How to factor x^3 - 4x^2 - 9x + 36 by grouping

Mathematics

2 answers:

const2013 [10]3 years ago

6 0

Answer:

(x-4) (x-3) (x+3)

Step-by-step explanation:

x^3 - 4x^2 - 9x + 36

Make 2 groups

x^3 - 4x^2 - 9x + 36

We can factor out x^2 from the first group and -9 from the second group

x^2 (x-4) - 9(x-4)

Now factor out (x-4)

(x-4) (x^2 -9)

This may be an answer choice but we can still factor

(x^2 -9) is the difference of squares

(x^2-9) = (x-3) (x+3)

Replacing this

(x-4) (x-3) (x+3)

alukav5142 [94]3 years ago

4 0

Answer:

(x - 4)(x - 3)(x + 3)

Step-by-step explanation:

x³ - 4x² - 9x + 36

x²(x - 4) - 9(x - 4)

(x - 4)(x² - 9)

(x - 4)(x² - 3²)

(x - 4)(x - 3)(x + 3)

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3 years ago

Read 2 more answers

Determine the quotient, q(x), and remainder, r(x) when

Vinvika [58]

ANSWER

Quotient:

$q(x) = 4 {x}^{2} + 3x + 2$

Remainder:

$r(x) = 3x + 1$

EXPLANATION

The given functions are

$f(x) = 12 {x}^{4} + 21 {x}^{3} + 31 {x}^{2} + 21x + 9$

and

$g(x) = 3 {x}^{2} + 3x + 4$

We want to find the remainder and quotient when f(x) is divided by g(x).

We perform the long division as shown in the attachment.

The quotient is

$q(x) = 4 {x}^{2} + 3x + 2$

The remainder is

$r(x) = 3x + 1$