Answer :
To factor the trinomial [tex]\( x^2 - 4x - 12 \)[/tex], follow these steps:
1. Identify the coefficients:
The trinomial is in the form [tex]\( ax^2 + bx + c \)[/tex], where:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = -4 \)[/tex]
- [tex]\( c = -12 \)[/tex]
2. Set up the factoring process:
We need to find two numbers that multiply to [tex]\( ac = (1)(-12) = -12 \)[/tex] and add up to [tex]\( b = -4 \)[/tex].
3. Find the pair of numbers:
Let's consider the factors of [tex]\(-12\)[/tex]:
- [tex]\( 1 \)[/tex] and [tex]\( -12 \)[/tex] (sums to [tex]\(-11\)[/tex])
- [tex]\( -1 \)[/tex] and [tex]\( 12 \)[/tex] (sums to [tex]\(11\)[/tex])
- [tex]\( 2 \)[/tex] and [tex]\( -6 \)[/tex] (sums to [tex]\(-4\)[/tex]) Hint: This pair works!
- [tex]\( -2 \)[/tex] and [tex]\( 6 \)[/tex] (sums to [tex]\(4\)[/tex])
- [tex]\( 3 \)[/tex] and [tex]\( -4 \)[/tex] (sums to [tex]\(-1\)[/tex])
- [tex]\( -3 \)[/tex] and [tex]\( 4 \)[/tex] (sums to [tex]\(1\)[/tex])
We observe that the pair [tex]\(2\)[/tex] and [tex]\(-6\)[/tex] multiply to [tex]\(-12\)[/tex] and add up to [tex]\(-4\)[/tex].
4. Rewrite the middle term:
Rewrite the trinomial by splitting the middle term using the pair found:
[tex]\[ x^2 - 4x - 12 = x^2 + 2x - 6x - 12 \][/tex]
5. Factor by grouping:
Group the terms in pairs:
[tex]\[ (x^2 + 2x) + (-6x - 12) \][/tex]
Factor out the greatest common factor from each pair:
[tex]\[ x(x + 2) - 6(x + 2) \][/tex]
6. Factor out the common binomial:
Notice that [tex]\( (x + 2) \)[/tex] is a common factor:
[tex]\[ (x - 6)(x + 2) \][/tex]
Thus, the factored form of the trinomial [tex]\( x^2 - 4x - 12 \)[/tex] is:
[tex]\[ (x - 6)(x + 2) \][/tex]
So, the correct choice is:
A. [tex]\( x^2 - 4x - 12 = (x - 6)(x + 2) \)[/tex]
1. Identify the coefficients:
The trinomial is in the form [tex]\( ax^2 + bx + c \)[/tex], where:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = -4 \)[/tex]
- [tex]\( c = -12 \)[/tex]
2. Set up the factoring process:
We need to find two numbers that multiply to [tex]\( ac = (1)(-12) = -12 \)[/tex] and add up to [tex]\( b = -4 \)[/tex].
3. Find the pair of numbers:
Let's consider the factors of [tex]\(-12\)[/tex]:
- [tex]\( 1 \)[/tex] and [tex]\( -12 \)[/tex] (sums to [tex]\(-11\)[/tex])
- [tex]\( -1 \)[/tex] and [tex]\( 12 \)[/tex] (sums to [tex]\(11\)[/tex])
- [tex]\( 2 \)[/tex] and [tex]\( -6 \)[/tex] (sums to [tex]\(-4\)[/tex]) Hint: This pair works!
- [tex]\( -2 \)[/tex] and [tex]\( 6 \)[/tex] (sums to [tex]\(4\)[/tex])
- [tex]\( 3 \)[/tex] and [tex]\( -4 \)[/tex] (sums to [tex]\(-1\)[/tex])
- [tex]\( -3 \)[/tex] and [tex]\( 4 \)[/tex] (sums to [tex]\(1\)[/tex])
We observe that the pair [tex]\(2\)[/tex] and [tex]\(-6\)[/tex] multiply to [tex]\(-12\)[/tex] and add up to [tex]\(-4\)[/tex].
4. Rewrite the middle term:
Rewrite the trinomial by splitting the middle term using the pair found:
[tex]\[ x^2 - 4x - 12 = x^2 + 2x - 6x - 12 \][/tex]
5. Factor by grouping:
Group the terms in pairs:
[tex]\[ (x^2 + 2x) + (-6x - 12) \][/tex]
Factor out the greatest common factor from each pair:
[tex]\[ x(x + 2) - 6(x + 2) \][/tex]
6. Factor out the common binomial:
Notice that [tex]\( (x + 2) \)[/tex] is a common factor:
[tex]\[ (x - 6)(x + 2) \][/tex]
Thus, the factored form of the trinomial [tex]\( x^2 - 4x - 12 \)[/tex] is:
[tex]\[ (x - 6)(x + 2) \][/tex]
So, the correct choice is:
A. [tex]\( x^2 - 4x - 12 = (x - 6)(x + 2) \)[/tex]
Answer is (x-6)(x+2)
There are many ways to factor an equation this is how I did it: I did a reverse foil method. Since x^2 is a perfect square because x • x is x^2 and 6 • 2 is 12 and when you subtract them it = 4. (I’m not great at explaining it sorry)
There are many ways to factor an equation this is how I did it: I did a reverse foil method. Since x^2 is a perfect square because x • x is x^2 and 6 • 2 is 12 and when you subtract them it = 4. (I’m not great at explaining it sorry)
