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How do you factor: x^3+3x^2-4

2007-04-15 17:02:12 · 3 answers · asked by Jonothan R 1 in Science & Mathematics Mathematics

3 answers

Take f(x) = x^3 + 3x^2 - 4.

Now f(1) = 0 showing that (x - 1) is a factor of f(x), by the Remainder Theorem

Hence we can write:

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

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

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

=(x - 1)(x + 2)^2 are the factors.

2007-04-15 17:10:22 · answer #1 · answered by quidwai 4 · 0 0

When the sum of the coefficients is 0, the polynomial has 1 as a root

Use synthetic division and solve the quadratic equation

....... 1....... 3 ..... 0 .... .-4
1............... 1.......4 .......4
.........1...... 4.......4 ....... 0

And x^2 + 4 x + 4 = (x+2)^2

So, your polynomials is (x-1)(x+2)^2

Ana

2007-04-16 00:06:14 · answer #2 · answered by MathTutor 6 · 1 0

hmmm - something seems wrong -
is there not an x on the end of the 4

x^3 +3x^2 - 4x......perhaps - then we would factor out an x
and go from there
x (x-1)(x+4)

double check - maybe it was copied wrong?

best of luck!

2007-04-16 00:08:19 · answer #3 · answered by tom4bucs 7 · 0 1

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