Math Problem Statement

Suku banyak berderajat 3, jika dibagi (x^2 + x - 2) bersisa (2x - 1). Jika dibagi (x^2 + x - 3) bersisa (3x - 3). Suku banyak tersebut adalah?

Solution

The problem from the image you uploaded is written in Indonesian and translates roughly to:

"A cubic polynomial, when divided by x2+x2x^2 + x - 2, gives a remainder of 2x12x - 1. When divided by x2+x3x^2 + x - 3, it gives a remainder of 3x33x - 3. What is the polynomial?"

This is a problem involving polynomial division with remainders. Here's the approach to solve it:

Let the cubic polynomial be P(x)P(x).

We know that:

  1. When divided by (x2+x2)(x^2 + x - 2), the remainder is 2x12x - 1. This means: P(x)=(x2+x2)Q1(x)+(2x1)P(x) = (x^2 + x - 2) \cdot Q_1(x) + (2x - 1) where Q1(x)Q_1(x) is the quotient when dividing P(x)P(x) by (x2+x2)(x^2 + x - 2).

  2. When

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Math Problem Analysis

Mathematical Concepts

Polynomial Division
Remainder Theorem

Formulas

P(x) = (x^2 + x - 2) * Q1(x) + (2x - 1)
P(x) = (x^2 + x - 3) * Q2(x) + (3x - 3)

Theorems

Polynomial Remainder Theorem

Suitable Grade Level

Grades 10-12