Question

ろぐちゃん

至急お願いします。この問題文がよくわからないのですが合っているか教えてください🙇‍♀️

Evaluate each function at the given value using the Remainder Theorem.
9) f(a) = aª − 3a²³ -6a² + 15a at a = 3
1 - 3-6 150
3 0 -18-9
1 0 -6 -3 -9
12:-9
f(a)=4

Answer 1

✨ ベストアンサー ✨

F

A.
f(a) = a^4 - 3a^3 - 6a^2 + 15a …★

f(a) = (a - 3)Q(a) + R(a),
f(3) = 3^4 - 3×3^3 - 6×3^2 + 15×3
= 81 - 81 -54 - 45
= -9

So,
f(a) = (a -3)Q(a) - 9 …❶

Here, hyponesis is written by,
Q(a) = a^3 + sa^2 + ta + u …❷

Func.❷ is inserted to Func.❶,
f(a) = (a-3)(a^3 + sa^2 + ta + u) - 9
= a^4 +(2s - 3)a^3 + (t - 3s)a^2 + (u - 3t)a - 3u - 9 …❸

check each coefficient against Func.★,

2s - 3 = -3
t - 3s = -6
u - 3t = 15
-3u -9 = 0

These give values,
s = 0
t = - 6
u = -3

Therefore,
f(a) = (a - 3)(a^3 - 6a -3) - 9

Fin.

ろぐちゃん

I appreciate so much for your time;)))

Answer 2

F

hyponesis → hypothesis

This issue ask us about expressing the function with Remainder Theorem, so we have to answer the arranged function, not value.