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McGraw Hill Integrated II, 2012 View details

1. Adding and Subtracting Polynomials

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Exercise 52 Page 11

The perimeter of a triangle is the sum of the measures of its sides.

Practice makes perfect

We have been given the triangle below, for which the measures of two sides are given as polynomials.

Our mission is to write the polynomial that represents the measure of the third side. To do that, recall that we are given the perimeter of the triangle. P = 3x^2-7x+2 Since the perimeter of a triangle is the sum of the measures of its sides, we can write and simplify the following equation.

P = (2x^2 - 10x+6) + (x^2-x-4) + q(x)

AssociativePropAdd

Associative Property of Addition

P = (2x^2+x^2) + (-10x-x) + (6-4) + q(x)

AddSubTerms

Add and subtract terms

P = 3x^2 -11x + 2 + q(x)

Next, we equate the equation above with the polynomial that represents the perimeter of the triangle. After this we will solve this equation for q(x).

P = 3x^2 -11x + 2 + q(x)

Substitute

P= 3x^2-7x+2

3x^2-7x+2 = 3x^2 -11x + 2 + q(x)

▼

Solve for q(x)

SubEqn

LHS-(3x^2-11x+2)=RHS-(3x^2-11x+2)

3x^2-7x+2 - (3x^2-11x+2) = 3x^2 -11x + 2 + q(x) - (3x^2-11x+2)

Distr

Distribute -1

3x^2-7x+2 - 3x^2+11x-2 = 3x^2 -11x + 2 + q(x) - 3x^2+11x-2