Adding and Subtracting Polynomials
What is a polynomial?
It is a monomial or the sum of monomials, each called a term of the polynomial.
Find the product.
5w(-3 w^2 + 2w - 4)
-15w^3+10w^2-20w
What is the formula for the square of sum?
(a+b)^2=a^2+2ab+b^2
Factor the following expression:
27 y^2 + 18y
9y(3y + 2)
Factor the following expression
x^2 + 9x + 20.
(x+4)(x+5)
What are the three types of polynomials
Monomial: 1 term
Binomial: 2 terms
Trinomial: 3 terms
Find the product:
c^2 d^3 (5c d^7 - 3 c^3 d ^2 - 4 d^3 )
5c^3d^10-3c^5d^5-4c^2d^6
What is the formula for the square of a difference?
(a-b)^2=a^2-2ab+b^2
Factor the following expression:
-4 a^2 b - 8 ab^2 + 2ab
2ab(-2a - 4b + 1)
Factor the following expression:
x^2 - 7x - 18
(x + 2)(x - 9)
Find the degree and leading coefficient of the following polynomial:
3x^2 +4x^5-7x
Degree: 5
Leading coefficient: 4
Simplify the expression
(2a - 9) (3 a^2 + 4a - 4)
6a^3-19a^2-44a+36
What is the formula for the difference of squares?
(a+b)(a-b)=a^2-b^2
Factor the following expression:
4qr + 8r + 3q + 6.
(4r + 3)(q + 2)
Solve the following equation:
x^2 + 6x = 27
x=3 and x=-9
Find the sum:
(3y + y^3 - 5) + (4 y^2 - 4y + 2 y^3 + 8)
3 y^3 + 4 y^2 - y + 3
Solve the equation:
t(2t + 3) + 20 = 2t(t - 3)
t=-20/9
Find the product.
(3q-5r)^2
9q^2-30qr+25r^2
Factor the following expression:
2mk - 12m + 42 - 7k
(2m - 7)(k - 6)
Factor the following expression:
4 x^2 - 3x + 5
It is a prime expression, hence it is not possible to factor.
Find the difference.
(7p + 4 p^3 - 8) - (3 p^2 + 2 - 9p)
4 p^3 - 3 p^2 + 16p - 10
Solve the equation:
a(a + 3) + a(a - 6) + 35 = a(a - 5) + a(a + 7)
a=7
Find the product.
(3t + 12)(3t - 12)
9x^2-144
Solve the equation:
20 p^2 - 15p = 0
x=0 and x=3/4
Solve the equation:
2 x^2 + 9x - 18 = 0
x=-6 and x=3/2