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Factor trinomial, or state that the trinomial is prime. 2x2 + 3xy + y2

Factor trinomial, or state that the trinomial is prime. 2x2 + 3xy + y2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question

Factor trinomial, or state that the trinomial is prime.

2x2 + 3xy + y2

Expert Solution
Step 1

Consider the given polynomial,

2x2 + 3xy + y2

The given is of the form ax2 + bxy + cy2, where a = 2, b = 3, c = 1

To find a factor of a given trinomial use ac-method.

So find two numbers whose sum is b and the product is a*c. 

That finds two numbers whose sum is 3 and the product is 2* 1 = 2.

The two numbers whose sum is 3 and product is 2 are 1 and 2 since 1+ 2 = 3 and 1*2 = 2. 

Write the middle term of trinomial 3xy in terms of these two numbers.

That is, 3xy = 2xy + 1xy

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