Question

complete the tasks to subtract the polynomials vertically.
(1.3t³ + 0.4t² - 24t) - (0.6t² + 8 - 18t)
what is the additive inverse of the polynomial being subtracted?
-0.6t² + (-8) + (-18t)
-0.6t² + (-8) + 18t
-0.6t² + 8 - 18t
0.6t² + (-8) + 18t
choose the correct values for a, b, c, and d that align like terms to find the sum vertically.
1.3t³ + 0.4t² + (-24t)
+ a + b + c + d
a = (-0.6t²) b = (-8) c = 18t d = 0t³
a = 0t³ b = (-0.6t²) c = 18t d = (-8)
a = 0t³ b = (-0.6t²) c = (-8) d = 18t
what is the difference of the polynomials?
0.7t³ - 0.2t² - 6t - 8
0.7t³ - t² - 6t - 8
1.3t³ - t² + 6t - 8
1.3t³ - 0.2t² - 6t - 8

Explanation:

Step1: Recall additive - inverse concept

The additive inverse of a polynomial \(a + b + c\) is \(-a - b - c\). The polynomial being subtracted is \(0.6t^{2}+8 - 18t\). Its additive inverse is \(-0.6t^{2}+(- 8)+18t\).

Step2: Align like - terms for addition

We have the first polynomial \(1.3t^{3}+0.4t^{2}-24t\). To subtract \(0.6t^{2}+8 - 18t\) (or add its additive inverse), we align like - terms. The additive inverse \(-0.6t^{2}+(-8)+18t\) can be written as \(0t^{3}-0.6t^{2}+18t - 8\). So \(A = 0t^{3}\), \(B=-0.6t^{2}\), \(C = 18t\), \(D=(-8)\).

Step3: Perform the subtraction (by addition of additive inverse)

\((1.3t^{3}+0.4t^{2}-24t)+(-0.6t^{2}-8 + 18t)=1.3t^{3}+(0.4t^{2}-0.6t^{2})+(-24t + 18t)-8=1.3t^{3}-0.2t^{2}-6t - 8\)

Answer:

The additive inverse of the polynomial being subtracted is \(-0.6t^{2}+(-8)+18t\).
\(A = 0t^{3}\), \(B=-0.6t^{2}\), \(C = 18t\), \(D=(-8)\)
The difference of the polynomials is \(1.3t^{3}-0.2t^{2}-6t - 8\)