Question

question 1-11
let ( f(x) = 3x + 5 ) and ( g(x) = x^2 + 5x - 6 ). find ( 3f(x) + 2g(x)
\bigcirc x^2 + 8x - 1
\bigcirc 2x^2 + 19x + 3
\bigcirc 2x^2 + 19x + 27
\bigcirc 3x^2 + 21x - 8 )

Explanation:

Step1: Substitute f(x) and g(x)

Given \( f(x) = 3x + 5 \) and \( g(x) = x^2 + 5x - 6 \), we substitute these into \( 3f(x) + 2g(x) \).
So, \( 3f(x)=3(3x + 5) \) and \( 2g(x)=2(x^2 + 5x - 6) \).

Step2: Expand the expressions

Expand \( 3(3x + 5) \): Using the distributive property \( a(b + c)=ab+ac \), we get \( 3\times3x+3\times5 = 9x + 15 \).
Expand \( 2(x^2 + 5x - 6) \): Using the distributive property, we get \( 2\times x^2+2\times5x+2\times(-6)=2x^2 + 10x - 12 \).

Step3: Combine like terms

Now, add the two expanded expressions: \( (9x + 15)+(2x^2 + 10x - 12) \).
Combine the \( x \)-terms: \( 9x+10x = 19x \).
Combine the constant terms: \( 15 - 12 = 3 \).
The \( x^2 \)-term remains \( 2x^2 \).
So, \( 3f(x)+2g(x)=2x^2 + 19x + 3 \).

Answer:

\( 2x^2 + 19x + 3 \) (corresponding to the option "2\(x^2\) + 19\(x\) + 3")