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Mathematics Warm Ups:
Solving Polynomial Expressions

1. Solve the following: (x3 + 2x2 - 5x + 7) + (4x3 - 5x2 + 3).

Answer:
= x3 + 4x3 + 2x2 - 5x2 - 5x + 7 + 3
= (1 + 4)x3 + (2 - 5)x2 - 5x + 10
= 5x3 - 3x2 - 5x + 10


2. Solve the following: (5x3 + 3x2 - 3) - (x3 - 4x2 - 6x + 5)

Answer:
= 5x3 + 3x2 - 3 - x3 + 4x2 + 6x - 5
= 5x3 - x3 + 3x2 + 4x2 + 6x - 3 - 5
= (5 - 1)x3 + (3 + 4)x2 + 6x - 8
= 4x3 + 7x2 + 6x - 8


3. Solve the following: (4x - 5)(2x2 - 5x + 9)

Answer:
= 4x(2x2 - 5x + 9) - 5(2x2 - 5x + 9)
= 8x3 - 20x2 + 36x - 10x2 + 25x - 45
= 8x3 + (-20 - 10)x2 + (36 + 25)x - 45
= 8x3 -30x2 + 61x - 45


4. Solve the following: (x2 - 4x + 2)(4x3 + 3x + 2)

Answer:
= x2(4x3 + 3x + 2) - 4x(4x3 + 3x + 2) + 2(4x3 + 3x + 2)
= 4x5 + 3x3 + 2x2 - 16x4 - 12x2 - 8x + 8x3 + 6x + 4
= 4x5 - 16x4 + (3 + 8)x3 + (2 - 12)x2 + (-8 + 6)x + 4
=4x5 - 16x4 + 11x3 - 10x2 - 2x + 4


5. Solve the following: (x2 + xy + y2)(x - y)

Answer:
= x(x2 + xy + y2) - y(x2 + xy + y2)
= x3 + x2y + xy2 - x2y - xy2 - y3
= x3 - y3



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