(2x+3)(x-2)
24
2x2 + 7x + 6 = 2x2 + 4x + 3x + 6 = 2x(x + 2) + 3(x + 2) = (x + 2)(2x + 3)
11x = 8x-6.............. 11x-8x = -6................... 3x= -6 x = -2
8x 97x 6= 4656
2x2-x-6 = (2x+3)(x-2)
That does not factor neatly.
2x2 = 8x x = 8x/2x x = 4 Check: 2(4)2 = 8(4) 2(16) = 32 32 = 32
2(x - 6)(x + 6)
-6
2x2-4x-3x+6 2x2-7x+6 (2x+3)(x+2)
The factor theorem states that for any polynomial function f(x), if f(a) = 0, then (x-a) is a factor of f(x). Let f(x) = x3-2x2-8x-5. If (x+1) is a factor, then f(-1) = 0. (x+1 = x - (-1)) Input x = -1 into f: (-1)3-2(-1)2-8(-1)-5 f(-1) = -1 -2 + 8 - 5 f(-1) = 0. Since f(-1) = 0, (x+1) is a factor of x3-2x2-8x-5. Q.E.D.
2x2 + 11x + 12 = 2x2 + 3x + 8x + 12 = x*(2x + 3) + 4*(2x + 3) = (2x + 3)*(x + 4)
x3 + 2x2 - 8x + 5 = 0 x(2x - 8) + 5 = 0
The GCF is 2.
y=-2x^2+8x+3
-1/2