Is x + 9 a factor of the polynomial P(x) = x^3 + 11x^2 + 15x -27? If so, write the polynomial as a product of two factors. If not, explain how you know.

The polynomial's factors are (x-1) and (x+3)

Step-by-step explanation:

If (x+9) is a factor of P(x)= x³+11x²+15x-27 then the P(x) must be completely divisible by (x+9)

After finding the polynomial, we need to factorise the polynomial by utilising the quadratic equation.

All the process has been described in image attached-

S₁, S₂, S₃ represents various steps involved in solving the problem.

It is found that (x+9) is a factor of   x³+11x²+15x-27

The polynomial found after dividing   x³+11x²+15x-27 by (x+9) is  x²+2x-3

Which can be further factorised by quadratic rule into the factors as (x-1) and (x+3)

Hence the factors are (x-1) and (x+3)

answer: ♡♡♡♡♡♡♡♡♡♡

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)