Use the remainder theorem to determine if the given binomial is a factor of f (x).
-$$f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 28 x - 84 ; \quad x - 5 \sqrt { 7 }$$
A) No
B) Yes

Question

Quizplus · Accepted Answer

By the Remainder Theorem, f(x) is divisible by (x - 5√7) if and only if f(5√7) = 0.f(5√7) = (5√7)³ + 3(5√7)² - 28(5√7) - 84= 1225√7 + 375√7 - 140√7 - 84= 1280√7 - 84= 0Therefore, (x - 5√7) is a factor of f(x).

Use the Remainder Theorem to Determine If the Given Binomial f(x)=x3+3x2−28x−84;x−57f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 28 x - 84 ; \quad x - 5 \sqrt { 7 }f(x)=x3+3x2−28x−84;x−57​

Use the Remainder Theorem to Determine If the Given Binomial $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 28 x - 84 ; \quad x - 5 \sqrt { 7 }$