Answer :
To factor the trinomial \( x^2 + 6x + 8 \), we need to find two binomials that multiply together to give us the original trinomial.
1. We start by identifying the trinomial in the standard form \( ax^2 + bx + c \), where in this case, \( a = 1 \), \( b = 6 \), and \( c = 8 \).
2. We need to find two numbers that multiply to \( c \) (which is 8) and add up to \( b \) (which is 6).
3. Looking at the possible pairs of factors of 8, we have:
- \( 1 \times 8 = 8 \) and \( 1 + 8 = 9 \)
- \( 2 \times 4 = 8 \) and \( 2 + 4 = 6 \)
4. The pair that fits our requirement is \( 2 \) and \( 4 \), since they multiply to 8 and add to 6.
5. With these factors, we can express the trinomial as a product of two binomials:
[tex]\[ x^2 + 6x + 8 = (x + 2)(x + 4) \][/tex]
Therefore, the correct binomials that are factors of \( x^2 + 6x + 8 \) are:
[tex]\[ \boxed{x+2 \text{ and } x+4} \][/tex]
So, the choices from the given options are:
B. \( x+4 \)
D. \( x+2 \)
These are the two binomials that factor the given trinomial correctly.
1. We start by identifying the trinomial in the standard form \( ax^2 + bx + c \), where in this case, \( a = 1 \), \( b = 6 \), and \( c = 8 \).
2. We need to find two numbers that multiply to \( c \) (which is 8) and add up to \( b \) (which is 6).
3. Looking at the possible pairs of factors of 8, we have:
- \( 1 \times 8 = 8 \) and \( 1 + 8 = 9 \)
- \( 2 \times 4 = 8 \) and \( 2 + 4 = 6 \)
4. The pair that fits our requirement is \( 2 \) and \( 4 \), since they multiply to 8 and add to 6.
5. With these factors, we can express the trinomial as a product of two binomials:
[tex]\[ x^2 + 6x + 8 = (x + 2)(x + 4) \][/tex]
Therefore, the correct binomials that are factors of \( x^2 + 6x + 8 \) are:
[tex]\[ \boxed{x+2 \text{ and } x+4} \][/tex]
So, the choices from the given options are:
B. \( x+4 \)
D. \( x+2 \)
These are the two binomials that factor the given trinomial correctly.
