Question

1 - For what value of n is 20 = n/5 + 10 ?

2 - p(x) = 2(x^2 +5x +3) - 3(x + n)
In the polynomial p(x) defined above, n is a constant. If p(x) is divisible by x, what is the value of n ?

a) -3
b) -2
c) 0
d) 2

PLEASE SHOW YOUR WORK FOR BOTH !

Answer 1

first one

20=n/5+10
minus 10 both sides
10=n/5
times 5 both sides
50=n


2.
hmm
expand
p(x)=2x^2+5x+3-3x-3n
p(x)=2x^2+2x+3-3n
it looks like the coefients of the x terms are divisble by 2
because
if we have
p(x)=2(something)
the p(x) is divisible by 2

therefor that factor is 2 or -2
find what value of n works
so
3-3n=a multipule of 2
we are given
-3,-2,0,2
try each
3-3(-3)=3+9=12, that's divisble by 2
3-3(-2)=3+6=9, that's not divisible by 2
3-3(0)=3, that's not divisble by 2
3-3(2)=3-6=3, that's not divisble by 2


the onnly one that woks is when n=-3

answer is A