Another maths question!...simplify a polynomial?

(2x²-1)(x+2)-4(x+2)²

(2x^3 +4x^2 - x - 2) - 4(x² + 4x + 4) =

(2x^3 + 4x^2 - x - 2) - 4x² - 16x - 16 =

2x^3 - 17x - 18

f(x) = 10x ^ 3 - 25x ^ 2 +20 f(x) = 5(2x^3 - 5x^2 x - (a million + sqrt(17))/4] [x - (a million - sqrt(17))/4) Set f(x) = 0 f(x) = 5(2x^3 - 5x^2 x - (a million + sqrt(17))/4] [x - (a million - sqrt(17))/4) = 0 Now seem for an undemanding answer from thi463069ae961ba6454086feff8fb1346cet of opportunities: {+/- a million/2, a million, 2, 4} Do you realize why this i463069ae961ba6454086feff8fb1346che set of opportunities? f(2) = 5(2(2)^3 - 5(2^2) x - (a million + sqrt(17))/4] [x - (a million - sqrt(17))/4)) = 5(sixteen - 20 x - (a million + sqrt(17))/4] [x - (a million - sqrt(17))/4) = 0 So x = 2 is a root of f(x) and thu463069ae961ba6454086feff8fb1346cx - 2) is a ingredient of f(x). Divide (2x^3 - 5x^2 x - (a million + sqrt(17))/4] [x - (a million - sqrt(17))/4) via (x - 2). effect: (2x^2 - x - 2) f(x) = 5(x - 2463069ae961ba6454086feff8fb1346c2x^2 - x - 2) Use the quadratic formula to locate roots of (2x^2 - x - 2463069ae961ba6454086feff8fb1346c = (a million +/- sqrt(a million 463069ae961ba6454086feff8fb1346c6))/4 = (a million +/- sqrt(17))/4 So: x = (a million 463069ae961ba6454086feff8fb1346cqrt(17))/4 and x = (a million - sqrt(17))/4 are roots of f(x). finished factorization of f(x): f(x) = 5(x - 2) [x - (a million 463069ae961ba6454086feff8fb1346cqrt(17))/4] [x - (a million - sqrt(17))/4]

You essentially have two terms here, (2x^2 -1)(x+2) and 4(x+2)^2. Notice that they each have (x+2) in common. So you can factor that out, in the same way that ac - bc = (a-b)c:

[ (2x^2 - 1) - 4(x+2) ] (x+2)

Now expand what's inside.

[ 2x^2 - 1 - 4x - 8 ] (x+2)

[ 2x^2 - 4x - 9 ] (x+2)

Normally you might be able to factor a quadratic, but in this case of 2x^2 - 4x - 9, you can't. So this is as far as you can take it.

>>but i am rubbish at maths! :|

If you don't want to go through the rest of your life as somebody who sucks at mathematics, then it's up to you to change that. Bad mathematics skills aren't genetic.

[(2x²-1)(x+2)] -4(x+2)²

solve the part under [ ] first

= [x(2x²-1) +2(2x²-1)] -4(x+2)²

expand the second bracket by using identity (a + b)² = a² +2ab + b²

= ( 2x^3 - x +4x² - 2) - 4(x² +4x + 4)

= ( 2x^3 +4x² - x - 2) -4x² - 16x - 16

= 2x^3 +4x² -x - 2 -4x² - 16x - 16

= 2x^3 - 17x - 18

(2x^2-1)(x+2) - 4(x+2)(x+2) now multiply the brackets

2x^3 + 4x^2 - x - 2 - 4(x^2 +2x +2x +4) multiply the 4 through

2x^3 + 4x^2 - x - 2 - 4x^2 - 8x - 8x - 16 now combine like terms

2x^3 + 4x^2 - 4x^2 - x - 8x - 8x - 2 - 16 now add he like terms

2x^3 - 17x -18

Multiply out the brackets to get

2x(cubed) -x +4x(squared) -2 -4x(squared)-16x-16

then put similar terms together to end up with

2x(cubed) -17x -18