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
complete
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
done

Explanation:

First Task: Additive Inverse of the Subtracted Polynomial

To find the additive inverse of a polynomial, we change the sign of each term. The polynomial being subtracted is \(0.6t^{2}+8 - 18t\). Changing the sign of each term: the sign of \(0.6t^{2}\) becomes \(- 0.6t^{2}\), the sign of \(8\) becomes \(-8\) (or \(+(-8)\)), and the sign of \(-18t\) becomes \(+18t\). So the additive inverse is \(-0.6t^{2}+(-8)+18t\), which matches the second option (the one with the checkmark).

Second Task: Finding A, B, C, D for Vertical Addition

We are adding the polynomial \(1.3t^{3}+0.4t^{2}+(-24t)\) with the additive inverse of the subtracted polynomial (which we found as \(-0.6t^{2}-8 + 18t\) or in terms of aligning like terms: \(0t^{3}-0.6t^{2}+18t-8\)). When aligning vertically, we match the degrees of \(t\):

• For \(t^{3}\) term: The first polynomial has \(1.3t^{3}\), the second (additive inverse) has \(0t^{3}\), so \(A = 0t^{3}\).
• For \(t^{2}\) term: The first polynomial has \(0.4t^{2}\), the second has \(-0.6t^{2}\), so \(B=-0.6t^{2}\).
• For \(t\) term: The first polynomial has \(-24t\), the second has \(18t\), so \(C = 18t\).
• For the constant term: The first polynomial has no constant term (or \(0\)), the second has \(-8\), so \(D=-8\). This matches the second option for A, B, C, D: \(A = 0t^{3}\), \(B=(-0.6t^{2})\), \(C = 18t\), \(D=(-8)\).

Answer:

s:

• Additive Inverse: The correct option is the one with \(-0.6t^{2}+(-8)+18t\) (the second option in the first set of choices).
• A, B, C, D: The correct option is \(A = 0t^{3}\), \(B=(-0.6t^{2})\), \(C = 18t\), \(D=(-8)\) (the second option in the second set of choices).