Question

Find all the zeroes of the polynomial x 3 + 4x 2 + x − 6 if one of its zeroes is -3.

Answer 1

Answer:

-2 , 1

Step-by-step explanation:

Given:

- 3 is the zero of above mentioned polynomial.

To find:

All zeroes

Solution:

Just Factories the question and you will get the answer.

So simple..... (^_^)

${x}^{3} + 4 {x}^{2} + x - 6 \\ \\ {x}^{3} + 3 {x}^{2} + {x}^{2} + 3x - 2x - 6 \\ \\ {x}^{2} (x + 3) + x(x + 3) - 2(x + 3) \\ \\ (x + 3)( {x}^{2}+x-2) \\ \\ (x + 3)( {x}^{2} + 2x - x - 2) \\ \\ (x + 3) \{ x(x + 2) - 1( x+ 2)\} \\ \\(x + 3)(x + 2)(x - 1)$

Therefore, The required zeros are -2 and 1 .

Zero Of A Polynomial

As we know a polynomial is consist of a variables with natural power and constant. Zero of polynomial means the specific value of variable be which the polynomial can become a zero.

i.e x + 1 , The zero of polynomial is - 1. Zero of polynomial is depend on degree of polynomial.

Answer 2

Step-by-step explanation:

Since x=-3 is a zero, (x+3) will be a factor

${x}^{3} + 4 {x}^{2} + x - 6 = 0 \\ {x}^{3} + 3 {x}^{2} + {x}^{2} +3 x - 2x - 6 = 0 \\ {x}^{2} (x + 3) + x(x + 3) - 2(x + 3) = 0 \\ (x + 3)( {x}^{2} + x - 2) = 0 \\ (x + 3)(x + 2)(x - 1) = 0 \\ x = - 3 \\ x = - 2 \\ x = 1$