Polynomial Functions and Theorems

The graph of every polynomial function of degree n has at most n-1 turning points.

<p>If f(x) is a polynomial of degree n where n&gt;0, then the equation f(x) = 0 has at least one solution in the set of complex numbers.</p> Signup and view all the answers

<p>If f(x) is a polynomial of degree n where n&gt;0, then the equation f(x)=0 has exactly n solutions, counting multiplicities.</p> Signup and view all the answers

<p>If f is a polynomial function with real coefficients, and a + bi is an imaginary zero of f, then a - bi is also a zero of f.</p> Signup and view all the answers

<p>If a + √b is a zero of f, then a - √b is also a zero of f.</p> Signup and view all the answers

<p>The number of positive real zeros of f equals the number of changes in sign of the coefficients of f(x) or is less by an even number.</p> Signup and view all the answers

<p>A solution.</p> Signup and view all the answers

<p>If f(x)=anx^n +...+ a, with integer coefficients, then every rational zero of f takes the form p/q = factor of constant term a / factor of leading coefficient an.</p> Signup and view all the answers

<p>±5, 7/2, 1.75.</p> Signup and view all the answers

<p>Non-imaginary (no i).</p> Signup and view all the answers

<p>A polynomial f(x) has a factor x - k if and only if f(k) = 0.</p> Signup and view all the answers

<p>If a polynomial f(x) is divided by x - k, then the remainder is r = f(k).</p> Signup and view all the answers

<p>A method of dividing polynomials, where the divisor is of the form (x - c).</p> Signup and view all the answers

<p>One method of dividing polynomials.</p> Signup and view all the answers

<p>For some polynomials, you can factor by grouping pairs of terms that have a common monomial factor.</p> Signup and view all the answers

<ol> <li>Find the cube root of first term (=a), 2. Find the cube root of the second term (=b), 3. Plug into S.O.A.P.</li> </ol> Signup and view all the answers

<ol> <li>Standard form? 2. Reduce? 3. Factor first term. 4. Check your signs. 5. Factor last term. 6. Check!</li> </ol> Signup and view all the answers

<p>a^3 - b^3 = (a - b)(a^2 + ab + b^2).</p> Signup and view all the answers

<p>a^3 + b^3 = (a + b)(a^2 - ab + b^2).</p> Signup and view all the answers

<p>A factorable polynomial with integer coefficients is factored completely if it is written as a product of unfactorable polynomials with integer coefficients.</p> Signup and view all the answers

<p>8x^2 + 20x = 4x(2x + 5).</p> Signup and view all the answers

<p>9x^2 - 1 = (3x + 1)(3x - 1).</p> Signup and view all the answers

<p>x^2 + 8x + 16 = (x + 4)^2.</p> Signup and view all the answers

<p>2x^2 - 3x - 20 = (2x + 5)(x - 4).</p> Signup and view all the answers

<p>Type: Quadratic, Standard Form: f(x) = ax^2 + bx + c.</p> Signup and view all the answers

<p>Type: Linear.</p> Signup and view all the answers