How do you factor $(x^{2} + 5) (x^{2} + 2 x - 3)$ $(x^2+5)(x^2+2x-3)$ ?

Question

How do you factor $(x^{2} + 5) (x^{2} + 2 x - 3)$ $(x^2+5)(x^2+2x-3)$ ?

1 Answer

Impact of this question

1921 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-20T18:23:48

$(x^{2} + 5) (x^{2} + 2 x - 3) = (x^{2} + 5) (x + 3) (x - 1)$ $(x^2+5)(x^2+2x-3) = (x^2+5)(x+3)(x-1)$

The factors $(x + 3)$ $(x+3)$ and $(x - 1)$ $(x-1)$ were found by looking for two numbers $a$ $a$ and $b$ $b$ such that $a \times b = 3$ $axxb = 3$ and $a - b = 2$ $a-b = 2$ .
Then $(x + a) (x - b) = x^{2} + (a - b) x - a b$ $(x+a)(x-b) = x^2+(a-b)x-ab$ .

This is as far as you can break down the original expression into factors, unless you are allowed complex numbers as coefficients. You can tell that $(x^{2} + 5)$ $(x^2+5)$ has no smaller factors with real coefficients - which would be linear - because $x^{2} + 5 > 0$ $x^2+5 > 0$ for all real values of $x$ $x$ .

On the other hand, if you are allowed complex coefficients, you can factor as:

$(x^{2} + 5) = (x + i \sqrt{5}) (x - i \sqrt{5})$ $(x^2+5) = (x+isqrt(5))(x-isqrt(5))$ , where $i = \sqrt{- 1}$ $i = sqrt(-1)$ , so

$(x^{2} + 5) (x^{2} + 2 x - 3)$ $(x^2+5)(x^2+2x-3)$

$= (x + i \sqrt{5}) (x - i \sqrt{5}) (x + 3) (x - 1)$ $= (x+isqrt(5))(x-isqrt(5))(x+3)(x-1)$

Science

Math

Humanities

... and beyond

How do you factor $(x^{2} + 5) (x^{2} + 2 x - 3)$ $(x^2+5)(x^2+2x-3)$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you factor (x2+5)(x2+2x−3)(x^2+5)(x^2+2x-3)?

1 Answer

Related questions

Impact of this question

How do you factor $(x^{2} + 5) (x^{2} + 2 x - 3)$ $(x^2+5)(x^2+2x-3)$ ?