DaddyKadyn
Answered

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What is the missing polynomial?

[tex]\( ? - (20 - 4x - 5x^2) = 20 - 7x^2 \)[/tex]

A. [tex]\( 4x - 12x^2 \)[/tex]
B. [tex]\( 4x - 2x^2 \)[/tex]
C. [tex]\( 40 - 4x - 12x^2 \)[/tex]
D. [tex]\( 40 - 4x - 2x^2 \)[/tex]

Sagot :

GinnyAnswer
To determine the missing polynomial, let’s solve the given equation step-by-step:

We start with the equation:
[tex]\[ ? - (20 - 4x - 5x^2) = 20 - 7x^2 \][/tex]

Let's first simplify the left-hand side (LHS) of the equation by distributing the negative sign within the parentheses.
[tex]\[ ? - 20 + 4x + 5x^2 = 20 - 7x^2 \][/tex]

To isolate the missing polynomial (denoted as "?"), we need to move the constant term and the polynomial terms from the LHS to the right-hand side (RHS).

To do this, add 20, subtract 4x, and subtract 5x^2 from both sides:

[tex]\[ ? = 20 - 7x^2 + 20 - 4x - 5x^2 \][/tex]

Combine the like terms on the RHS:

1. Combine the constant terms:
[tex]\[ 20 + 20 = 40 \][/tex]

2. Combine the [tex]\(x\)[/tex] terms:
[tex]\[ 0x - 4x = -4x \][/tex]

3. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ -7x^2 - 5x^2 = -12x^2 \][/tex]

So, the resulting polynomial on the right-hand side is:
[tex]\[ 40 - 4x - 12x^2 \][/tex]

Therefore, the missing polynomial is:
[tex]\[ 40 - 4x - 12x^2 \][/tex]

This matches one of the provided answer choices: [tex]\( \boxed{40 - 4x - 12x^2} \)[/tex].
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