If c(x) = 4x – 2 and d(x) = x2 + 5x, what is (c*d)(x)

Question

mathstudent55 · Answer

Multiply the functions together.

solomonzelman · Answer

$\color{#000000 }{ ^{\Large \bf For~example:}_{\Huge \color{red}{\text{____________}}}  }$$ \tiny \[0.7em]$
$\color{#000000 }{ \displaystyle h(x) =5x+6 }$
$\color{#000000 }{ \displaystyle k(x) =2x^2+3 }$

$\color{#000000 }{ \displaystyle {\rm Suppose~you~are~asked~to~find:~~}(h\times k)(x) }$
$\color{#000000 }{ \displaystyle \rm Then,~the~solution~is: }$

$\color{#000000 }{ \displaystyle (h\times k)(x) =h(x)\times k(x) }$ $\tiny \[0.5em]$
$\color{#000000 }{ \displaystyle (h\times k)(x) =(5x+6)(2x^2+3) }$ $\tiny \[0.5em]$
$\color{#000000 }{ \displaystyle (h\times k)(x) =5x(2x^2+3)+6(2x^2+3) }$ $\tiny \[0.5em]$
$\color{#000000 }{ \displaystyle (h\times k)(x) =10x^3+15x+12x^2+18\quad \quad {\rm (the~answer)}}$