if $m(x)=x^{2}+3$ and $n(x)=5x + 9$, which expression is equivalent to $(mn)(x)$?\n$5x^{3}+9x^{2}+15x +…

if $m(x)=x^{2}+3$ and $n(x)=5x + 9$, which expression is equivalent to $(mn)(x)$?\n$5x^{3}+9x^{2}+15x + 27$\n$25x^{2}+90x + 84$\n$x^{2}+5x + 12$\n$5x^{2}+24$

if $m(x)=x^{2}+3$ and $n(x)=5x + 9$, which expression is equivalent to $(mn)(x)$?\n$5x^{3}+9x^{2}+15x + 27$\n$25x^{2}+90x + 84$\n$x^{2}+5x + 12$\n$5x^{2}+24$

Answer

Explanation:

Step1: Recall the definition of function - product

$(mn)(x)=m(x)\times n(x)$ Since $m(x)=x^{2}+3$ and $n(x)=5x + 9$, then $(mn)(x)=(x^{2}+3)(5x + 9)$.

Step2: Use the distributive property (FOIL - like for binomials extended)

$(x^{2}+3)(5x + 9)=x^{2}(5x + 9)+3(5x + 9)$.

Step3: Distribute again

$x^{2}(5x + 9)=5x^{3}+9x^{2}$ and $3(5x + 9)=15x + 27$.

Step4: Combine like - terms

$(5x^{3}+9x^{2})+(15x + 27)=5x^{3}+9x^{2}+15x + 27$.

Answer:

A. $5x^{3}+9x^{2}+15x + 27$