + bx +c
In order to factor the equation, we need to bust up the b value in our equation into 2 parts.
2x2+5x+3
1. Multiply the "a" by the "c" value: 2 x 3 = 6
2. What are the factors of this new value that add to the "b" value: factors of 6 that add to 5?
3. Those two factors will "bust the b": 2 + 3
4. 5. Divide both constant factors by the leading coefficient, in this case 2 Ask: What are the factors of "a" x "c" that add to "b" ?
6. If the constant divides without any remainders, simplify. If there would be a remainder, move the bottom number up in front of the Answer: (x+1) (2x+3)
1
8­7 Solving ax2 +bx +c =0.notebook
Factor the trinomial: 7x2 +29x +4
January 25, 2015
Factor the trinomial: 6x2 +22x ­8
Hint: Is there anything in common to take out before you "bust the b"?
(5x+3)(x+2)
2(3x­1)(x+4)
Factor the trinomial: 10y2 ­35y +30
Factor the trinomial: 2n2 ­n ­1
(n­1)(2n+1)
5(2y­3)(y­2)
2
8­7 Solving ax2 +bx +c =0.notebook
Prime Polynomial: a polynomial that cannot be written as a product of two polynomials with integral coefficients.
January 25, 2015
Factor the polynomial, if possible. If the polynomial cannot be factored using integers, write prime: 4r2 ­r +7
prime
Factor the polynomial, if possible. If the polynomial cannot be factored using integers, write prime: 2x2 +3x ­5
(2x+5)(x­1)
3
8­7 Solving ax2 +bx +c =0.notebook
January 25, 2015
A person throws a ball upward from a 506­foot tall building. The ball's height h in feet after t seconds is given by the equation h = ­16t2 +48t +506. The ball lands on a balcony that is 218 feet above the ground. How many seconds was it in the air?
6 sec
8­7 Assignment: p. 513: 11­31 odd
4