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Possible Rational Roots III
Problem 263: Given the polynomial list the possible rational roots. Solution: To find the possible roots of this polynomial we have to consider the possible factors of leading coefficient (call it ) and the constant coefficient (call it ). That is, the possible factors of 1 are: . The possible factors of -14…
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Possible Rational Roots II
Problem 262: Given the polynomial list the possible rational roots. Solution: First, we need to rearrange the given polynomial from highest to smallest. To find the possible roots of this polynomial we have to consider the possible factors of leading coefficient (call it ) and the constant coefficient (call it )….
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Possible Rational Roots
Problem 261: Given the polynomial list the possible rational roots. Solution: To find the possible roots of this polynomial we have to consider the possible factors of leading coefficient (call it ) and the constant coefficient (call it ). That is, the possible factors of 10 are: -10, -1, 1, 10, -2, -5,…
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Roots of a Cubic Polynomial
Problem 260: Find the other two roots of the polynomial if is a root. Solution: Since we are given one of the roots, we can use root to set up a binomial term as follow: One can now use this binomial and long division to find a quadratic polynomial which we…
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Using Long Division to Divide Polynomial
Problem 259: Compute the quotient of . Solution: Rewrite the problem as a long division problem. One can now perform the long division. The answer is given by the quotient. That is, .
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Dividing Polynomial Using Long Division
Problem 258: Let’s divide by . Solution: Write the problem as a long division problem. When doing long division, we make sure that the dividend is in descending order of degree. In this case, it is. We start the long division by dividing (the first term in the dividend) by (the first term…
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Finding the Inverse of a Function II
Problem 257: If , find the inverse function. Solution: We let . Interchange and . Solve for . The new we call it . That is,
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Finding the Inverse of a Function
Problem 256: If , find the inverse function . Solution: We will let so that Now, we switch and . Solve for . The new found we call it . Thus,
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Calculating the Difference Quotient II
Problem 255: Consider . Compute Solution: One can compute the pieces of the quotient first and then put it all together. Putting all together. Since we can’t simplify further, we leave our answer like that.
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Calculating the Difference Quotient
Problem 254: Consider . Calculate Solution: One can compute the pieces of the quotient first and then put it all together. Putting it all together we have.
One Problem at a Time
