Question

Q1 What is the difference?
3x12-6x12

Answer 1

Q2 Write the polynomial in standard form. Then name the polynomial based on its degrees and number of terms.
4x3+2x2+1-3x

Standard Form:
Name based on degree:
Name based on number of terms:

Answer 2

Q3 Add the following polynomials
(3c2+6c+3)+(4c2-5c+1)

Answer 3

Q4 Simplify.
(7x11x)-(2x30)

Answer 4

Q5 Simplify the product using the distributive property
(3x-5)(5x+4)

Answer 5

Q6 If r=2x+5 Find the value of S, given the equation S=4r2

Answer 6

The difference between 3x12 and 6x12 is 36.

Answer 7

Standard Form: 4x^3 + 2x^2 - 3x + 1

Name based on degree: This polynomial is a cubic polynomial because the highest degree term is 4x^3.

Name based on number of terms: This polynomial is a quadrinomial because it has four terms.

Answer 8

To add the polynomials (3c^2 + 6c + 3) and (4c^2 - 5c + 1), we combine like terms:

(3c^2 + 4c^2) + (6c - 5c) + (3 + 1)
= 7c^2 + 1c + 4

So, the sum of the two polynomials is 7c^2 + c + 4.

Answer 9

To simplify (7x^11)-(2x^30), we multiply the coefficients and subtract the exponents of x:

7x^11 - 2x^30

Thus, the simplified form of the expression is 7x^11 - 2x^30.

Answer 10

To simplify the product (3x-5)(5x+4) using the distributive property, we multiply each term in the first polynomial by each term in the second polynomial:

(3x-5)(5x+4)
= 3x(5x) + 3x(4) - 5(5x) - 5(4)
= 15x^2 + 12x - 25x - 20
= 15x^2 - 13x - 20

Thus, the simplified form of the product is 15x^2 - 13x - 20.

Answer 11

To find the value of S, given the equation S = 4r^2 and r = 2x + 5, we substitute the value of r into the equation:

S = 4(2x + 5)^2

To simplify, we start by squaring the expression (2x + 5):

S = 4(4x^2 + 20x + 25)

Next, we distribute the 4 to each term inside the parentheses:

S = 16x^2 + 80x + 100

Thus, the value of S, given the equation S = 4r^2 and r = 2x + 5, is 16x^2 + 80x + 100.