Question

Let's start form the product `x^{2}+11x+30,` and get back to the binomials we started with. Show your steps.

Answer 1

Answer:

Then, the polynomial $x^{2}+11\cdot x + 30$ is equal to the product of the binomials $(x+5)$ and $(x+6)$.

Step-by-step explanation:

The polynomial $x^{2}+11\cdot x + 30$ is a polynomial of the form $x^{2} - (r_{1}+r_{2})\cdot x + r_{1}\cdot r_{2} = (x-r_{1})\cdot (x-r_{2})$, where $r_{1}$ and $r_{2}$ are the roots of the polynomial. Then, we find the following system of equations:

$-r_{1}-r_{2} = 11$ (1)

$r_{1}\cdot r_{2} = 30$ (2)

After some algebraic handling, the solution of this system is $r_{1} = -5$ and $r_{2} = -6$.

Then, the polynomial $x^{2}+11\cdot x + 30$ is equal to the product of the binomials $(x+5)$ and $(x+6)$.