1.3 Polynomien jakoalgoritmi
https://peda.net/id/3bd617665d3
2020-03-03T12:39:17+02:00
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141
https://peda.net/id/8974eb8e5d4
2020-03-05T19:12:38+02:00
a)<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0A%263x%5E2%2B3x%2B1%5C%5C%0A%5Chline%0Ax%2B5%263x%5E3%2B18x%5E2%2B16x%2B5%5C%5C%0A%263x%5E3%2B15x%5E2%5C%5C%0A%26---------%5C%5C%0A%263x%5E2%2B16x%2B5%5C%5C%0A%263x%5E2%2B15x%5C%5C%0A%26---------%5C%5C%0A%26x%2B5%5C%5C%0A%26x%2B5%5C%5C%0A%26---------%5C%5C%0A%260%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} &3x^2+3x+1\\ \hline x+5&3x^3+18x^2+16x+5\\ &3x^3+15x^2\\ &---------\\ &3x^2+16x+5\\ &3x^2+15x\\ &---------\\ &x+5\\ &x+5\\ &---------\\ &0 \end{array}"/><br/>
b)<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0A%26x%5E2-2x-7%5C%5C%0A%5Chline%0Ax-2%26x%5E3-3x-2%5C%5C%0A%26x%5E3-2x%5E2%5C%5C%0A%26------%5C%5C%0A%26-2x%5E2-3x-2%5C%5C%0A%26-2x%5E2-4x%5C%5C%0A%26------%5C%5C%0A%26-7x-2%5C%5C%0A%26-7x-2%5C%5C%0A%26------%5C%5C%0A%260%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} &x^2-2x-7\\ \hline x-2&x^3-3x-2\\ &x^3-2x^2\\ &------\\ &-2x^2-3x-2\\ &-2x^2-4x\\ &------\\ &-7x-2\\ &-7x-2\\ &------\\ &0 \end{array}"/><br/>
c)<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0A%26x%5E2-%5Cfrac%7B7%7D%7B3%7Dx%2B%5Cfrac%7B10%7D%7B9%7D%5C%5C%0A%5Chline%0A3x%5E2-2x%263x%5E4-5x%5E3%2B8x%5E2-4x%2B2%5C%5C%0A%263x%5E4-2x%5E3%5C%5C%0A%26------%5C%5C%0A%26-7x%5E3%2B8x%5E2%5C%5C%0A%26-7x%5E3%2B%5Cfrac%7B14%7D%7B3%7Dx%5E2%5C%5C%0A%26------%5C%5C%0A%26%5Cfrac%7B10%7D%7B3%7Dx%5E2-4x%2B2%5C%5C%0A%26%5Cfrac%7B10%7D%7B3%7Dx%5E2-%5Cfrac%7B20%7D%7B9%7Dx%5C%5C%0A%26------%5C%5C%0A%26%5Cfrac%7B16%7D%7B9%7Dx%2B2%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} &x^2-\frac{7}{3}x+\frac{10}{9}\\ \hline 3x^2-2x&3x^4-5x^3+8x^2-4x+2\\ &3x^4-2x^3\\ &------\\ &-7x^3+8x^2\\ &-7x^3+\frac{14}{3}x^2\\ &------\\ &\frac{10}{3}x^2-4x+2\\ &\frac{10}{3}x^2-\frac{20}{9}x\\ &------\\ &\frac{16}{9}x+2 \end{array}"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-%5Cfrac%7B7%7D%7B3%7Dx%2B%5Cfrac%7B10%7D%7B9%7D%7B%2C%7D%5C%20j%C3%A4%C3%A4%5C%20%5Cfrac%7B16%7D%7B9%7Dx%2B2" alt="x^2-\frac{7}{3}x+\frac{10}{9}{,}\ jää\ \frac{16}{9}x+2"/>
2020-03-03T14:14:31+02:00