- d.Find the x-values that make the expression
on the left side equal to zero. Begin by factor-
ing the polynomial:
x^2 – 9x+ 20 = x^2 – 5x– 4x+ 20 = (x^2 – 5x) –
(4x– 20) = x(x– 5) – 4(x– 5) = (x– 4)(x– 5)
Set each factor equal to zero, then solve for x
to find the zeros of the polynomial, which are
4 and 5. Now, assess the sign of the expression
on the left side on each subinterval formed
using these values. To this end, form a number
line, choose a real number in each subinterval,
and record the sign of the expression above
each:
The inequality does not include “equals,” so we
exclude those values from the number line that
make the polynomial equal to zero. Therefore,
the solution set is (4,5).
458. d. First, find thex-values that make the expres-
sion on the left side equal to zero. Doing so
requires that we factor the polynomial:
12 x^2 –37x– 10 = 12x^2 + 3x– 40x– 10 =
3 x(4x+ 1) – 10(4x+ 1) = (3x– 10)(4x+ 1)
Next, set each factor equal to zero and solve
for xto conclude that the zeros of the polyno-
mial are ^130 and –^14 . Now, we assess the sign of
the expression on the left side on each subin-
terval formed using these values. To this end,
we form a number line, choose a real number
in each subinterval, and record the sign of the
expression above each, as follows:
Because the inequality does not include
“equals,” we exclude those values from the
number line that make the polynomial equal
to zero. The solution set is(–^14 ,^130 ).
- d.Determine the x-values that make the
expression on the left side equal to zero. To do
this, we first factor the polynomial:
9 – 7x– 2x^2 = 9 + 2x– 9x– 2x^2 = 1(9 + 2x) –
x(9 + 2x) = (9 + 2x)(1 –x)
Next, set each factor equal to zero and solve
for xto find the zeros of the polynomial which
are –^92 and 1. Now, we assess the sign of the
expression on the left side on each subinterval
formed using these values. Form a number line,
choose a real number in each subinterval, and
record the sign of the expression above each:
The inequality does not include “equals,” so we
do not include those values from the number
line that make the polynomial equal to zero.
The solution set is (–^92 ,1).
- b.The strategy is to determine the x-values
that make the expression on the left side equal
to zero. First, factor the polynomial:
2 x^3 + 6x^2 + 4x= 2x(x^2 + 3x+ 2) =
2 x(x^2 + x+ 2x+ 2)
= 2x(x(x+ 1) + 2(x+ 1)) = 2x(x+ 2)(x+ 1)
Next, set each factor equal to zero and solve
for xto conclude that the zeros of the polyno-
mial are –2, –1, and 0. Now, we assess the sign
of the expression on the left side on each
subinterval formed using these values. To this
end, we form a number line, choose a real
1
1
4
10
3
+ – +
45
+ – +
ANSWERS & EXPLANATIONS–
