(cache)Solved Question 12 Difficulty: Ill A function is defined as

This problem has been solved!

You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Question: Question 12 Difficulty: Ill A function is defined as follows: h(x)=(q2x2+2pqx+p2)2. When h(x) is divided by (x+2), the remainder is 16 . When h(x) is divided by (x−3), the remainder is 1 . The values of p and q can be written in the form p=5a and q=5b,a,b∈Z, assuming that the conditions p>2q and 3q+p>0 apply. Determine the values of a and b, writing your
Show transcribed image text
There are 2 steps to solve this one.
Solution
Answered by
Algebra expert
Chegg expert since 2020
Step 1
$Step 1 : Apply the Remainder Theorem$

The Remainder Theorem states that if a polynomial $ f(x) $ is divided by $ (x - r) $, the remai...
View the full answer
Step 2
Unlock
Answer
Unlock
Previous question Next question

Transcribed image text:

Question 12 Difficulty: Ill A function is defined as follows:

h (x) = (q^{2} x^{2} + 2 pq x + p^{2})^{2} .

When

h (x)

is divided by

(x + 2)

, the remainder is 16 . When

h (x)

is divided by

(x - 3)

, the remainder is 1 . The values of

p

and

q

can be written in the form

p = \frac{a}{5}

and

q = \frac{b}{5}, a, b \in Z

, assuming that the conditions

p > 2 q

and

3 q + p > 0

apply. Determine the values of

a

and

b

, writing your answer in the form

a, b