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Are you ready to test your knowledge of polynomial division? Do you know all there is to know about synthetic division? Get ready to test your knowledge!
NOTE:
You will probably want to have a piece of scrap paper and a pencil nearby to write with!
Questions and Answers
1.
Which of the following is a polynomial term?
A.
365
B.
5x + 6874
C.
6874
D.
2
Correct Answer B. 5x + 6874
Explanation A polynomial contains two or more terms.
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2.
After the dividend is divided by the divisor, the left- over part is the
Correct Answer remainder
Explanation After the dividend is divided by the divisor, the leftover part is known as the remainder. The remainder represents the amount that is left over after the division process is complete. It is the difference between the dividend and the product of the divisor and quotient. The remainder can be expressed as a whole number or a fraction, depending on the type of division being performed.
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3.
After the expression 5x + 35 is divided by 5, what is the remainder?
Correct Answer x + 7 , x+7
Explanation When the expression 5x + 35 is divided by 5, the remainder is 0. This means that the expression is divisible by 5 without any remainder. Therefore, the remainder is x + 7, which is equivalent to 0 when divided by 5.
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4.
What is the Greatest Common Factor in the following expression?
32x^{2}-80x^{3}+16x^{ }
A.
16x
B.
16
C.
8x
D.
2
Correct Answer A. 16x
Explanation The greatest common factor (GCF) is the largest number or term that divides evenly into all the terms in an expression. In this case, the GCF of 32x^2, -80x^3, and 16x is 16x. This is because 16x is a common factor of all the terms, and there is no larger factor that can divide evenly into all the terms.
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5.
Divide x^{2}-9x-10 by (x+1)
Correct Answer x-10, x - 10, x- 10 , X- 10
Explanation The given expression is x^2-9x-10 and we need to divide it by (x+1). To divide, we can use long division method. By dividing x^2-9x-10 by (x+1), we get x-10 as the quotient and the remainder is 0. Therefore, the correct answer is x-10, x - 10, x- 10 , X- 10.
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6.
What is the remainder when dividing
2x^{3} – 9x^{2} + 15 by 2x – 5?
A.
3
B.
2x-5
C.
-5
D.
-10
Correct Answer D. -10
Explanation When dividing 2x^3 - 9x^2 + 15 by 2x - 5 using long division, we get a quotient of x^2 - 2x - 3 and a remainder of -10. Therefore, the remainder when dividing the polynomial by 2x - 5 is -10.
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7.
Name two things that you have to watch out for when dividing polynomials!
8.
How would you check to make sure that your answer is correct?
A.
The coeffiecients will all add up to be 37.
B.
When multiplied times the divisor, the product is the original expression
C.
There is no way to check this kind of math. (duh!)
D.
Ask your neighbor in the seat next to you.
Correct Answer B. When multiplied times the divisor, the product is the original expression
Explanation To check if the answer is correct, you can multiply the coefficients by the divisor and see if the product matches the original expression.
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9.
Divide x^{2}+9x+14 by x+7.
Correct Answer x+2, x+ 2, x + 2
Explanation The given expression x^2 + 9x + 14 can be factored as (x + 2)(x + 7). When we divide this expression by x + 7, we are left with (x + 2) as the quotient. Therefore, the correct answer is x + 2.
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10.
Factor out x^{2} + 9x + 14 note: type in the answer with NO spaces and using ( & )
Correct Answer (x+7)(x+2), (x+2)(x+7)
Explanation The given expression, x^2 + 9x + 14, can be factored as (x+7)(x+2) or (x+2)(x+7). Both of these factorizations are equivalent and correct.
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11.
Now divide it by (x+7) Easier?
12.
CHALLENGE: Divide 3x^{3} – 5x^{2} + 10x – 3 by 3x + 1note: enter the answer with no spaces, the exponents as large numbers (ex- 3x^{3} = 3x3), and the remainder as a quantity. {ex- (-45/3x+8)}
Correct Answer x2-2x+4+(-7/3x+1)
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