Lessons Grade 7

Chapter 13

Chapter 13: Polynomials

13.1 Introduction to Polynomials

A polynomial is an expression made up of terms that involve only non-negative integer powers of variables. A general polynomial looks like this:

P(x)=anxn+an−1xn−1+⋯+a1x+a0P(x) = a_nx^n + a_{n-1}x^{n-1} + dots + a_1x + a_0P(x)=an​xn+an−1​xn−1+⋯+a1​x+a0​

Where an,an−1,…,a1,a0a_n, a_{n-1}, dots, a_1, a_0an​,an−1​,…,a1​,a0​ are constants, and xxx is the variable.

13.2 Operations on Polynomials

Addition and Subtraction: Combine like terms.

Multiplication: Multiply each term in the first polynomial by each term in the second polynomial.

Division: Divide the terms of the polynomial by the divisor, similar to long division.

Exercises

Exercise 1: Add or subtract the following polynomials:

(2x2+3x+4)+(x2−2x+5)(2x^2 + 3x + 4) + (x^2 - 2x + 5)(2x2+3x+4)+(x2−2x+5)

(3x3−x2+4x)−(x3+2x2−5x)(3x^3 - x^2 + 4x) - (x^3 + 2x^2 - 5x)(3x3−x2+4x)−(x3+2x2−5x)

(4x2+5x+6)+(2x2−3x+4)(4x^2 + 5x + 6) + (2x^2 - 3x + 4)(4x2+5x+6)+(2x2−3x+4)

(7x2−3x)−(5x2+4x)(7x^2 - 3x) - (5x^2 + 4x)(7x2−3x)−(5x2+4x)

(6x3−2x2+x)+(3x2−x)(6x^3 - 2x^2 + x) + (3x^2 - x)(6x3−2x2+x)+(3x2−x)

Exercise 2: Multiply the following polynomials:

(x+2)(x+3)(x + 2)(x + 3)(x+2)(x+3)

(x−1)(x+4)(x - 1)(x + 4)(x−1)(x+4)

(2x+5)(x−3)(2x + 5)(x - 3)(2x+5)(x−3)

(x+4)(x2−2x+3)(x + 4)(x^2 - 2x + 3)(x+4)(x2−2x+3)

(3x−2)(2x+1)(3x - 2)(2x + 1)(3x−2)(2x+1)