a:14:{i:0;a:13:{s:2:"id";s:4:"1752";s:4:"name";s:212:"<p>Wyraz wolny wielomianu <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3D(x%2B1)%5E5-(x-1)%5E5" alt="W(x)=(x+1)^5-(x-1)^5" />  jest równy:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:1;a:13:{s:2:"id";s:4:"1753";s:4:"name";s:241:"<p>Współczynnik przy x<sup>3</sup> w wielomianie <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3D(x%5E2-4x%2B2)(x-1)%5E2" alt="W(x)=(x^2-4x+2)(x-1)^2" />  jest równy:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:2;a:13:{s:2:"id";s:4:"1754";s:4:"name";s:221:"<p>Wielomian <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3D(x%2B1)%5E3-(x-1)%5E3" alt="W(x)=(x+1)^3-(x-1)^3" />  ma w postaci standardowej postać:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:3;a:13:{s:2:"id";s:4:"1755";s:4:"name";s:208:"<p>Wielomian <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3D(2-x)(x-1)(x%2B1)" alt="W(x)=(2-x)(x-1)(x+1)" />  jest równy wielomianowi:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:4;a:13:{s:2:"id";s:4:"1756";s:4:"name";s:314:"<p>Stopień wielomianu <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3D%20%5Cleft%5B%20%5C(-2x%5E5%2Bx%5E2-3x%2B1%5C)%5C(2x%5E5-x%5E2%2B3x%2B1%5C)%5Cright%5D%5E2" alt="W(x)= \left[ \(-2x^5+x^2-3x+1\)\(2x^5-x^2+3x+1\)\right]^2" />  jest równy:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:5;a:13:{s:2:"id";s:4:"1757";s:4:"name";s:380:"<p>Wartość wielomianu <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3Dax%5E4-5" alt="W(x)=ax^4-5" /> dla <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=x%3D%5Csqrt%7B5%7D" alt="x=\sqrt{5}" /> wynosi 0. Wtedy współczynnik <em>a</em> jest równy:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:6;a:13:{s:2:"id";s:4:"1758";s:4:"name";s:691:"<p>Wartość wielomianu <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3Dax%5E3-b" alt="W(x)=ax^3-b" /> dla <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=x%3D%5Csqrt%7B2%7D" alt="x=\sqrt{2}" /> wynosi 0 a dla <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=x%3D-%5Csqrt%7B2%7D" alt="x=-\sqrt{2}" /> wynosi <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=-2%5Csqrt%7B2%7D" alt="-2\sqrt{2}" />. Wtedy współczynniki <em>a, b</em> są równe:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:7;a:13:{s:2:"id";s:4:"1759";s:4:"name";s:215:"<p>Wielomian <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=x%5E3%2B3x%5E2%2B3x%2B1" alt="x^3+3x^2+3x+1" />  jest podzielny bez reszty przez dwumian:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:8;a:13:{s:2:"id";s:4:"1760";s:4:"name";s:221:"<p>Wielomian <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3Dx%5E8%2Bx%5E6-x%5E2-1" alt="W(x)=x^8+x^6-x^2-1" />  nie jest podzielny bez reszty przez:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:9;a:13:{s:2:"id";s:4:"1761";s:4:"name";s:317:"<p>Niech <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3D(x%5E2-x%2B1)(x%5E2%2B1)%2C%20%5C%20P(x)%3D(-x%5E2%2Bx-1)(x%5E2-1)" alt="W(x)=(x^2-x+1)(x^2+1), \ P(x)=(-x^2+x-1)(x^2-1)" />.  Liczba punktów wspólnych wykresów tych wielomianów wynosi:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:10;a:13:{s:2:"id";s:4:"1762";s:4:"name";s:376:"<p>Niech <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3D(x-1)%5E3" alt="W(x)=(x-1)^3" />.  Wielomian <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x%2B1)%20-%20W(x)" alt="W(x+1) - W(x)" /> ma współczynnik przy najwyższej potędze równy:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:11;a:13:{s:2:"id";s:4:"1763";s:4:"name";s:353:"<p>Niech <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3Dx%5E2%2B1%2C%5C%20P(x)%3Dx%5E2-1" alt="W(x)=x^2+1,\ P(x)=x^2-1" />.  Wielomian <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(P(x))" alt="W(P(x))" /> jest równy:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:12;a:13:{s:2:"id";s:4:"1764";s:4:"name";s:385:"<p>Reszta z dzielenia wielomianu <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3D-2x%5E5%2Bx%5E4-x%5E3%2Bx%5E2-3x-6" alt="W(x)=-2x^5+x^4-x^3+x^2-3x-6" /> przez jednomian  <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=x%2B1" alt="x+1" />  jest równa:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}i:13;a:13:{s:2:"id";s:4:"1765";s:4:"name";s:222:"<p>Rozkład wielomianu <img class="latex" src="https://chart.googleapis.com/chart?cht=tx&amp;chf=a,s,000000|bg,s,FFFFFF00&amp;chl=W(x)%3Dx%5E3%2B2x%5E2-4x-8" alt="W(x)=x^3+2x^2-4x-8" /> na czynniki liniowe ma postać:</p>";s:9:"hide_time";s:1:"0";s:11:"one_is_good";N;s:13:"feedback_good";s:0:"";s:14:"feedback_wrong";s:0:"";s:4:"help";s:0:"";s:4:"icon";s:0:"";s:5:"movie";s:0:"";s:14:"movie_duration";N;s:4:"type";s:1:"1";s:6:"active";s:1:"1";s:4:"test";s:3:"489";}}