Rewriting Quadratic Functions
Rewrite the quadratic function in standard form by completing the square: f(x) = - x^2 - 10x + 3
f(x) = -(x+5)^2 + 28
Determine which functions are polynomials, and for those that are, state their degree:
g(x) = (x + 2)^3(x - 35)^2
polynomial: degree 5
Find all the real zeros (and state their multiplicities) of each polynomial function: f(x) = 2(x - 3)(x + 4)^3
zero at 3,multiplicity of 1;zero at -4,multiplicity of 3
Express the answer in the form Q(x) = ?, r(x) = ?: (x^2 - 5x + 6) / (x-2)
Q(x) = x - 3 r(x) = 0
Divide the polynomials. Indicate the quotient Q(x) and the remainder r(x): (3x^2 + 7x + 2) / (x+2)
Q(x) = 3x + 1 r(x) = 0
Rewrite the quadratic function in standard form by completing the square: f(x) = 2x^2 + 8x - 2
f(x) = 2(x+2)^2 - 10
Determine which functions are polynomials, and for those that are, state their degree: h(x) = √x + 1
not a polynomial
Find all the real zeros (and state their multiplicities) of each polynomial function:
f(x) = 4x^2(x - 7)^2 (x + 4)
zero at 0,multiplicity of 2;zero at 7,multiplicity of 2;
zero at -4, multiplicity of 1
Express the answer in the form Q(x) = ?, r(x) = ?: (3x^2 - 9x - 5) / (x-2)
Q(x) = 3x - 3 r(x) = -11
Divide the polynomials. Indicate the quotient Q(x) and the remainder r(x): (7x^2 - 3x + 5) / (x+1)
Q(x) = 7x - 10 r(x) = 15
Rewrite the quadratic function in standard form by completing the square: f(x) = -4x^2 + 16x - 7
f(x) = - 4(x - 2)^2 + 9
Determine which functions are polynomials, and for those that are, state their degree:
F(x) = x^⅓ + 7x^2 - 2
not a polynomial
Find all the real zeros (and state their multiplicities) of each polynomial function:
f(x) = 4x^2 (x - 1)^2 (x^2 + 4)
zero at 0, multiplicity of 2; zero at , multiplicity of 2
Divide the polynomials. Express the answer in the form Q(x) = ?, r(x) = ?: (-2x^5 + 3x^4 - 2x^2) / (x^3 - 3x^2 + 1)
Q(x) = - 2x^2 - 3x - 9 r(x) = -27x^2 + 3x +9
Divide the polynomials. Indicate the quotient Q(x) and the remainder r(x): (x^4 + 1) / (x+1)
Q(x) = -x^3 + 3x - 2 r(x) = 0