Maths — Pure 2

If we divide by $x-1$ , the remainder is?

Review question2.1.2

If we divide by $x-1$ , the remainder is?

Question

When $1 + 3x + 5x^2 + 7x^3 + \dots + 99x^{49}$ is divided by $x-1$ the remainder is

$2000$ ,

$2500$ ,

$3000$ ,

$3500$ .

Solution

The remainder theorem tells us that when a polynomial $p(x)$ is divided by $x-1$ then the remainder is $p(1)$ , which in this case is $1 + 3 + 5 + 7 + \dots + 99.$ This is an arithmetic progression, and so sums to $\frac{1}{2}\times 50(1+99) = 2500$ and the answer is (b).

If we divide by

x-1

, the remainder is?

Question

When

1 + 3x + 5x^2 + 7x^3 + \dots + 99x^{49}

is divided by

x-1

the remainder is

2000

2500

3000

3500

Solution

The remainder theorem tells us that when a polynomial

p(x)

is divided by

x-1

then the remainder is

p(1)

, which in this case is

1 + 3 + 5 + 7 + \dots + 99.

This is an arithmetic progression, and so sums to

\frac{1}{2}\times 50(1+99) = 2500

and the answer is (b).

If we divide by x−1x-1x−1, the remainder is?

Question

Solution

If we divide by x−1x-1x−1, the remainder is?

Question

Solution

If we divide by $x-1$ , the remainder is?

If we divide by $x-1$ , the remainder is?