All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in factored form. P(x)=x3−4x2−19x−14

Question

All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in factored form.  P(x)=x3−4x2−19x−14

Durst37 · Accepted Answer

Step 1  Given polynomial is, P(x)=x3−4x2−19x−14  In factored form, it is written as follows:  x3−4x2−19x−14=x3+x2−5x2−5x−14x−14  =x2(x+1)−5x(x+1)−14(x+1)  =(x+1)(x2−5x−14)  =(x+1)(x(x+2)-7(x+2))  =(x+1)(x+2)(x-7)  Step 2  It zeroes are find by putting it equal to zeros.  x3−4x2−19x−14=0  (x+1)(x+2)(x-7)=0  x+1=0 or x+2=0 or x-7=0  x=-1, x=-2, x=7

Ella Williams · Accepted Answer

P(x)=x3−4x2−19x−14  rational roots of the function are  x=+-{1,2,7,14}  actual roots occur at  x = -1 , -2 , 7  hence zeros are  x = -1 , -2 , 7  polynomial in factored form is  P(x) = (x+1) ( x+2) (x-7)