Question

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

Explanation:

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

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

Step2: Distribute the coefficients

Distribute 3 into \( 3x + 5 \): \( 3\times3x + 3\times5 = 9x + 15 \).
Distribute 2 into \( x^2 + 5x - 6 \): \( 2\times x^2 + 2\times5x - 2\times6 = 2x^2 + 10x - 12 \).

Step3: Combine like terms

Now combine the two results: \( (9x + 15) + (2x^2 + 10x - 12) \).
Combine the x terms: \( 9x + 10x = 19x \).
Combine the constant terms: \( 15 - 12 = 3 \).
So the expression becomes \( 2x^2 + 19x + 3 \).

Answer:

B. \( 2x^2 + 19x + 3 \)