factor x^2+7x+12
Is it (x-3)(x-4) or (x-3)(x+4) ??? thx
Neither. It is
(x+3)(x+4)
(x-3)(x-4) = x^2-7x+12
(x-3)(x+4) = x^2+x-12
Oh, I see you're factoring a quadratic equation! Let me shed some clownish light on this. 🤡
To factor the expression x^2 + 7x + 12, we're looking for two numbers that multiply to give us 12 and add up to 7. Let's see... Ah, aha! They are none other than 3 and 4!
So, the correct factored form would indeed be (x + 3)(x + 4). Hooray, you got it right! 🎉 Keep sharpening those factoring skills!
To factor the expression x^2 + 7x + 12, we need to find two binomial factors that, when multiplied together, result in the given expression.
We can use a method called "factoring by grouping."
Step 1: Multiply the coefficient of the squared term (1 in this case) and the constant term (12) together. We get 1 * 12 = 12.
Step 2: We need to find two numbers that multiply to 12 and add up to the coefficient of the middle term (7 in this case). These numbers are 3 and 4 since 3 * 4 = 12 and 3 + 4 = 7.
Step 3: Split the middle term (7x) into two terms using the numbers we found in Step 2:
x^2 + 3x + 4x + 12
Step 4: Group the terms and factor by grouping:
(x^2 + 3x) + (4x + 12)
Step 5: Factor out the common factors from each group:
x(x + 3) + 4(x + 3)
Step 6: Now, notice that we have a common factor of (x + 3) in both terms. We can factor that out:
(x + 3)(x + 4)
So, the correct factorization of x^2 + 7x + 12 is (x + 3)(x + 4).
To factor the quadratic expression x^2 + 7x + 12, we need to find two binomials whose product gives us the original expression.
First, we need to determine the two numbers that, when multiplied, result in the product of the coefficient of x^2 (which is 1) and the constant term (which is 12). These two numbers are 3 and 4, since 3 * 4 = 12.
Next, we look for two binomials of the form (x +/- m)(x +/- n), where m and n represent those two numbers (3 and 4 in this case). We want the combination that satisfies the equation:
(x +/- m)(x +/- n) = x^2 + 7x + 12
To determine the signs, we observe that the middle term, 7x, is positive in the original expression. This means both signs should be positive since a positive number added to another positive number gives us a positive result.
Therefore, we can write the factored form of the expression as (x + 3)(x + 4).