MA1210 College Assignment: Factoring Polynomials And Solving Rational Expressions Week 2 Lab
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MA1210 College Assignment: Factoring Polynomials and Solving
Rational Expressions Week 2 Lab
Factorizing Polynomials and Solving Rational Expressions
Answer the following questions and show all your calculations. There are different
methods for factoring. All methods involve some sort of trial and error. That’s why it is
always important to check your answer by foiling.
1. Factor a trinomial whose leading coefficient is 1. Pick any one of the problems and
solve the trinomial. If the trinomial is prime, state this and explain why.
a. x2 + 8x + 15 = (x + 3)(x + 5)
b. x2– 4x – 5 = (x - 5)(x + 1)
c. x2– 14x + 45 = (x - 9)(x - 5)
Answer: Let's go through each trinomial and factor them one by one.
1. a. x2+8x+15x^2 + 8x + 15
We need to factor the trinomial x2+8x+15x^2 + 8x + 15.
• Step 1: The leading coefficient is 1, so the factors of 15 need to add up to 8.
• Step 2: The factors of 15 are (1, 15), (3, 5), (-1, -15), and (-3, -5).
• Step 3: The pair that adds up to 8 is 3 and 5.
Thus, the factored form of the trinomial is:
x2+8x+15=(x+3)(x+5)x^2 + 8x + 15 = (x + 3)(x + 5)
1. b. x2−4x−5x^2 - 4x - 5
Now, let's factor x2−4x−5x^2 - 4x - 5.
• Step 1: The leading coefficient is 1, so we look for factors of -5 that add up to -4.
• Step 2: The factors of -5 are (1, -5) and (-1, 5).
• Step 3: The pair that adds up to -4 is -5 and 1.
Thus, the factored form of the trinomial is:
x2−4x−5=(x−5)(x+1)x^2 - 4x - 5 = (x - 5)(x + 1)
1. c. x2−14x+45x^2 - 14x + 45
MA1210 College Assignment: Factoring Polynomials and Solving
Rational Expressions Week 2 Lab
Factorizing Polynomials and Solving Rational Expressions
Answer the following questions and show all your calculations. There are different
methods for factoring. All methods involve some sort of trial and error. That’s why it is
always important to check your answer by foiling.
1. Factor a trinomial whose leading coefficient is 1. Pick any one of the problems and
solve the trinomial. If the trinomial is prime, state this and explain why.
a. x2 + 8x + 15 = (x + 3)(x + 5)
b. x2– 4x – 5 = (x - 5)(x + 1)
c. x2– 14x + 45 = (x - 9)(x - 5)
Answer: Let's go through each trinomial and factor them one by one.
1. a. x2+8x+15x^2 + 8x + 15
We need to factor the trinomial x2+8x+15x^2 + 8x + 15.
• Step 1: The leading coefficient is 1, so the factors of 15 need to add up to 8.
• Step 2: The factors of 15 are (1, 15), (3, 5), (-1, -15), and (-3, -5).
• Step 3: The pair that adds up to 8 is 3 and 5.
Thus, the factored form of the trinomial is:
x2+8x+15=(x+3)(x+5)x^2 + 8x + 15 = (x + 3)(x + 5)
1. b. x2−4x−5x^2 - 4x - 5
Now, let's factor x2−4x−5x^2 - 4x - 5.
• Step 1: The leading coefficient is 1, so we look for factors of -5 that add up to -4.
• Step 2: The factors of -5 are (1, -5) and (-1, 5).
• Step 3: The pair that adds up to -4 is -5 and 1.
Thus, the factored form of the trinomial is:
x2−4x−5=(x−5)(x+1)x^2 - 4x - 5 = (x - 5)(x + 1)
1. c. x2−14x+45x^2 - 14x + 45
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Document Details
University
ITT Technical Institute Chantilly
Subject
Mathematics