Polynomial Sample Question

In mathematics, a polynomial is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents. Polynomials appear in a wide variety of areas of mathematics and science. Polynomials can be written as sum of one or more terms. (Source: Wikipedia).

Examples for polynomial sample question

Find the factors values of the given polynomial quadratic function x2 - 20x + 96 = 0.

Solution:

Given polynomial function is x2 - 20x + 96 = 0.

First we find the sum of two numbers is (- 20x) and its product is 96x2.

x2 - 20x + 96 = 0

x2 - 12x - 8x + 96 = 0

Grouping the first two terms and second two terms, we get

(x2 - 12x) (- 8x + 96) = 0

Take common terms, we get

x (x - 12) - 8 (x - 12) = 0

(x - 6) (x - 12) = 0

The factors are (x - 6) and (x - 12)

Answer:

The final answer is (x - 6) and (x - 12)

Polynomial sample question 2:

Add the given two polynomial expressions (18.4x3 - 56.9x2 + 73.5x) and (4.8x4 - 3.2x3 + 25.8x2)

Solution:

The given two expressions are (18.4x3 - 56.9x2 + 73.5x) and (4.8x4 - 3.2x3 + 25.8x2)

Add the each terms of the first expression to the second expression, we get

= 18.4x3 - 56.9x2 + 73.5x + 4.8x4 - 3.2x3 + 25.8x2

= 4.8x4 + 18.4x3 - 3.2x3 - 56.9x2 + 25.8x2 + 73.5x

= 4.8x4 + 15.2x3 - 31.1x2 + 73.5x

Answer:

The final answer is 4.8x4 + 15.2x3 - 31.1x2 + 73.5x

Polynomial sample question 3:

Given polynomial equation is f (x) = x3 - x2 + 7x + 175. Find the value of f (3).

Solution:

Given polynomial function is f (x) = x3 - x2 + 7x + 175.

Substitute x = 3 in the given equation, we get

f (3) = (3)3 - (3)2 + (7 * 3) + 175

= 27 - 9 + 21 + 175

= 214

Answer:

The final answer is f (3) = 214.

I am planning to write more post on Property Number and Sample Space Example. Keep checking my blog.

Practice problems for polynomial sample question

1)Find the factors values of the given polynomial quadratic function x2 - 5x - 50 = 0.

Answer:  The final answer is x = 10, x = - 5.

2)Find the factors values of the given polynomial quadratic function x2 + 3x - 108 = 0. Answer:

The final answer is x = 9, x = - 12.

3)Find the value of f (1) for the given polynomial equation f (x) = x + 12x7   Answer:  The final answer is f (1) = 1