I have several of these problems and am having trouble getting the hang of it.
Can you help me?
Factor. If the result is the square of a binomial, write it as such. If the result is prime, so state.
Here are the first couple of problems.
1) x^2 + 7x + 12
2) x^2 - x - 12
3) x^2 - 4x - 12
With these easy ones that start with 1x^2
look at the last term
e.g for x^2 + 7x + 12
last term is 12,
can you find two factors of 12 that have a sum of the middle term, namely 7 ?
yes: 3 and 4
3x4 =12
3+4 = 7
so the factors are (x+3)(x+4)
2nd:
s^2 - x -12
can you find two factors of -12 that have a sum of -1 ?
yes! , -4 and 3
-4(3) = -12
-4 + 3 = -1
so (x-4)(x+3)
you try the last one, let me know what you got
Of course, I'd be happy to help you with factoring these problems!
To factor each expression, we'll be looking for two binomials that, when multiplied together, give us the original expression. Let's go through each problem step by step:
1) x^2 + 7x + 12:
First, we'll look for two numbers whose product is 12 and whose sum is 7. After some experimentation, we see that 3 and 4 fit the criteria. Now, we'll use these numbers to rewrite the middle term of the expression:
x^2 + 3x + 4x + 12
Next, we'll group the terms into two pairs and factor out the greatest common factor in each pair:
(x^2 + 3x) + (4x + 12)
x(x + 3) + 4(x + 3)
Finally, we'll notice that we have a common factor, which is (x + 3), in both terms:
(x + 3)(x + 4)
So, the factored form of the expression x^2 + 7x + 12 is (x + 3)(x + 4).
2) x^2 - x - 12:
Again, we'll look for two numbers whose product is -12 and whose sum is -1. In this case, the numbers are -4 and 3. We'll use these numbers to rewrite the middle term of the expression:
x^2 - 4x + 3x - 12
Next, we'll group the terms into two pairs and factor out the greatest common factor in each pair:
(x^2 - 4x) + (3x - 12)
x(x - 4) + 3(x - 4)
Now, we'll notice that we have a common factor, which is (x - 4), in both terms:
(x - 4)(x + 3)
So, the factored form of the expression x^2 - x - 12 is (x - 4)(x + 3).
3) x^2 - 4x - 12:
Once again, we'll look for two numbers whose product is -12 and whose sum is -4. The numbers that satisfy these conditions are -6 and 2. We'll use these numbers to rewrite the middle term of the expression:
x^2 - 6x + 2x - 12
Next, we'll group the terms into two pairs and factor out the greatest common factor in each pair:
(x^2 - 6x) + (2x - 12)
x(x - 6) + 2(x - 6)
Now, we'll notice that we have a common factor, which is (x - 6), in both terms:
(x - 6)(x + 2)
So, the factored form of the expression x^2 - 4x - 12 is (x - 6)(x + 2).
I hope these step-by-step explanations help you with your factoring problems! Let me know if you have any further questions.