Given g(x) = 5x^2 - 4x and h(x) = 3x + 9 how do you find g(h(x))?

Feb 3, 2016

This means that you must plug in h into g

Explanation:

g(h(x)) = g(3x + 9)

= $5 {\left(3 x + 9\right)}^{2} - 4 \left(3 x + 9\right)$

= $5 \left(9 {x}^{2} + 54 x + 81\right) - 12 x - 36$

= $45 {x}^{2} + 270 x + 405 - 12 x - 36$

= $45 {x}^{2} + 258 x + 369$

Hopefully this helps!

Feb 3, 2016

$g \left(h \left(x\right)\right) = 45 {x}^{2} + 258 x + 369$

Explanation:

g(x)=5x^2−4x , $h \left(x\right) = 3 x + 9$
$g \left(h \left(x\right)\right) = g \left(3 x + 9\right)$
$= 5 {\left(3 x + 9\right)}^{2} - 4 \left(3 x + 9\right)$
$= 5 \left(9 {x}^{2} + 54 x + 81\right) - 12 x - 36$
$= 45 {x}^{2} + 270 x + 405 - 12 x - 36$
$= 45 {x}^{2} + 258 x + 369$ => expanded form

$3 \left(15 {x}^{2} + 86 x + 123\right)$
$= 3 \left(15 x + 41\right) \left(x + 3\right)$=> factored form