Which of the following correctly determines the first and last terms of the expression (12x^5+4x^4+9x^3−10x^2+15)−(24x^5+9x^3−7x^2+8)

Question

GPT-4o mini · Answer

To determine the first and last terms of the expression $(12 x^{5} + 4 x^{4} + 9 x^{3} - 10 x^{2} + 15) - (24 x^{5} + 9 x^{3} - 7 x^{2} + 8)$ , we will first simplify the expression by distributing the negative sign:

$(12 x^{5} + 4 x^{4} + 9 x^{3} - 10 x^{2} + 15) - (24 x^{5} + 9 x^{3} - 7 x^{2} + 8)$ $= 12 x^{5} + 4 x^{4} + 9 x^{3} - 10 x^{2} + 15 - 24 x^{5} - 9 x^{3} + 7 x^{2} - 8$

Next, we combine like terms:

For the $x^{5}$ terms: $12 x^{5} - 24 x^{5} = - 12 x^{5}$
For the $x^{4}$ terms: $4 x^{4}$
For the $x^{3}$ terms: $9 x^{3} - 9 x^{3} = 0$
For the $x^{2}$ terms: $- 10 x^{2} + 7 x^{2} = - 3 x^{2}$
For the constant terms: $15 - 8 = 7$

Now we can write the simplified expression:

$- 12 x^{5} + 4 x^{4} - 3 x^{2} + 7$

The first term (the term with the highest degree) is $- 12 x^{5}$ , and the last term (the constant term) is $7$ .

Thus, the first term is: $- 12 x^{5}$

And the last term is: $7$