Question

Use the Remainder Theorem to find the remainder for (x^4+x^2+2) divide by (x-3) a. 8 c. 63 b. 92 d. 0

Answer 1

Answer:92

Explanation:

f(3)=3^4+3^2+2=81+9+2=90+2=92

Answer 2

Remainder Theoram:

The Remainder Theorem states that

⇛ If a polynomial f(x) is divided by a linear divisor (x – a), the remainder is f(a)

`\Large{ \boxed{ \bf{ \color{green}{Solution:}}}}`

Given,

• p(x) = x^4 + x^2 + 2
• g(x) = x - 3

We don't need to divide by (x−3) ...

☃️Just calculate p(3):

Then, Using remainder theoram,

➝ (3)^4 + (3)^2 + 2

➝ 81 + 9 + 2

➝ 92

☘️ So, The remainder is 92

Option B

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