IDNLearn.com is designed to help you find reliable answers quickly and easily. Receive prompt and accurate responses to your questions from our community of knowledgeable professionals ready to assist you at any time.
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).
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Find clear and concise answers at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.