Write TRUE if the statement is true. Otherwise, modify the underlined word(s) to make it true. 2. Every polynomial equation of degree n has n – 1 real roots. Polynomial Equation: "Every polynomial equation of degree n has n - 1 real roots." This statement is false and in order to make it a true statement it should be... "every polynomial equation of degree n has at most n real roots" which is a consequence of the Fundamental Theorem of Algebra. Definition: A polynomial equation is any polynomial equated to zero . Examples: x - 2 = 0 x² + 2x + 5 = 0 5x + 1 = 0 x³ - 2x² - 4x + 8 = 0 x(x - 4) = 0 Explanation: x - 2 = 0 the number of root(s) is just 1 since it is a polynomial of the first degree. x² + 2x + 5 = 0 the number of root(s) is 2 since it is a polynomial of the second degree. 5x + 1 = 0, there is only 1 root because it is a polynomial equation of the first degree. x³ - 2x² - 4x + 8 = 0 have 3 roots since its high...
Which of the following is the factored form of x^3 + 3x^2 – 10x – 24? a. (x + 4)(x – 3)(x + 2) b. (x – 4)(x – 3)(x – 2) c. (x – 4)(x – 3)(x + 2) d. (x + 4)(x + 3)(x – 2) Factoring Polynomials: Listing Method: The factored form of x³ + 3x² – 10x – 24 is (x + 4)(x – 3)(x + 2). Solution: List all the possible factors of the first term. x³ = (x)(x)(x) 2. List all the possible factors of the last term. -24 = (1)(-24); (-1)(24); (2)(-12); (-2)(12); (3)(-8); (-3)(8); (4)(-6); (-4)(6) 3. From the list above, form the factors. Make sure that the 3 factors of -24 will have a sum of -10 which is the middle term of the given polynomial. (x + 2)(x – 3)(x + 4) 4. To check multiply (x + 2)(x – 3)(x + 4). x + 2 x – 3 x² + 2x -3x – 6 x² – x – 6 x + 4 x³ – x² – 6x 4x² – 4x – 24 x³ + 3x² – 10x - 24 De...
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