Exercise \(\PageIndex{A}\) 1) If division of a polynomial by a binomial results in a remainder of zero, what can be conclude? 2) If a polynomial of degree \(n\) is divided by a
binomial of degree \(1\), what is the degree of the quotient? 1. The binomial is a factor of the polynomial. B: Perform Polynomial Long DivisionExercise \(\PageIndex{B}\) \( \bigstar \) Use long division to divide. Also specify the quotient and the remainder.
\( \bigstar \) Divide.
C: Use Long Division to Rewrite a PolynomialExercise \(\PageIndex{C}\) \( \bigstar \) Use polynomial long division to perform the indicated division. Write the polynomial dividend in the form \(p(x) = d(x)q(x) + r(x)\).
23. \(4x^2+3x-1 = (x-3)(4x+15) + 44\) 25. \(2x^3-x+1 = \left(x^2+x+1\right)(2x-2)+(-x+3)\) 27. \(5x^{4} - 3x^{3} + 2x^{2} - 1 = \left(x^{2} + 4 \right) \left(5x^{2} - 3x - 18 \right) + (12x + 71)\) 29. \(-x^{5} + 7x^{3} - x = \left(x^{3} - x^{2} + 1 \right) \left(-x^{2} - x + 6 \right) + \left(7x^{2} - 6 \right)\) 31. \(9x^{3} + 5 =(2x - 3) \left(\frac{9}{2}x^{2} + \frac{27}{4}x + \frac{81}{8} \right) + \frac{283}{8}\) 33. \(4x^2 - x - 23 = \left(x^{2} - 1 \right)(4) + (-x - 19)\) D: Perform Synthetic DivisionExercise \(\PageIndex{D}\) \( \bigstar \) Use synthetic division to divide. Also state the quotient and remainder.
\( \bigstar \)For the exercises below, use synthetic division to find the quotient.
E: Use Synthetic Division to Rewrite a PolynomialExercise \(\PageIndex{E}\) \( \bigstar \) For the exercises below, use synthetic division to determine whether the first expression is a factor of the second. If it is, write the second expression as a product of two factors.
\( \bigstar \) In the exercises below, use synthetic division to perform the indicated division. Write the polynomial in the form\(p(x) = d(x)q(x) + r(x)\).
81. \(\left(4x^4-12x^3+13x^2 -12x+9\right) = \left(x - \frac{3}{2} \right) \left(4x^3-6x^2+4x-6 \right)+0\) 83. \(\left(x^6-6x^4+12x^2-8\right) = \left(x +\sqrt{2} \right) \left(x^5-\sqrt{2} \, x^4-4x^3+4\sqrt{2} \, x^2+4x-4\sqrt{2}\right) + 0\) F: Synthetic Division with Complex NumbersExercise \(\PageIndex{F}\) \( \bigstar \) For the exercises below, use synthetic division to determine the quotient involving a complex number.
\( \bigstar \) Find the remainder.
G: Construct a polynomial from a graph and a given FactorExercise \(\PageIndex{G}\) \( \bigstar \) Use the graph of the third-degree polynomial and one factor to write the factored form of the polynomial suggested by the graph. The leading coefficient is one.
How do you divide using synthetic division?Synthetic division is another way to divide a polynomial by the binomial x - c , where c is a constant.. Step 1: Set up the synthetic division. ... . Step 2: Bring down the leading coefficient to the bottom row.. Step 3: Multiply c by the value just written on the bottom row. ... . Step 4: Add the column created in step 3.. What is division of polynomials using long division and synthetic division?Long and synthetic division are two ways to divide one polynomial (the dividend) by another. polynomial (the divisor). These methods are useful when both polynomials contain more than. one term, such as the following two-term polynomial: 2 + 3.
How do I divide polynomials?Dividing Polynomials Using Long Division. Divide the first term of the dividend (4x2) by the first term of the divisor (x), and put that as the first term in the quotient (4x).. Multiply the divisor by that answer, place the product (4x2 - 12x) below the dividend.. Subtract to create a new polynomial (7x - 21).. |
Dividing polynomials using synthetic division worksheet answers
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