2x^3+x^2-27x-36 - factor theorms?

Question

please give details. thanks

Answer 1

f(x) = 2x³ + x² - 27x - 36
f(-3) = - 54 + 9 + 81 - 36 = 0
Thus x + 3 is a factor of f (x).
To find other factors , use synthetic division:-
-3|2__1__-27__-36
_|___-6__15___36
_|2__-5__-12___0

f(x) = (x + 3)(2x² - 5x - 12)
f(x) = (x + 3)(2x + 3)(x - 4)

Answer 2

27 X 36

Answer 3

f(x) = 2x^3 + x^2 - 27x - 36

if a is root of the polynomial (x-a) is a factor and f(a) = 0

f(-3) = 2(-3)^3 +(-3)^2 - 27(-3) - 36 = -54 + 9 + 81 - 36 = 0

so x = -3 is a root and (x+3) is factor

divide f(x) by x+3

x+3)2x^3+x^2-27x-36(2x^2
___2x^3+6x^2
_________________
_______-5x^2-27x(-5x
_______-5x^2-15x
________________
___________-12x-36(-12
___________-12x-36
__________________
_______________0

so the quotient is 2x^2 - 5x - 12

factorise the quotient

2x^2 -8x+3x -12

2x(x-4)+3(x-4)

(x-4)(2x+3)

x = 4 and -3/2 are other roots

so all the three roots are -3, 4 and -3/2

Answer 4

that expression factored would be

x(2x^2 + x -27 - 36/x)

Answer 5

DesCartes's Rule of signs sys there is only one real root. The other two are a complex pair.

The real root is irrational and has a value of about 2.4624.