https://peda.net/id/a50bb8c85c4 2020-03-02T08:25:43+02:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/a9d5e1245d4 2020-03-03T13:18:09+02:00 A4<br/> B2<br/> C3<br/> D1 2020-03-03T13:18:09+02:00 https://peda.net/id/2f4135445d4 2020-03-03T13:14:44+02:00 a)<br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=3x%5E2-6x%2B3%3D3%5Cleft(x-1%5Cright)%5Cleft(x-1%5Cright)" alt="3x^2-6x+3=3\left(x-1\right)\left(x-1\right)"/></div> <div>b)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=2x%5E2-7x-4" alt="2x^2-7x-4"/></div> <div>lasketaan nollakohdat</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%3D4%5C%20tai%5C%20x%3D-%5Cfrac%7B1%7D%7B2%7D" alt="x=4\ tai\ x=-\frac{1}{2}"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=2%5Cleft(x-4%5Cright)%5Cleft(x%2B%5Cfrac%7B1%7D%7B2%7D%5Cright)" alt="2\left(x-4\right)\left(x+\frac{1}{2}\right)"/></div> <div>c)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%5E3-2x%5E2%2B3x" alt="x^3-2x^2+3x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cleft(x%5E2-2x%2B3%5Cright)" alt="x\left(x^2-2x+3\right)"/></div> 2020-03-03T13:14:44+02:00 https://peda.net/id/11577c105d3 2020-03-03T13:06:44+02:00 <div>a)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=P%5Cleft(x%5Cright)%3D2x%5E2%2B8x%2B8" alt="P\left(x\right)=2x^2+8x+8"/></div> <div>jaetaan tekijöihin laskemalla nollakohdat</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-2" alt="x=-2"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=2%5Cleft(x%2B2%5Cright)%5Cleft(x%2B2%5Cright)%3D%5Cleft(2x%2B4%5Cright)%5Cleft(x%2B2%5Cright)" alt="2\left(x+2\right)\left(x+2\right)=\left(2x+4\right)\left(x+2\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7BP%5Cleft(x%5Cright)%7D%7Bx%2B2%7D%3D2x%2B4" alt="\frac{P\left(x\right)}{x+2}=2x+4"/><br/> b)<br/> <div>selvitetään onko polynomi P(x) jaollinen polynomilla x+1</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=P%5Cleft(x%5Cright)%3Dx%5E2%2B2x%2B2" alt="P\left(x\right)=x^2+2x+2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=P%5Cleft(-1%5Cright)%3D2%5Cne0" alt="P\left(-1\right)=2\ne0"/></div> <div>ei ole jaollinen<br/> <br/> </div> </div> 2020-03-03T13:06:44+02:00 https://peda.net/id/aa73987a5c5 2020-03-02T09:44:36+02:00 <div>a)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=Q%5Cleft(x%5Cright)%3Dx%2B2%3Dx-%5Cleft(-2%5Cright)" alt="Q\left(x\right)=x+2=x-\left(-2\right)"/></div> <div>Q(x) on polynomin P(x) tekijä jos ja vain jos P(-2)=0</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=P%5Cleft(-2%5Cright)%3D%5Cleft(-2%5Cright)%5E3-3%5Ccdot%5Cleft(-2%5Cright)%5E2-5%5Ccdot%5Cleft(-2%5Cright)%2B15%3D5" alt="P\left(-2\right)=\left(-2\right)^3-3\cdot\left(-2\right)^2-5\cdot\left(-2\right)+15=5"/></div> <div>siis, P(x) ei ole jaollinen polynomilla Q(x)</div> <div>b)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=Q%5Cleft(x%5Cright)%3Dx-3" alt="Q\left(x\right)=x-3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=P%5Cleft(3%5Cright)%3D0" alt="P\left(3\right)=0"/></div> <div>polynomi P(x) on jaollinen Q(x)</div> 2020-03-02T09:44:36+02:00