Question

UJUU J

Given p(a) = (a^4 - 6a^3 + 3a^2 + 26a – 24) = 0
a) Check by the remainder or factor theorems which of these is a factor of the polynomial
p(a): (a - 1), (a - 2) or (a + 4).
b) By the remainder theorem, state the remainder when p(a) is divided by the binomial
which are not its factors.
c) Use the factor from (a) to divide p(a) by long division.
d) Use the factor from (a) to divide p(a) by synthetic division. (your answer should
correspond with that from (c)).​

Answer 1

Plese read the complete procedure below:

Explanation:

The polynomial is p(a) = (a^4 - 6a^3 + 3a^2 + 26a – 24)

a)

1 -6 3 26 -24 | 1

1 -5 -2 24

1 -5 -2 24 0

The remainder is zero, then (a-1) is a factor of the polynomial

b)

1 -6 3 26 -24 | 2

2 -8 10 72

1 -4 5 36 48

When p(a) is divided by (a-2) the remainder 28/p(a)

1 -6 3 26 -24 | - 4

-4 40 172 -792

1 -10 43 198 -816

When p(a) is divided by (a-2) the remainder -816/p(a)

c) I attached an image of the long division below: