WebStep 1: Determine the value of x for the divisor Given equation is x 3 + 3 x 2 + 3 x + 1 which is divided by x + π. Put divisor x + π = 0 ⇒ x = - π Step 2: Determine the Remainder Consider the equation x 3 + 3 x 2 + 3 x + 1 By remainder theorem, Putting x = - π ∴ Remainder is p π = π 3 + 3 π 2 + 3 π + 1 = - π 3 + 3 π 2 - 3 π + 1 WebJul 27, 2024 · Explanation: The Remainder Theorem states that: if the polynomial P (x) is divided by (x − a) the remainder is P (a) In this case we have P (x) = kx3 +3x +1 and the divisor (x + 2) ⇒ a = − 2 ∴ P ( −2) = 3 ∴ P ( −2) = k( −2)3 + 3 × −2 +1 = 3 ⇒ −8k −6 +1 = 3 −8k − 5 = 3 −8k = 8 ⇒ k = − 1 Answer link
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WebDivisibility by 2: The number should have. 0, 2, 4, 6, 0, \ 2, \ 4, \ 6, 0, 2, 4, 6, or. 8. 8 8 as the units digit. Divisibility by 3: The sum of digits of the number must be divisible by. 3. 3 3. Divisibility by 4: The number formed by the tens and … WebFeb 23, 2024 · Step-by-step explanation: The binomial x + 1 divides the polynomial ƒ (x) only if x = -1 is a root of the polynomial, i.e., f (-1) = 0. So, we must evaluate f (-1) for …
WebWe have to prove that the polynomial is divisible by x² - 3x + 2 without actual division. Given, the factor is x² - 3x + 2 On factoring x² - 3x + 2 by splitting the middle term, x² - 3x + 2 = x² - 2x - x + 2 = x (x - 2) - 1 (x - 2) = (x - 1) (x - 2) Therefore, the factors are (x - 1) and (x - 2) Let p (x) = 2x⁴ - 5x³ + 2x² - x + 2 Let q (x) = x - 1 WebMar 19, 2024 · If a polynomial is divided by (ax - b), then remainder will be after substituting the value of [ax - b = 0 ⇒ ax = b ⇒ x = (b/a)] in given polynomial. Calculation: Divisor = x 2 - 3x + 2 Now we calculate the factor of x 2 - 3x + 2 Then, x 2 - 3x + 2 = 0 ⇒ x 2 - 2x - x + 2 = 0 ⇒ x (x - 2) - 1 (x - 2) = 0 ⇒ (x - 2) (x - 1) = 0
WebDivide 3x^{3}+3x^{2}-x-1 by x+1 to get 3x^{2}-1. To factor the result, solve the equation where it equals to 0. x=\frac{0±\sqrt{0^{2}-4\times 3\left(-1\right)}}{2\times 3} WebGiven. Write you 1. Divisible by 3? 8 101 4633 2. Divisible by 3 084 5 678 7400 ...
WebA whole number is said to be divisible by 3 if the sum of all digits of that whole number is a multiple of 3 or exactly divisible by 3.. Divisibility Rule of 3 with Examples. The divisibility rule for 3 can be understood with the help of the following examples.. Example: Test the divisibility of the following numbers by 3. a.) 1377. b.) 2130. c.) 3194. Solution: a) In …
WebMay 21, 2024 · In finding the correct polynomial that is exactly divisible by (3x + 1), we need to do a trial and error. Divide each polynomial to (3x + 1) and if it gives a quotient … download film top gun 2 maverick sub indoWebApr 8, 2011 · 6. Divisible by 4, 8, 11, and 124 8 11 12200 104 121 36. Answer: 200 is divisible by 4,8 but not 11 and 12. 104 is divisible by 4,8 but not 11 and 12. 121 is … clark tait eye center michiganWebMay 17, 2024 · n^2+n = n(n+1) is not divisible by 3 => n-1 is divisible by 3 IF N is no equal to 0,1,-1 else this wont hold true, thus not sufficient. I guess you overlooked some facts, Let me try to explain them with examples, Say, n=0 then n(n+1) = 0 -> which is divisble by 3 and hence the st 1 is not valid for this example download film top gun maverick 2022WebYou can put this solution on YOUR website! Which of the following polynomials is exactly divisible by (3x + 1)? A. 6x2 + 17x + 5 C. 3x3 + 4x2 – 8x – 3 B. 9x2 + 6x + 1 D. all of the above download film top gun 2022WebQ: Which of the following polynomials is exactly divisible by (3x+1)? A. 6x2+17x+5 B. 9x2+6x+1 C.… A: We have to check which of the given polynomials is exactly divisible by 3x+1. Factor theorem states… download film top gun maverick lk21WebAssume x 2 = 3, it follows that x 3 = (3x 2 + 5) mod 7 = (3 3+5) mod 7 = 14 mod 7 = 0 options a, c are not true. x 3 = 5 x 4 = (3x 3 + 5) mod 7 = 20 mod 7 = 6 option d is not true. ... Find a recursive definition for the set of positive integers NOT divisible by 3. a. 1 S, and x S x+1 S, x+2 S. b. 1 S, and x S x+3 S. c. 1 S, 2 S, and x S x+3 S. download film top gun 2 maverickWebA polynomial is an expression that consists of a sum of monomials, like 3 x 2 + 6 x − 1 3x^2+6x-1 3 x 2 + 6 x − 1 3, x, squared, plus, 6, x, minus, 1. What we will learn in this lesson In this lesson, we will explore the relationship between factors and divisibility in … clark talking dead