To write 11x2+17x-10 in factored form, Diego first listed pairs of factors of - 10. ( _+5) ( _+-2) ( _+2) ( _+-5) ( _+10) ( _+-1) ( _+1) ( _+-10) Use what Diego started to complete the rewriting. Only one of the factored forms needs to be used and completed.

The factored form of the polynomial is 11 * (x+2) * (x-5/11). The root found was r = - 2

Step-by-step explanation:

If you take a positive value of x, you will most likely obtain positive results, since 11x² + 17x ≥ 11 + 17 = 28 for x ≥1, which means that 11x²+17x-10 ≥ 28-10 = 18 > 0.

Therefore, we prove with negative values.

x = - 1: 11 * (-1) ²+17 * (-1) - 10 = - 16 x = - 2: 11 * (-2) ² + 17 * (-2) - 10 = 44-34-10 = 0

Therefore, - 2 is a root. We can find the other knowing that

p (x) = 11 * (x-r₁) * (x-r₂) = 11 * (x - (-2)) * (x-r₂) = 11 * (x+2) * (x-r₂)

The independent term is 11*2 * (-r₂) = - 22r₂ = - 10

thus, r₂ = - 10/-22 = 5/11.

Therefore, p (x) = 11 * (x+2) * (x-5/11)