Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To factor the trinomial \( 2x^2 + 8x + 6 \) completely, let's go through the steps:
1. Identify the coefficients:
The trinomial is in the standard form \( ax^2 + bx + c \) where \( a = 2 \), \( b = 8 \), and \( c = 6 \).
2. Look for the greatest common factor (GCF):
First, check if there is a GCF among all the terms. Here, the GCF is 2. Factor out the GCF:
[tex]\[ 2x^2 + 8x + 6 = 2(x^2 + 4x + 3) \][/tex]
3. Factor the quadratic expression inside the parentheses:
Now, focus on factoring \( x^2 + 4x + 3 \).
- Find two numbers that multiply to the constant term \( 3 \) and add up to the linear coefficient \( 4 \).
- These numbers are \( 1 \) and \( 3 \), because \( 1 \times 3 = 3 \) and \( 1 + 3 = 4 \).
4. Write the expression as a product of binomials:
Rewrite \( x^2 + 4x + 3 \) as:
[tex]\[ x^2 + 4x + 3 = (x + 1)(x + 3) \][/tex]
5. Combine with the GCF:
Now, include the GCF we factored out earlier:
[tex]\[ 2(x^2 + 4x + 3) = 2(x + 1)(x + 3) \][/tex]
Thus, the trinomial \( 2x^2 + 8x + 6 \) factors completely as:
[tex]\[ 2(x + 1)(x + 3) \][/tex]
Answer choice: [tex]\( \boxed{C} \)[/tex] [tex]\( 2(x + 3)(x + 1) \)[/tex] ───────────────────────────────────────────────────────
1. Identify the coefficients:
The trinomial is in the standard form \( ax^2 + bx + c \) where \( a = 2 \), \( b = 8 \), and \( c = 6 \).
2. Look for the greatest common factor (GCF):
First, check if there is a GCF among all the terms. Here, the GCF is 2. Factor out the GCF:
[tex]\[ 2x^2 + 8x + 6 = 2(x^2 + 4x + 3) \][/tex]
3. Factor the quadratic expression inside the parentheses:
Now, focus on factoring \( x^2 + 4x + 3 \).
- Find two numbers that multiply to the constant term \( 3 \) and add up to the linear coefficient \( 4 \).
- These numbers are \( 1 \) and \( 3 \), because \( 1 \times 3 = 3 \) and \( 1 + 3 = 4 \).
4. Write the expression as a product of binomials:
Rewrite \( x^2 + 4x + 3 \) as:
[tex]\[ x^2 + 4x + 3 = (x + 1)(x + 3) \][/tex]
5. Combine with the GCF:
Now, include the GCF we factored out earlier:
[tex]\[ 2(x^2 + 4x + 3) = 2(x + 1)(x + 3) \][/tex]
Thus, the trinomial \( 2x^2 + 8x + 6 \) factors completely as:
[tex]\[ 2(x + 1)(x + 3) \][/tex]
Answer choice: [tex]\( \boxed{C} \)[/tex] [tex]\( 2(x + 3)(x + 1) \)[/tex] ───────────────────────────────────────────────────────
The answer is C. Because you 1st need to factor out a 2 from 2x^2+8x+6.
Then you should be able to get 2(x^2+4x+3).
With (x^2+4x+3), you have to find to numbers that multiply to equal 3, and add up to equal 4x. Those numbers are 3 and 1.
The final factored form should be
2(x+3)(x+1).
Then you should be able to get 2(x^2+4x+3).
With (x^2+4x+3), you have to find to numbers that multiply to equal 3, and add up to equal 4x. Those numbers are 3 and 1.
The final factored form should be
2(x+3)(x+1).
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
