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.