The Factoring Calculator transforms complex expressions into a product of simpler factors. If (x – c) is a factor of P(x), then c is a root of the equation P(x) = 0, and conversely. Definition 2. In practice, the Factor Theorem is used when factoring polynomials "completely". About the calculator: This super useful calculator is a product of wolfram alpha, one of the leading breakthrough technology & knowledgebases to date. This smart calculator is provided by wolfram alpha. In such cases, the polynomial is said to "factor over the rationals." A root or zero is where the polynomial is equal to zero. For right triangles only, enter any two values to find the third. Factor Theorem Calculator. See the solution with steps using the Pythagorean Theorem … Enter the expression you want to factor in the editor. Solution: The zero of x + 2 is –2. Factorization Of Polynomials Using Factor Theorem Factor Theorem: If p(x) is a polynomial of degree n 1 and a is any real number, then (i) x – a is a factor of p(x), if p(a) = 0, and (ii) p(a) = 0, if x – a is a factor of p(x). There are two ways to interpret the factor theorem's definition, but both imply the same meaning. If the remainder is not equal to , it means that is not a factor for . Remainder and Factor Theorem The synthetic division template may be used to find the depressed polynomial and remainder but you may also solve using alternative methods. Factor Theorem Example Problems With Solutions Example 1: Examine whether x + 2 is a factor of x 3 + 3x 2 + 5x + 6 and of 2x + 4. When using the sythetic division template, hit ENTER after each input to move to the next logical cell. Definition 1. A polynomial f(x) has a factor x – c if and only if f(c) = 0.. This calculator solves the Pythagorean Theorem equation for sides a or b, or the hypotenuse c. The hypotenuse is the side of the triangle opposite the right angle. It can factor expressions with polynomials involving any number of vaiables as well as more complex functions. Proof: By the Remainder Theorem, p(x) = (x – a) q(x) + p(a). Wolfram alpha paved a completely new way to get knowledge and information. This precalculus video tutorial provides a basic introduction into the factor theorem and synthetic division of polynomials. Advertisement. Difference of Squares: a 2 – b 2 = (a + b) (a – b) Step 2: Find the Factors Using the Factor Theorem, Divide using synthetic division and check if the remainder is equal to . https://www.khanacademy.org/.../v/polynomial-remainder-theorem-to-test-factor To do the required verification, I need to check that, when I use synthetic division on f (x), with x = –4, I get a zero remainder: The remainder is zero, so the Factor Theorem says that: x + 4 is a factor of 5x 4 + 16x 3 – 15x 2 + 8x + 16. 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