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Let [tex]$P(x)=6x[tex]$[/tex] and [tex]$[/tex]Q(x)=2x^3+3x^2+1[tex]$[/tex]. Find [tex]$[/tex]P(x)+Q(x)$[/tex].

A. [tex]$11x^6+1$[/tex]
B. [tex]$2x^3+3x^2+6x+1$[/tex]
C. [tex]$8x^4+3x^2+1$[/tex]



Answer :

GinnyAnswer
Let's find \( P(x) + Q(x) \) step-by-step given the functions \( P(x) \) and \( Q(x) \) defined as:

[tex]\[ P(x) = 6x \][/tex]
[tex]\[ Q(x) = 2x^3 + 3x^2 + 1 \][/tex]

To find \( P(x) + Q(x) \), we simply need to add these two functions together:

[tex]\[ P(x) + Q(x) = 6x + (2x^3 + 3x^2 + 1) \][/tex]

Now, let's combine like terms:

[tex]\[ P(x) + Q(x) = 2x^3 + 3x^2 + 6x + 1 \][/tex]

Our resulting expression for \( P(x) + Q(x) \) is:

[tex]\[ 2x^3 + 3x^2 + 6x + 1 \][/tex]

Next, let's compare this result with the given choices:

A. \( 11x^6 + 1 \)
B. \( 2x^3 + 3x^2 + 6x + 1 \)
C. \( 8x^4 + 3x^2 + 1 \)

Clearly, the correct answer matches choice B:

[tex]\[ 2x^3 + 3x^2 + 6x + 1 \][/tex]

Therefore, the correct choice is:

[tex]\[ \boxed{B} \][/tex]

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