Math Problem Statement

If (x-2) is one of the factors of P(x)=x^3-2x^2-x-2, find the other two factors.

Solution

Let's break down the mathematical problems based on the image you've uploaded:

Problem 23

You need to find the other two factors of the polynomial P(x)=x32x2x2P(x) = x^3 - 2x^2 - x - 2, given that (x2)(x - 2) is one of the factors.

To solve this, we can use factorization methods, such as synthetic or long division. Since we know one factor is (x2)(x - 2), we can divide the polynomial by (x2)(x - 2) to find the other factors.

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For the other problems in the image:

  1. Problem 22 involves factoring a polynomial using an identity.
  2. Problem 24 involves circle geometry, where you need to find angles using properties of cyclic quadrilaterals.
  3. Problem 25 involves a Cartesian plane and determining the type of shape formed by points.

Would you like detailed solutions for all or a specific one? Let me know how you'd like to proceed!

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Math Problem Analysis

Mathematical Concepts

Algebra
Factorization
Polynomials

Formulas

Synthetic Division
Long Division

Theorems

Factor Theorem

Suitable Grade Level

Grades 9-12

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