By dividing 14528 by a certain number, rita gets 83 as quotient and 3 as remainder. what is the divisor?

3. Find the quotient and remainder using long division. x3 + 7x2 − x + 1 x + 8 quotient = ? remainder = ? 4. Simplify using long division. (Express your answer as a quotient + remainder/divisor.) f( x) = 8 x 2 − 6 x + 3 g( x) = 2 x + 1 5. Find the quotient and remainder using long division. 9x 3 + 3x 2 + 22x 3x 2 + 5 quotient remainder 6. Use the Remainder Theorem to evaluate P( c). P(x) = x 4 + 7x 3 − 6x − 12,c = −1 f(−1) = 7. Use the Remainder Theorem to evaluate P( c). P(x) = 9x 5 − 3x 4 + 4x 3 − 2x 2 + x − 6,c = −6 P(−6) = 8. Consider the following. P(x) = x 3 − 9x 2 + 27x − 27 Factor the polynomial as a product of linear factors with complex coefficients. 9. Consider the following. P(x) = x 3 + 2x 2 − 3x − 10 Factor the polynomial as a product of linear factors with complex coefficients. 10. The polynomial P( x) = 5 x 2( x − 1) 3( x + 9) has degree (?). It has zeros 0, 1, and (?). The zero 0 has multiplicity (?), and the zero 1 has multiplicity (?). (answer all (?) 12. Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.) f(x) = 6x 3 + x 2 − 41x + 30;x + 3 x = 13. Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.) f(x) = 3x 3 − 17x 2 + 30x − 16;x − 1 x = 14. Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separ...

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Division is one of the basic arithmetic operations, the others being multiplication (the inverse of division), addition, and subtraction. The arithmetic operations are ways that numbers can be combined in order to make new numbers. Division can be thought of as the number of times a given number goes into another number. For example, 2 goes into 8 4 times, so 8 divided by 4 equals 2. Division can be denoted in a few different ways. Using the example above: 8 ÷ 4 = 2 8/4 = 2 8 4 = 2 In order to more effectively discuss division, it is important to understand the different parts of a division problem. Components of division Generally, a division problem has three main parts: the dividend, divisor, and quotient. The number being divided is the dividend, the number that divides the dividend is the divisor, and the quotient is the result: One way to think of the dividend is that it is the total number of objects available. The divisor is the desired number of groups of objects, and the quotient is the number of objects within each group. Thus, assuming that there are 8 people and the intent is to divide them into 4 groups, division indicates that each group would consist of 2 people. In this case, the number of people can be divided evenly between each group, but this is not always the case. There are two ways to divide numbers when the result won't be even. One way is to divide with a remainder, meaning that the division problem is carried out such that the quotient is an inte...

Purplemath The Remainder Theorem is useful for evaluating polynomials at a given value of x, though it might not seem so, at least at first blush. This is because the tool is presented as a theorem with a proof, and you probably don't feel ready for proofs at this stage in your studies. Fortunately, you don't "have" to understand the proof of the Theorem; you just need to understand how to use the Theorem. The Remainder Theorem starts with an unnamed polynomial p( x), where " p( x)" just means "some polynomial p whose variable is x". Then the Theorem talks about dividing that polynomial by some linear factor x− a, where a is just some number. Then, as a result of the q( x), with the " q" standing for "the quotient polynomial"; and some remainder r( x), the r standing for "the remainder, after division". This remainder may be a proper variable-containing polynonial, or it may be just a number. As a concrete example of p, a, q, and r, let's look at the polynomial p( x) = x 3−7 x−6, and let's divide by the linear factor x−4 (so a=4): Advertisement Back when you were learning about long division of regular numbers, you learned that your remainder (if there was one) had to be smaller than whatever you had divided by. In polynomial terms, since we're dividing by a linear factor (that is, a factor in which the degree on x is just an understood " 1"), then the remainder must be a constant value. That is, when you divide any polynomial by the linear divisor " x− a", your remainder ...