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  • ...n be divided out of <math>P(x)</math> using [[Synthetic division|synthetic division]], and the roots of the resulting quotient will be the remaining roots of < ...erms of the coefficients using only addition, subtraction, multiplication, division, powers, and radicals.
    8 KB (1,427 words) - 20:37, 13 March 2022
  • ...find that <math>x=0</math> and <math>x=2</math> are both roots. Synthetic division gives
    4 KB (686 words) - 11:52, 13 June 2024
  • ...th> (the [[Rational Root Theorem]] may be used here, along with synthetic division).
    4 KB (672 words) - 09:17, 17 March 2023
  • In a similar manner, we can apply synthetic division. We are looking for <math>\frac{n^3 + 100}{n + 10} = n^2 - 10n + 100 - \fra
    2 KB (338 words) - 18:56, 15 October 2023
  • ...ind that one of the solutions is <math>r = \frac12.</math> Using synthetic division leads to the quadratic <math>4x^2 - 2x - 1 = 0.</math> This has roots <math
    4 KB (710 words) - 15:06, 2 June 2024
  • ...l root theorem, we see that <math> x=2 </math> is a root. We use synthetic division to factor the equation as: <math> (x-2)(3x^{2}+x-10). </math> The roots of
    9 KB (1,364 words) - 14:59, 21 July 2006
  • ...<math>c-bp+ap^2-p^3</math>, so we can replace it in our original synthetic division equation with <math>\frac {d}{-k}</math>.
    7 KB (1,304 words) - 08:53, 5 October 2024
  • ==Solution 4 (Synthetic Division)== Through synthetic division (ignoring the remainder as we can set <math>b</math> and <math>d</math> to
    8 KB (1,347 words) - 20:14, 9 November 2024
  • Using synthetic division, we get that the remainder is <math>\boxed{\textbf{(D)}\ 2}</math>.
    1 KB (150 words) - 21:14, 6 February 2023
  • ...math>. We can easily see that 1 is a root of this polynomial. By synthetic division, the new polynomial is <math>x^2 + x + 10</math>, which has no real roots.
    1 KB (157 words) - 17:25, 5 June 2015
  • ...th> is a root as established by triangle <math>T</math>! So, use synthetic division to obtain <math>2c^2-c-4=0</math>, upon which <math>c=\frac{1+\sqrt{33}}{4}
    5 KB (912 words) - 21:32, 7 June 2021
  • ...factoring can be done using <math>(a^3-b^3) = (a-b)(a^2+a b+b^2)</math> or synthetic divison once it is realized that <math>a = 1</math> is a root): ...learly <math>n=4m</math> for some <math>m</math>. Substitution and another division by 4 gets <math>256m^3+48m^4+3m=p</math>. Since <math>p</math> is prime and
    6 KB (1,031 words) - 22:19, 23 January 2024
  • ...p</math> is a factor of <math>100</math>. Testing the factors in synthetic division would lead <math>x = \frac{10}{3}</math>, giving us our desired answer <mat
    16 KB (2,824 words) - 22:49, 23 November 2024
  • ..., we divide <math>x^8</math> by <math>x+\frac{1}{2}</math> using synthetic division or some other method. The quotient is <math>x^7-\frac{1}{2}x^6+\frac{1}{4}x
    2 KB (330 words) - 19:34, 29 August 2024
  • ...Polynomial Remainder Theorem''' states that the remainder upon [[Synthetic division | dividing]] any [[polynomial]] <math>P(x)</math> by a linear polynomial <m By polynomial division with dividend <math>P(x)</math> and divisor <math>x-a</math>, that exist a
    3 KB (414 words) - 22:39, 1 April 2023
  • <math>x=1</math> is a root, so using synthetic division results in <math>(x-1)(x^3-2x^2+2x-1)=0.</math> <math>x=1</math> is a root, so using synthetic division results in <math>(x-1)^2(x^2-x+1)=0.</math>
    10 KB (1,578 words) - 05:18, 15 December 2024
  • ...h>3x^3-9x^2+4x-12</math>, and it can be factored (by grouping or synthetic division) into
    990 bytes (158 words) - 10:26, 30 July 2022
  • ...of <math>b^2=\frac{3a^2}{a-2}</math>, you can actually just use synthetic division and arrive at the same place ~ Anonymous
    7 KB (1,150 words) - 02:15, 1 February 2024
  • ...math>(y-1)</math> (through either long or [[synthetic division|synthetic]] division), we get a remainder <math>R_1=m+3</math>. Similarly, dividing <math>h(y)</
    1 KB (233 words) - 19:21, 18 July 2024
  • Doing Synthetic Division, we find that <math>3</math> is a root of the cubic:
    7 KB (1,111 words) - 20:00, 21 February 2024

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