For all values of x , x 2 + 6 x − 2 = ( x + p ) 2 + q Find the value of p and the value of q .

p = 3 and q = 7

Step-by-step explanation:

Given the equation x^2 + 6 x − 2 = ( x + p )^2 + q we are to find the value of p and the value of q .

x^2 + 6 x − 2 = ( x + p )^2 + q

Using the completing the square method on x^2 + 6 x − 2

x^2 + 6 x − 2

= x^2+6x+ 9 - 2 + 9

= (x^2+3x+3x+9)+7

= x(x+3)+3(x+3) + 7

= (x+3)(x+3)+7

= (x+3)^2+7

Compare to the right hand side

(x+3)^2+7 =  ( x + p )^2 + q

p = 3 and q = 7

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source

$15 each

step-by-step explanation:

$45/3 children= $15 each