Polynomial And Synthetic Division

1. After the dividend is divided by the divisor, the left- over part is the

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.

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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2. Divide x²+9x+14 by x+7.

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.

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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3. Which of the following is a polynomial term?

365

5x + 6874

6874

2

A polynomial contains two or more terms.

Explanation

A polynomial contains two or more terms.

4. Divide x²-9x-10 by (x+1)

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.

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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5. How would you check to make sure that your answer is correct?

The coeffiecients will all add up to be 37.

When multiplied times the divisor, the product is the original expression

There is no way to check this kind of math. (duh!)

Ask your neighbor in the seat next to you.

To check if the answer is correct, you can multiply the coefficients by the divisor and see if the product matches 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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7. After the expression 5x + 35 is divided by 5, what is the remainder?

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.

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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8. What is the Greatest Common Factor in the following expression?

32x²-80x³+16x

16x

16

8x

2

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.

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.

9. What is the remainder when dividing 2x³ – 9x² + 15 by 2x – 5?

3

2x-5

-5

-10

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.

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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