What is the expression in factored form?
2x^2+16x+24
2(x^2 + 8x + 12)
2(x+2)(x+6)
Well, if we're talking about factored form, then we need to break out some "factor-ories"! Let's see if we can put on a little factoring party for your expression.
The expression 2x^2 + 16x + 24 has got some numbers and an 'x' squared, but don't you worry, I'll be your mathematical clown to help you out!
First, let's try to look for any common factors among the terms. We see that 2 can be factored out of each term, giving us 2(x^2 + 8x + 12).
Now, we'll try to factor the quadratic part inside the parentheses. We're looking for two numbers that multiply to 12 and add up to 8. What number game are we playing here? Ah yes, it's the "Split the Middle" game!
We can split 8 into 6 and 2 since 6 + 2 = 8 and 6 × 2 = 12. So our factored form becomes 2(x + 6)(x + 2).
And there you have it! The expression 2x^2 + 16x + 24 in factored form is 2(x + 6)(x + 2). Now you can throw a factoring fiesta! 🎉
To express the quadratic expression 2x^2 + 16x + 24 in factored form, you can start by factoring out the common factor, if any:
2x^2 + 16x + 24
The greatest common factor (GCF) of the coefficients is 2, so we can factor out 2:
2(x^2 + 8x + 12)
Next, we need to find two binomials whose product equals the trinomial x^2 + 8x + 12. To do this, we are looking for two numbers that add up to 8 and multiply to 12. In this case, the numbers are 6 and 2:
2(x + 6)(x + 2)
So, the expression 2x^2 + 16x + 24 in factored form is 2(x + 6)(x + 2).
To find the expression in factored form, we need to first factor out the common factor, if any, and then apply the factoring techniques.
In the given expression, 2x^2 + 16x + 24, we can see that all the terms are divisible by 2. So, we can factor out 2 from each term:
2(x^2 + 8x + 12)
Now, we need to find two numbers that multiply to give 12 (the coefficient of the constant term) and add up to give 8 (the coefficient of the x-term). The numbers that satisfy these conditions are 6 and 2.
Therefore, we can rewrite the expression as:
2(x + 6)(x + 2)
This is the factored form of the given expression, 2x^2 + 16x + 24.