Question

2. Find the remainder when x3 – ax2 + 6x – a is divided by x — a.
3. Check whether 7 + 3x is a factor of 3xcube + 7x.​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Hey buddy , here's your answer-

2.By remainder theorem,

when a polynomial p(x) is divided by another linear polynomial, the remainder is the root of the divisor put in in place of x I. e., let y be the root of the divisor then, p(y) will be the remainder.

Here, in the divisor (x-a), a is the root.

Remainder =p(a)=(a) ^3-a(a)^2+6(a)-a=a^3-a^3+6a-a=5a

The remainder is 5a.

3.A polynomial is a factor of the other when the remainder on division is 0.

To find the root of the divisor, we have to equate it with 0 I. e.,

7+3x=0

3x=-7

x=-7/3

By remainder theorem,

p(-7/3)=3(-7/3)^3+7(-7/3)

p(-7/3)=3(-343/27)-49/3

p(-7/3)=(-343/9)-49/3=(-343-98)/9

p(-7/3)=(-441)/9

For (7+3x) to be a factor of 3x^3+7x,

p(-7/3) should have been 0.

But, -441/9 is not 0.

Therefore, 3x+7 is not a factor of 3x^3+7x.

Hope it helps.