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Let [tex]M(x) = 4x^2 - 3x[/tex] and [tex]N(x) = -5x^3 - 6x^2 - 3[/tex]. Find [tex]M(x) + N(x)[/tex].

A. [tex]-10x^8 - 3[/tex]
B. [tex]-5x^3 - 2x^2 - 3x - 3[/tex]
C. [tex]-x^3 - 9x^2 - 3[/tex]
D. [tex]-x^5 - 9x^3 - 3[/tex]

Sagot :

GinnyAnsweridn
Let's solve the problem step-by-step.

Given:
[tex]\[ M(x) = 4x^2 - 3x \][/tex]
[tex]\[ N(x) = -5x^3 - 6x^2 - 3 \][/tex]

We need to find \( M(x) + N(x) \).

1. Identify the terms in \( M(x) \):
- \( 4x^2 \) (a term with \( x^2 \))
- \( -3x \) (a term with \( x \))

2. Identify the terms in \( N(x) \):
- \( -5x^3 \) (a term with \( x^3 \))
- \( -6x^2 \) (a term with \( x^2 \))
- \( -3 \) (a constant term)

3. Combine like terms:
- There are no \( x^3 \) terms in \( M(x) \), so the \( x^3 \) term in the sum is simply \( -5x^3 \).
- The \( x^2 \) terms are \( 4x^2 \) from \( M(x) \) and \( -6x^2 \) from \( N(x) \). Combined, they make:
[tex]\[ 4x^2 - 6x^2 = -2x^2 \][/tex]
- The \( x \) term from \( M(x) \) is \( -3x \), and there are no \( x \) terms in \( N(x) \). So the \( x \) term in the sum is \( -3x \).
- The constant term is \( -3 \) from \( N(x) \), and there are no constant terms in \( M(x) \). So the constant term in the sum is \( -3 \).

4. Combine all the terms:
- The combined expression is:
[tex]\[ -5x^3 - 2x^2 - 3x - 3 \][/tex]

Therefore, the sum \( M(x) + N(x) \) is:

[tex]\[ M(x) + N(x) = -5x^3 - 2x^2 - 3x - 3 \][/tex]

Thus, the correct answer is \( \boxed{-5x^3 - 2x^2 - 3x - 3} \).

Comparing this with the provided options, the correct choice is:
B. [tex]\( -5x^3 - 2x^2 - 3x - 3 \)[/tex]
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