Factor theorem. Car Modification Games For Pc on this page. Use polynomial division in real-life problems, such as finding a production level that yields a certain profit in Example 5. To combine two real-life. Remainder Theorem and Factor Theorem. Or: how to avoid Polynomial Long Division when finding factors. Do you remember doing division in Arithmetic?

When we divide by a polynomial of degree 1 (such as 'x−3') the remainder will have degree 0 (in other words a constant, like '4'). And we will use that idea in the 'Remainder Theorem': The Remainder Theorem When we divide a polynomial f(x) by x-c we get: f(x) = (x−c)q(x) + r(x) But r(x) is simply the constant r (remember? When we divide by (x-c) the remainder is a constant). So we get this: f(x) = (x−c)q(x) + r Now see what happens when we have x equal to c: f(c) = (c−c)q(c) + r f(c) = (0)q(c) + r f(c) = r So we get this. Example: 2x 3−x 2−7x+2 The polynomial is degree 3, and could be difficult to solve. So let us plot it first: The curve crosses the x-axis at three points, and one of them might be at 2.

We can check easily: f(2) = 2(2) 3−(2) 2−7(2)+2 = 16−4−14+2 = 0 Yes! F(2)=0, so we have found a root and a factor. So (x−2) must be a factor of 2x 3−x 2−7x+2 How about where it crosses near −1.8?

F(−1.8) = 2(−1.8) 3−(−1.8) 2−7(−1.8)+2 = −11.664−3.24+12.6+2 = −0. Game Of Thrones Doll Maker Azalea more. 304 No, (x+1.8) is not a factor. But we could try some other values close.