Which of the following polynomial identities would result from dividing x3+a3 by x+a ? Enter the option number of the correct answer. Option #1: x2+a2 Option #2: x2−ax+a2 Option #3: x2+ax+a2

The correct answer is Option #2: x2−ax+a2.

Which of the following polynomial identities would result from dividing x2−a2 by x−a ? Enter the option number of the correct answer. Option #1: x2−a2=(x−a)(x+a) Option #2: x2−a2=(x−a)(x−a) Option #3: x2−a2=(x+a)(x+a)

The correct answer is Option #1: x2−a2=(x−a)(x+a).

Which of the following polynomial identities would result from dividing x2+(a+b)x+ab by x+a ? Enter the option number of the correct answer. Option #1: x2+(a+b)x+ab=(x+a)(x−b) Option #2: x2+(a+b)x+ab=(x−a)(x+b) Option #3: x2+(a+b)x+ab=(x+a)(x+b)

The correct answer is Option #3: x2+(a+b)x+ab=(x+a)(x+b).

Use the polynomial identity of the difference of two squares to write a product equal to 81−16 .

The polynomial identity of the difference of two squares states that a^2 - b^2 = (a + b)(a - b). Using this identity, we can write 81 - 16 as (9)^2 - (4)^2.

Therefore, 81 - 16 = (9 + 4)(9 - 4) = 13 * 5 = 65.

Divide the polynomial x3−a3 by x−a . Which polynomial identity does this establish?(1 point) Responses x3−a3=(x−a)(x2+ax+a2) x cubed minus a cubed equals left parenthesis x minus a right parenthesis left parenthesis x squared plus a x plus a squared right parenthesis x3−a3=(x−a)(x2+ax−a2) x cubed minus a cubed equals left parenthesis x minus a right parenthesis left parenthesis x squared plus a x minus a squared right parenthesis x3−a3=(x−a)(x2−ax−a2) x cubed minus a cubed equals left parenthesis x minus a right parenthesis left parenthesis x squared minus a x minus a squared right parenthesis x3−a3=(x−a)(x2−ax+a2)

The correct answer is: x3−a3=(x−a)(x2+ax+a2)

Use the polynomial identity x2+2ax+a2=(x+a)(x+a) to rewrite x2+4x+4 . Which polynomial does this establish?(1 point) Responses x2+4x+4=(x+2)(x+2) x squared plus 4 x plus 4 equals left parenthesis x plus 2 right parenthesis left parenthesis x plus 2 right parenthesis x2+4x+4=(x−2)(x−2) x squared plus 4 x plus 4 equals left parenthesis x minus 2 right parenthesis left parenthesis x minus 2 right parenthesis x2+4x+4=(x+4)(x+4) x squared plus 4 x plus 4 equals left parenthesis x plus 4 right parenthesis left parenthesis x plus 4 right parenthesis x2+4x+4=(x−4)(x−4)