Remainder | MCQs

Explanation

When 16025 ÷ 1000, the quotient is 16 and the remainder is 25.

Because 1000 × 16 = 16000, and 16025 − 16000 = 25.

Explanation

There are 14 numbers between 1 and 100 that are divisible by 7.

Numbers between 1 and 100 divisible by 7:

7×1=7

7×2=14

7×3=21

7×4=28

7×5=35

7×6=42

7×7=49

7×8=56

7×9=63

7×10=70

7×11=77

7×12=84

7×13=91

7×14=98

Explanation

The value that should be added to the polynomial to make it perfectly divisible by x + 1 is 0.

Explanation

To find the remainder, we can use the Remainder Theorem, which states that the remainder of a polynomial f(x) divided by x - a is f(a). In this case, we need to divide by x + 2, so we'll use x = -2.

f(x) = 2x⁴ - 3x² + 5x - 7

f(-2) = 2(-2)⁴ - 3(-2)² + 5(-2) - 7

= 2(16) - 3(4) - 10 - 7

= 32 - 12 - 10 - 7

= 32 - 29

= 3

Explanation

To find the remainder when 2x² + 1 is divided by x - 1:

Use the Remainder Theorem:

Remainder = f(a), where a is the root of the divisor (x - 1 = 0)

a = 1

Substitute a into the polynomial:

Remainder = f(1)

= 2(1)² + 1

= 2 + 1

= 3

Explanation

When a quadratic polynomial (degree 2) is divided by a linear factor (degree 1), the quotient will have a degree one less than the original polynomial.

That means the result will be a linear polynomial (degree 1).

Explanation