Answer
(a) $450,000$
(b) $480,000$
(c) $30(-x^2+6x+7)$
Work Step by Step
$-30x^2+180x+210$
$x$ represents the years since 2003
(a) Let $x=2$ because 2005 is 2 years since 2003 and evaluate: $-30x^2+180x+210$
$-30(2)^2+180(2)+210$
$=-30(4)+360+210$
$=-120+570$
$=450$
This answer is in thousands of visitors so the approximate number of visitors to the White House in 2005 is $450,000$.
(b) To find the approximate number of visitors to the White House in 2006, set $x=3$ because 2006 is 3 years since 2003 and evaluate $-30x^2+180x+210$
$-30(3)^2+180(3)+210$
$=-30(9)+540+210$
$=-270+750$
$=480$
Once again, the answer above is in thousands of visitors so the correct answer is $480,000$ visitors to the White House in 2006.
(c) The greatest common factor, or GCF, in $-30x^2+180x+210$ is $30$:
$30\bullet-x^2+30\bullet6x+30\bullet7$
$=30(-x^2+6x+7)$
