How would you factor this polynomial?
-20y^2 + 60y - 45
2006-12-07 01:49:32 · 7 answers · asked by The Ultimate Answerer 3 in Science & Mathematics ➔ Mathematics
= -5(4y² - 12y + 9)
= -5(2y - 3)²
Need to recognize the square... b²-4ac = 0...
2006-12-07 01:54:19 · answer #1 · answered by Anonymous · 1⤊ 0⤋
Find the roots of the polynomial:
D = 60² - 4.45.20 = 3600 - 3600 = 0
y = -60 / -40 = 3/2 is a double root
-20 (y-3/2)² = -5 (2y - 3)²
Check: -20 (y² -3y + 9/4) = -20y² + 60y - 45 -> yahoo!
2006-12-07 09:56:48 · answer #2 · answered by anton3s 3 · 0⤊ 0⤋
-20y^2 + 60y - 45 = -20 * (y^2 - 3y + 9/4)
-20y^2 + 60y - 45 = -20 * (y - 3/2)^2.
2006-12-07 10:04:39 · answer #3 · answered by Anonymous · 0⤊ 0⤋
-20y^2 + 60y - 45
= -5 [4y^2 - 12y + 9]
= -5 [4y^2 - 6y - 6y + 9]
= -5 [2y*(2y - 3) - 3(2y - 3)]
= -5 [(2y - 3)(2y - 3)]
I hope that it is clear now.
All the best.
2006-12-07 09:58:51 · answer #4 · answered by Paritosh Vasava 3 · 1⤊ 0⤋
divide everything by -20
y^2 - 3y + 45/20
Use Quadratic Formula
Y= [-b+- sqr (b^2 - 4ac) ] / 2a
Y= [-3 +- sqr( 3^2 - 4*1*(45/20))] 2 (1)
(-3 +- 0) / 2
Y= -3/2
Y= -.3/2
(Y+3/2 (Y+ 3/2)
2006-12-07 10:04:44 · answer #5 · answered by john 2 · 0⤊ 0⤋
- 20x² + 60y - 45
- 5(4y² - 12y + 9
- 5(2y - 3)(2y - 3)
- - - - - -s-
2006-12-07 11:20:41 · answer #6 · answered by SAMUEL D 7 · 0⤊ 0⤋
first pull out -5
-5(4y^2 - 6y +9)
-5 (2y -3)(2y-3) = 0
y = 3/2
2006-12-07 10:04:11 · answer #7 · answered by rjc 2 · 0⤊ 0⤋