How do you write $y = x^{3} + 6 x^{2} - 25 x - 150$ $y=x^3+6x^2-25x-150$ in factored form?

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How do you write $y = x^{3} + 6 x^{2} - 25 x - 150$ $y=x^3+6x^2-25x-150$ in factored form?

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Answer 1 · 2018-04-21T02:59:03

$y = (x - 5) (x + 5) (x + 6)$ $y = (x-5)(x+5)(x+6)$

Explanation:

The difference of squares identity can be written:

$A^{2} - B^{2} = (A - B) (A + B)$ $A^2-B^2 = (A-B)(A+B)$

We will use this with $A = x$ $A=x$ and $B = 5$ $B=5$ .

Given:

$y = x^{3} + 6 x^{2} - 25 x - 150$ $y = x^3+6x^2-25x-150$

Note that the ratio between the first and second terms is the same as that between the third and fourth terms.

So this cubic will factor by grouping:

$y = x^{3} + 6 x^{2} - 25 x - 150$ $y = x^3+6x^2-25x-150$

$y = (x^{3} + 6 x^{2}) - (25 x + 150)$ $color(white)(y) = (x^3+6x^2)-(25x+150)$

$y = x^{2} (x + 6) - 25 (x + 6)$ $color(white)(y) = x^2(x+6)-25(x+6)$

$y = (x^{2} - 25) (x + 6)$ $color(white)(y) = (x^2-25)(x+6)$

$y = (x^{2} - 5^{2}) (x + 6)$ $color(white)(y) = (x^2-5^2)(x+6)$

$y = (x - 5) (x + 5) (x + 6)$ $color(white)(y) = (x-5)(x+5)(x+6)$

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How do you write $y = x^{3} + 6 x^{2} - 25 x - 150$ $y=x^3+6x^2-25x-150$ in factored form?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

How do you write y=x^3+6x^2-25x-150y=x3+6x2−25x−150y=x^3+6x^2-25x-150 in factored form?

1 Answer

Explanation:

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Impact of this question

How do you write $y = x^{3} + 6 x^{2} - 25 x - 150$ $y=x^3+6x^2-25x-150$ in factored form?