Synthetic And Long Division Test! Trivia Quiz

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1. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mn»5«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»17«/mn»«mi»x«/mi»«mo»-«/mo»«mn»12«/mn»«mo»)«/mo»«mo»§#247;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»4«/mn»«mo»)«/mo»«/math»

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Synthetic And Long Division Test! Trivia Quiz - Quiz

The 'Synthetic and Long Division Test! Trivia' assesses understanding of polynomial division techniques. It challenges misconceptions about synthetic division applicability and explores the Remainder Theorem, enhancing algebraic skills.

2. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mn»3«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»17«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»15«/mn»«mi»x«/mi»«mo»-«/mo»«mn»25«/mn»«mo»)«/mo»«mo»§#247;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»5«/mn»«mo»)«/mo»«/math»

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3. The ________________ theorem allows you to evaluate a function at a given value of x by simply using synthetic division and using the given value of x as the number used as the divisor in the synthetic division. 

Explanation

The remainder theorem allows you to evaluate a function at a given value of x by using synthetic division. In synthetic division, the given value of x is used as the divisor, and the resulting remainder is obtained. Therefore, the correct answer is "remainder."

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4. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mn»2«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»10«/mn»«mi»x«/mi»«mo»+«/mo»«mn»12«/mn»«mo»)«/mo»«mo»§#247;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«mo»)«/mo»«/math»

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5. When dividing «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mn»9«/mn»«msup»«mi»x«/mi»«mn»4«/mn»«/msup»«mo»-«/mo»«mn»625«/mn»«mo»)«/mo»«/math»  by  «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mn»3«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»25«/mn»«mo»)«/mo»«/math»  ,  the constant in the answer is _______ . 

Explanation

When dividing any number by itself, the result is always 1. In this case, when dividing -25 by -25, the constant in the answer is indeed -25.

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6. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mn»4«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»7«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»11«/mn»«mi»x«/mi»«mo»+«/mo»«mn»5«/mn»«mo»)«/mo»«mo»§#247;«/mo»«mo»(«/mo»«mn»4«/mn»«mi»x«/mi»«mo»+«/mo»«mn»5«/mn»«mo»)«/mo»«/math»

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7. Synthetic division can always be used when dividing polynomials.

Explanation

Synthetic division can only be used when dividing a polynomial by a linear factor of the form (x - a). It cannot be used for dividing polynomials by factors that are not linear. Therefore, the statement that synthetic division can always be used when dividing polynomials is false.

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8. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»§#247;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«/math»

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9. When dividing a polynomial of degree 6 by a polynomial of degree 2, the quotient will be a polynomial of degree 3.

Explanation

When dividing a polynomial of degree 6 by a polynomial of degree 2, the quotient will not always be a polynomial of degree 3. The degree of the quotient depends on the degree of the dividend and the divisor. In this case, since the dividend has a degree of 6 and the divisor has a degree of 2, the quotient can have a degree of either 4 or 5, but not 3. Therefore, the statement is false.

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10. «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»-«/mo»«mn»2«/mn»«msup»«mi»x«/mi»«mn»7«/mn»«/msup»«mo»+«/mo»«mn»12«/mn»«msup»«mi»x«/mi»«mn»6«/mn»«/msup»«mo»-«/mo»«mn»6«/mn»«msup»«mi»x«/mi»«mn»5«/mn»«/msup»«mo»+«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»6«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»3«/mn»«mi»x«/mi»«mo»)«/mo»«mo»§#247;«/mo»«mo»(«/mo»«mo»-«/mo»«mn»2«/mn»«msup»«mi»x«/mi»«mn»4«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«/math»

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The ________________ theorem allows you to evaluate a function at a...
When dividing   by    ,  the constant in the...
Synthetic division can always be used when dividing polynomials.
When dividing a polynomial of degree 6 by a polynomial...
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