Question

solve g(x)=x³+5x²-2x-10​

Answer 1

Solution:

g(x) = x^3 + 5x^2 - 2x - 10

Find the roots of the polynomial using factor theorem/remainder theorem

When we divide f(x) by the simple polynomial x - c we get:

f(x) = (x - c) * q(x) + r(x)

Or if we calculate f(c) and it is 0

... that means the remainder is 0, and

(x - c) must be a factor of the polynomial

If x = -5, then substitute to the given function.

x^3 + 5x^2 - 2x - 10

-5^3 + 5(-5)^2 - 2(-5) - 10

= -125 + 125 + 10 - 10 = 0

Therefore, x + 5 is the root of x^3 + 5x^2 - 2x - 10.

x^3 + 5x^2 - 2x - 10 = (x + 5) ( ?)

Using long division method.

(x^3 + 5x^2 - 2x - 10)/(x + 5) = (x^2 - 2)


x^3 + 5x^2 - 2x - 10 = (x + 5)(x^2 - 2)

(x + 5)(x^2 - 2) = 0

x + 5 = 0 or x^2 - 2 = 0

x = -5 or x = √2, -√2

x^2 - 2 = 0 The expression is not factorable with rational numbers.

Hope this will be helpful to you.