Mathematics: Khan Academy Factor using polynomial division The polynomial p(x) = x3 + 7x2 – 36 has a known factor of (x + 3). Rewrite p(x) as a product of linear factors. p(x)=

A 7/4 because the slope of the line is 7/4...

Khan Academy Factor using polynomial division

austinpace423

10.02.2022

p(x) as a product of linear factors. p(x)=(x+3)(x-2)(x+6)

Step-by-step explanation:

(x+3) is the factor of polynomial p(x) = x^3 + 7x^2 - 36

So, we can divide p(x) = x^3 + 7x^2 - 36 by (x+3) to find other factors

The division is shown in figure attached.

The quotient is: x^2+4x-12

Now factoring the quotient to find linear factors

$x^2+4x-12\\=x^2+6x-2x-12\\=x(x+6)-2(x+6)\\=(x-2)(x+6)$

The factors are (x+3)(x-2)(x+6)

So, p(x) as a product of linear factors. p(x)=(x+3)(x-2)(x+6)

0,0(0 оценок)