Polynomials
100
Simplify (-5a^5x)(-9a^3x^7)
(–5a^5x)(–9a^3x^7) = (–5 ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ x )(–9 ⋅ a ⋅ a ⋅ a ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x) Definition of exponents = (–5)(–9) ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ a ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x Commutative Property = 45a^8x^8Definition of exponents
200
Multiply (3xy + 2x)(x^2 + 2xy^2)
Multiply the first terms of each bi- nomial. (F) 3xy * x^2 = 3x3y Multiply the outside terms of each bi- nomial. (O) 3xy * 2xy2 = 6x2y3 Multiply the inside terms of each bi- nomial. (I) 2x * x2 = 2x3 Multiply the last terms of each bi- nomial. (L) 2x * 2xy2 = 4x2y2 Combine like terms if you can. 3x^3y + 6x^2y3 + 2x3 + 4x2y2
300
Factor 6x^2-5x-4
Factor 6x^2-5x-4 6 *-4 +-5 ^ ^ ^ 2 3 1 * -4 1+-4 (2x+1)(3x-4)
400
Use long division to find (x^3-8x^2+4x-9)/(x-4)
Use long division to find (x^3-8x^2+4x-9)/(x-4) x^2-4x-12 X-4/x^3-8x^2+4x-9 (-)x^3-4x^2 -4x^2+4x (-) -4x^2+16x -12x-9 (-)-12x+48 -57 The quotient is x^2-4x-12, and the remainder is -57
500
Simplify 12p^3t^2r-21p^2qtr^2-9p^3tr 3p^2tr
12p^3t^2r-21p^2qtr^2-9p^3tr 12p^3t^2r -21p^2qtr^2 9p^3tr 3p^2tr = 3p^2tr - 3p^2tr - 3p^2tr = 12 21 9 3 p^3-2t^2-1r^1-1 - 3 p^2-2qt1-1r^2-1- 3p^3-2t^1-1r1-1 = 4pt-7qr-3p
M
e
n
u