Apolynomial ppp has zeros when x=-2x=−2x, equals,

Ответ:

natalie2sheffield

09.01.2022

Polynomial equation is, p=(x+2)(3x-1)(x-3)=3x^3-4x^2-17x+6

Step-by-step explanation:

Given:

The zeros of the polynomial, , are $x=-2,\frac{1}{3}, 3$ .

Therefore,

$x= -2\\(x+2)=0$

So, (x+2) is a factor of the polynomial.

$x=\frac{1}{3}\\3x=1\\3x-1=0$

So, (3x-1) is a factor of the polynomial.

$x=3\\x-3=0$

So, (x-3) is also a factor of the polynomial.

Therefore, a polynomial can be expressed in terms of the product of its factors.

Thus, p=(x+2)(3x-1)(x-3)

Expanding $(x+2)\textrm{ and }(3x-1)$ , we get

(x+2)(3x-1)=3x^2-x+6x-2=3x^2+5x-2

Now, expanding $(3x^2+5x-2)\textrm{ and }(x-3)$ , we get

(3x^2+5x-2)(x-3)=3x^3-9x^2+5x^2-15x-2x+6=3x^3-4x^2-17x+2

Therefore, the polynomial could be p=(x+2)(3x-1)(x-3)=3x^3-4x^2-17x+6

0,0(0 оценок)