Question

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
Answer
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)
Answer
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)
Answer
Use the polynomial identity of the difference of two squares to write a product equal to 81−16 .
Answer
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)
Answer
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)
Answer
Which of the following endpoints is best suited for using polynomial identities to convert differences of numerical squares into products?(1 point) Responses 8 and 11.5 8 and 11.5 8.4 and 11.1 8.4 and 11.1 8 and 10 8 and 10 7.2 and 10
Answer
How can 13×19 be rewritten using the difference of two squares identity?(1 point) Responses (11−3)(11+3) left parenthesis 11 minus 3 right parenthesis left parenthesis 11 plus 3 right parenthesis (13−3)(19+3) left parenthesis 13 minus 3 right parenthesis left parenthesis 19 plus 3 right parenthesis (16−3)(16+3) left parenthesis 16 minus 3 right parenthesis left parenthesis 16 plus 3 right parenthesis (10+3)(22−3) left parenthesis 10 plus 3 right parenthesis left parenthesis 22 minus 3 right parenthesis
Answer
pick an answe
Answer
Hiram has a blanket measuring 55 inches by 43 inches. Which of the following expressions can he use to find the area of the blanket?(1 point) Responses 492+62 49 squared plus 6 squared 492−62 49 squared minus 6 squared 552+432 55 squared plus 43 squared 552−432
Answered by GPT 3.5
The correct answer is Option #2: x2−ax+a2.
Answered by GPT 3.5
The correct answer is Option #1: x2−a2=(x−a)(x+a).
Answered by GPT 3.5
The correct answer is Option #3: x2+(a+b)x+ab=(x+a)(x+b).
Answered by GPT 3.5
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.
Answered by GPT 3.5
The correct answer is: x3−a3=(x−a)(x2+ax+a2)
Answered by GPT 3.5
The correct answer is: x2+4x+4=(x+2)(x+2)
Answered by GPT 3.5
The best-suited endpoints for using polynomial identities to convert differences of numerical squares into products are: 8 and 11.5.
Answered by GPT 3.5
To rewrite 13×19 using the difference of two squares identity, we need to find two numbers that can be squared to obtain these values.

In this case, 13 and 19 are not perfect squares. Therefore, we cannot rewrite 13×19 using the difference of two squares identity.
Answered by GPT 3.5
Sorry, I made a mistake in my response. My apologies for the confusion.

To rewrite 13×19 using the difference of two squares identity, we can express them as:

(16−3)(16+3) = 13×19.

Therefore, the correct answer is: (16−3)(16+3).
Answered by GPT 3.5
To find the area of the blanket, Hiram can use the expression 55 squared multiplied by 43 squared.

Therefore, the correct answer is: 55 squared plus 43 squared.