Answer:
Then, the polynomial [tex]x^{2}+11\cdot x + 30[/tex] is equal to the product of the binomials [tex](x+5)[/tex] and [tex](x+6)[/tex].
Step-by-step explanation:
The polynomial [tex]x^{2}+11\cdot x + 30[/tex] is a polynomial of the form [tex]x^{2} - (r_{1}+r_{2})\cdot x + r_{1}\cdot r_{2} = (x-r_{1})\cdot (x-r_{2})[/tex], where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the roots of the polynomial. Then, we find the following system of equations:
[tex]-r_{1}-r_{2} = 11[/tex] (1)
[tex]r_{1}\cdot r_{2} = 30[/tex] (2)
After some algebraic handling, the solution of this system is [tex]r_{1} = -5[/tex] and [tex]r_{2} = -6[/tex].
Then, the polynomial [tex]x^{2}+11\cdot x + 30[/tex] is equal to the product of the binomials [tex](x+5)[/tex] and [tex](x+6)[/tex].
