Algebra Answers

Use the Remainder Theorem to determine the remainder when P(x) is divided by D(x). Determine if D(x) is a factor of P(x).

1. P(x) = x³ - x² + x - 1; D(x) = x - 1
2. P(x) = 20x³ - 17x² + 6x - 26; D(x) = x + 1
3. P(x) = 2x³ - 5x + x² + 2; D(x) = x + 2
4. P(x) = 12x³ - 8x² + 4x - 3; D(x) = 2x - 1

Determine if each function is a polynomial function or not. Determine the leading term, the constant term, and the degrees of each polynomial function.

1. p(z) = z² + 3z + 2017
2. q(x) = 3x/2 + ⁴√x
3. r(x) = x(x - 1) (x -2)²
4. f(s) = 2017^-3 + 2s^-4 - 3s⁸
5. A =  πr²
6. A(e) = 6e²

True or False

Write True if the statement is true and False if the statement is false. Give reasons.

1. In the division algorithm, the degree of P(x) is greater than or equal to the degree of R(x).
2. If a is a factor of the constant term of P(x), then a is a possible rational zero of P(x).
3. Every factor of P(x) is of the form (x-c), where c is the real number.
4. The remainder when P(x) is divided by D(x) is always a real number.
5. If the number of the variations in sign in P(x) is 1, then P(x) has exactly one positive real zero.
6. The number of the possible positive and negative real zeros of P(x) is never equal.

A postage box should weigh 1.0 pound. If there is a 5% error on the weight , what is the range of acceptable weight

the length of the of a triangle are in ratios 4:5:9 the perimeter of the triangle 72 cm what are the length of the side

New cars depreciate about 12% of their value each year. Determine the original cost of the car if it depreciated $3,600 in the first year.

The number of new photos p added to the 17 old photos equals 29. Compute p.

92 divided by 7

You also discussing buy a 111 that there approximately 4 million births per year in the United States express the quantity In births per minute

2. There are ‘x’ children and ‘y’ puppies in the park. The total number of legs is 28. Express this as an equation.