Factoring
This factoring technique divides a common factor from two or more terms.
What is the Greatest Common Factor?
ab + ac = a(b + c)
This is a series of terms with integer exponents ordered by decreasing degree.
What is a Polynomial?
anxn+an-1xn-1+...+a1x1+a0
This theorem states that f(a) reveals the remainder of f(x) when divided by (x - a).
What is the Remainder Theorem?
This second-degree polynomial can be factored as:
(x - 2)(x + 2)
What is x2 - 4?
This factoring technique results in the sum and difference of square roots.
What is the Difference of Perfect Squares (DOPS)?
(a2 - b2) = (a + b)(a - b)
This form reveals the zeros of a polynomial function.
What is the Factored Form?
f(x) = (x + a)(x + b)
This theorem states that if f(a) = 0, then (x - a) is a factor of f(x).
What is the Factor Theorem?
This polynomial can be factored as:
(3x + 2)(x - 1)
What is 3x2 - x - 2?
This factoring technique for four terms includes two steps of GCF.
What is Factoring by Grouping?
x3 + x2 + x + 1
x2(x + 1) + (x + 1)
(x2 + 1)(x + 1)
This form reveals the end behavior and y-intercept of a polynomial function.
What is the Standard Form?
f(x) = ax2 + bx + c
This theorem states that the number of zeros greater than "a" is equal to the number of sign switches when f(-x) is divided by (x - a).
What is Descartes' Rule of Signs?
This second-degree polynomial has zeros at -1 and -3 and goes through the point (2,30).
What is 2(x + 1)(x + 3)?
OR
What is 2x2 + 8x + 6?
This is a second-degree polynomial.
What is a Quadratic?
f(x) = x2
This theorem states that if f(a) < 0 and f(b) > 0, then there exists a zero within the interval (a,b).
What is the Fundamental Theorem of Algebra?
This is a third-degree polynomial.
What is a Cubic?
f(x) = x3