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Which expression can be used to find the sum of the polynomials?

[tex]\[
\left(9-3x^2\right) + \left(-8x^2 + 4x + 5\right)
\][/tex]

A. \(\left[\left(-3x^2\right) + \left(-8x^2\right)\right] + 4x + [9 + (-5)]\)

B. \(\left[3x^2 + 8x^2\right] + 4x + [9 + (-5)]\)

C. \(\left[3x^2 + \left(-8x^2\right)\right] + 4x + [9 + 5]\)

D. [tex]\(\left[\left(-3x^2\right) + \left(-8x^2\right)\right] + 4x + [9 + 5]\)[/tex]

Sagot :

GinnyAnswer
To find the sum of the polynomials \(\left(9 - 3x^2\right) + \left(-8x^2 + 4x + 5\right)\), we need to combine like terms. Let's break this down step by step:

1. Combine the \(x^2\) terms:
[tex]\[ (-3x^2) + (-8x^2) = -11x^2 \][/tex]

2. Combine the \(x\) terms:
[tex]\[ 4x \][/tex]
(There is only one \(x\) term in the given polynomials.)

3. Combine the constant terms:
[tex]\[ 9 + 5 = 14 \][/tex]

So, the expression to find the sum of the polynomials is \(-11x^2 + 4x + 14\).

The correct intermediate steps to arrive at this result are:
[tex]\[ \left[(-3x^2) + (-8x^2)\right] + 4x + [9 + 5] \][/tex]

Thus, the correct option that represents the steps to find this sum is:
[tex]\[ \left[\left(-3 x^2\right)+\left(-8 x^2\right)\right]+4 x+[9+5] \][/tex]
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