Answer:
[tex]2x^3+ 3x^2-5x-6 = (x+2)(x+1)(2x+3)[/tex]
Step-by-step explanation:
Given polynomial [tex]g[/tex]:
[tex]g(x) = 2x^3+ 3x^2-5x-6[/tex]
A factor of polynomial is [tex](x+2)[/tex].
To find:
Equation of the polynomial as the product of linear factors.
Solution:
First of all, let us divide the polynomial [tex]g[/tex] with [tex](x+2)[/tex] to find the other factors.
As degree of polynomial is 3, when divided by a linear equation, it will result in a quadratic.
That quadratic will have 2 solutions.
Solving the quadratic in linear will give us the answer.
Result of division:
[tex]\dfrac{2x^3+ 3x^2-5x-6}{x+2} =2x^2-x-3[/tex]
Now, solving the quadratic:
[tex]2x^2-x-3 = 2x^2-3x+2x-3 \\\Rightarrow x(2x-3)+1(2x-3)\\\Rightarrow (x+1)(2x-3)[/tex]
So, the linear equation can be written as:
[tex]2x^3+ 3x^2-5x-6 = (x+2)(x+1)(2x+3)[/tex]
