Problem Solving Involving Polynomials

Find the product:
(3x + 2)(2x + 4)

• 6x² + 16x + 8
• 5x² +11x + 6
• 5x² + 16x + 6
• 6x² + 11x + 8

Multiply:
(3x – 1)(x + 5) 

• 3x² + 4x + 5
• 3x² + 4x - 5
• 3x² + 14x + 5
• 3x² + 14x - 5

The side length of a square is (x - 7), which of the following below would represent the area?

• x²-49

• x²+49

• x²-14x+49

• x²-14x-49

Which of the following is equivalent to the area of a square with a length of (x + 10)?

• x² + 100

• x² + 20

• (x + 10)(x + 10)

• 2(x + 10)

A rectangle has a width of (6x + 4x⁴ - 3x²) and a of (7x⁴ + 5x² + 8x). What would the perimeter of the rectangle be?

• 22x⁴ + 4x² + 28x

• 32x⁴ + 2x² + 28x

• 22x⁴ + 2x² + 28x

• 22x⁴ + 4x² + 20x

What is the perimeter of a triangle who's side lengths are (2x - 4xy + 3y), (x + 5xy - 5y), and (7y + xy +12x)?

• 15x + 10xy + 15y

• 15x + 15y

• 15x + 2xy + 5y

• 13x - 8xy + 5y

Find the sum.

(3 - 2x + 2x²) + (4x - 5 + 3x²)

• 7x - 7x + 5x²

• 5x² + 2x - 2

• 5x²

• 5x² + 6x + 8

The perimeter of the triangle is 3x³ + 4x² + 8x + 15. If the shortest side is  2x² + 12x, the longest side (the hypotenuse) is x³ – 8x + 7, then what is the missing side length?

• 2x³ + 2x² + 4x + 8
• 4x³ + 6x² + 12x + 22
• 2x³ + 6x² + 28x + 8
• 4x³ + 2x² - 12x + 22

A = 2x² + 3x + 5
C = 3x² - 7x + 12
If A + B = C,
what must B equal?

• x² - 10x + 7
• 5x² - 4x + 17
• x² - 4x + 7
• 5x² - 10x + 17

A rectangle has a length of (15x² + 7x) and a width of (7x² + x). What is the difference between the area and perimeter of the rectangle?

• 105x⁴ + 64x³ - 37x² - 16x

• 105x² + 64x³ - 15x² - 8x

• 105x⁴ - 15x² +8x

• 105x⁴ -37x² -16x