x = -16 or x = 5
Solution:
Given polynomial:
[tex]x^{2}+11 x-80=0[/tex]
To find the roots of the polynomial.
Split the middle term 11x.
11x = 16x - 5x
[tex]x^{2}+11 x-80=0[/tex]
[tex]x^{2}+16x-5x-80=0[/tex]
[tex](x^{2}+16x)+(-5x-80)=0[/tex]
Take the x common in first 2 terms an -5 common in next 2 terms.
[tex]x(x+16)-5(x+16)=0[/tex]
Take (x + 16) common in both terms.
[tex](x+16)(x-5)=0[/tex]
x + 16 = 0 or x - 5 = 0
x = -16 or x = 5
Hence x = -16 or x = 5.
