Polynomials Test

Result

Polynomials Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

What is the degree of the polynomial 8a⁴ − 3a⁵+ 4a³ + 9a?

A
9

B
8

C
5

D
4

Solution

The highest power of x in a polynomial p(x) is called the degree of the polynomial p(x).

Thus, the degree of the polynomial 8a⁴ − 3a⁵+ 4a³ + 9a is 5.

The correct answer is C.
Question 2
1 / -0

If the area of a rectangle is 4x² + 8x − 5, then what is its perimeter?

A
x + 4

B
2x + 2

C
4x + 8

D
8x + 8

Solution

The area of the rectangle is given as 4x² + 8x − 5.

The expression 4x² + 8x − 5 can be factorised as:

4x² + 8x − 5 = 4x² + 10x − 2x − 5

= 2x (2x + 5) − 1 (2x + 5)

= (2x − 1) (2x + 5)

The area of a rectangle equals the product of its length and breadth.

Thus, for the given rectangle:

Length × Breadth = (2x − 1) (2x + 5)

∴ Length of the rectangle = 2x + 5

Breadth of the rectangle = 2x − 1

∴ Perimeter of the rectangle = 2 (Length + Breadth)

= 2 (2x − 1 + 2x + 5)

= 2 (4x + 4)

= 8x + 8

Thus, the perimeter of the given rectangle is 8x + 8.

The correct answer is D.