Math Problem Statement

Jika P(x) = ax^3 + bx^2 + (a - 2b)x - a habis dibagi oleh x^2 + 2 dan x + b, maka nilai ab adalah...

Solution

The problem in the image reads:

"Jika P(x)=ax3+bx2+(a2b)xaP(x) = ax^3 + bx^2 + (a - 2b)x - a habis dibagi oleh x2+2x^2 + 2 dan x+bx + b, maka nilai abab adalah..."

This translates to:

"If P(x)=ax3+bx2+(a2b)xaP(x) = ax^3 + bx^2 + (a - 2b)x - a is divisible by x2+2x^2 + 2 and x+bx + b, then the value of abab is..."

We are given that P(x)P(x) is divisible by two factors x2+2x^2 + 2 and x+bx + b. Therefore, we

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Math Problem Analysis

Mathematical Concepts

Polynomial Division
Roots of Polynomials
Factor Theorem

Formulas

P(x) division by factors
Factor Theorem: If x - r is a factor of P(x), then P(r) = 0

Theorems

Factor Theorem
Remainder Theorem

Suitable Grade Level

Grade 10-12