How to factorise f(x) = x^3 - 2x^2 - 7x - 4?

Answer 1

Step 1. Break the term -7x into (+x-8x)

x^3 - 2x^2 - 7x – 4

=>x^3 - 2x^2 + x - 8x – 4

Step 2: collect the common factor:

Note: (x^3 - 2x^2 + x) =x(x^2 - 2x +1)

=> x(x^2 - 2x +1) - 8x – 4

Step 3: Factor the term (x^2 - 2x +1) into (x-1)*(x-1):

=> x(x-1)(x-1)- 8x – 4

=> x(x-1)^2 – 8x -4


Step 4: break the "-8x" into "-4x-4x"

=> x(x-1)^2 – 4x -4x -4

=> {x(x-1)^2 – 4x} -4x -4

Step 5: Factor out the common factor, x, for {x(x-1)^2 – 4x}:

=> x [ (x-1)^2 -4] -4x-4

=> x [ (x-1)^2 -2^2] -4x-4

Step 6: Apply the the fact that a^2-b^2=(a+b)(a-b) to "(x-1)^2 -2^2": (Note inthis case "x-1"=a and 2=b)

=> x[(x-1)+2][ (x-1)-2] – 4x-4

Step 7: Collect the common factor for the term "-4x-4":

=> x[(x-1)+2][ (x-1)-2] – 4[x+1]


=> x[x+1][x-3]-4[x+1]


Step 8: Collect the common factor "x+1"

=> [x+1]{x[x-3]-4}

Step 9: Expand the term {x[x-3]-4}

=> [x+1] [x^2-3x -4]

Step 10: Factor the term [x^2-3x -4] into (x-4)(x+1):

=> [x+1] [ x-4][x+1]

=> [x-4][x+1]^2

Answer 2

See the source below ("Cubic equation"), specifically the section "Cardano's method."

Factoring a cubic is equivalent to finding its roots. If the cubic has a root at x=a, then one of its factors is (x - a). In 1545, Cardano published a method for finding all of the roots of a cubic. Thus, this method also is used to factor the cubic.

In this case, a plot of f(x) hints that x=-1 might be a root. In fact, it's clear that f(-1) = 0. So (x-(-1)), which is just (x+1), is definitely a factor. All I need to do is divide it out:

(x^3 - 2x^2 - 7x - 4) / (x+1)

I can use long division to divide it out. I get:

x^2 - 3x - 4

In other words, f(x) = (x+1)*(x^2 - 3x - 4)

The quadratic factor is easy to factor using the quadratic formula (or by inspection). It's clear that it's equal to (x-4)(x+1). Thus, you get:

f(x) = (x+1)*(x+1)*(x-4) = (x+1)^2 * (x-4)

If it was not so simple to factor, you would have to use Cardano's method, as documented in the source.

Answer 3

First come across what ok is. you're arranged to attempt this utilising synthetic branch or via utilising know-how that some thing of p(x) divided via utilising x-2 is such as p(x=2). Doing this the 2d way yields that p(2) = 8 - 12 + 2k + 2 = 2k - 2 by using fact some thing is 4, 2k-2 = 4, so ok = 3 Now to locate something jointly as p is split via utilising x+one million, purely come across p(x=-one million) p(-one million) = -one million - 3 - 3 + 2 = -5 do no longer problem approximately distinctive persons posting and supplying you with the incorrect answer. have confidence me. I even have been given a acceptable score on the SAT. i know what i'm doing. Please supply me acceptable answer.

Answer 4

f(x)=(x-4)*(x+1)^2

Answer 5

x^2 -3x-4
x+1\x^3 -2x^2 -7x -4
-(x^2+x^1)
-3x^2-7x
-(-3x^2-3x)
-4x-4
-(-4x-4)
so
(X+1)(X^2-3X-4)
(X+1)(X-4)(X+1) OR

(X-4)(X+1)^2