Express the sum of the polynomial 5x^2+6x-17 and the square of the binomial (x+6) as a polynomial in standard form.

6x^2 + 18x + 19

Step-by-step explanation:

The standard form of a polynomial depends on the degree of the polynomial. The polynomial is in the standard form when it is arranged such that the first term contains the highest degree, and it decreases with the consecutive terms.

The square of the binomial is (x+6) ^2

(x+6) ^2 = (x+6) (x+6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36

The sum of the two polynomials will be 5x^2+6x-17 + x^2 + 12x + 36

Collecting like terms,

5x^2 + x^2 + 6x + 12x + 36 - 17

= 6x^2 + 18x + 19

6x^2 + 18x + 19.

Step-by-step explanation:

5x^2 + 6x - 17 + (x + 6) ^2

= 5x^2 + 6x - 17 + x^2 + 12x + 36

= 6x^2 + 18x + 19.