Answer:
c = -9
Step-by-step explanation:
Knowing that -2 is a root, you can do the synthetic division with an unknown value for c. Then solve for the value of c that makes the remainder be zero. See the attachment for the work.
The second attachment shows that (x+2) is a factor of the resulting cubic.
Answer:
Slope (m) =
Step-by-step explanation:
X = 4 – 1 = 3
Y = 4 – 2 = 2
Equation of the line:
y = 0.66666666666667x + 1.3333333333333
or
When x=0, y = 1.3333333333333
When y=0, x = -2
Roots with imaginary parts always occur in conjugate pairs. Three of the four roots are known and they are all real, which means the fourth root must also be real.
Because we know 3 and -1 (multiplicity 2) are both roots, the last root is such that we can write
There are a few ways we can go about finding , but the easiest way would be to consider only the constant term in the expansion of the right hand side. We don't have to actually compute the expansion, because we know by properties of multiplication that the constant term will be
.
Meanwhile, on the left hand side, we see the constant term is supposed to be 9, which means we have
so the missing root is 3.
Other things we could have tried that spring to mind:
- three rounds of division, dividing the quartic polynomial by , then by
twice, and noting that the remainder upon each division should be 0
- rational root theorem