Question

factor of polynomial (8x³ + 8x - 5).​

Answer 1

Answer:

(2x+5y)(2x−5y)

Step-by-step explanation:

Explanation: 8x3+125y3 is (2x)3+(5y)3. the sum of two cubes formula a3+b3=(a+b)(a2−ab+b2). so. (2x)3+(5y)3.

Answer 2

Given:

A polynomial equation 8x³ + 8x - 5=0.

To Find:

One of the factors of the given polynomial equation.

Solution:

The given problem can be solved using the concepts of the trial and error method.

1. The given polynomial equation is 8x³ + 8x - 5=0.

2. Check the values of the equation for random values of x,

=> For x = 1, the value of the polynomial is 8 (1)³ - 8 (1) -5,

=> For x = 1, the value of the polynomial is -5 which doesnot satisfy the equation.

=> For x = -1 the value of the polynomial is   8 (-1)³ - 8 (-1) -5,

=> For x = -1 the value of the polynomial is   -5 which doesnot satisfy the equation.

=> For x = 1/2, the value is 8 (1/2)³ - 8(1/2) -5,

=> For x = 1/2, the value of the polynomial is 0 which satisifies the equation.

3. For x =1/2 the value of the polynomial is zero. Hence x = 1/2 is the factor of the given polynomial.

=> (x-1/2) is the factor of the given polynomial. (OR) (2x-1) is the factor of the given polynomial.

Therefore, the factor of the polynomial  (8x³ + 8x - 5) is (x-(1/2)) (OR) (2x-1).