Polynomials and Polynomial Equations

Which of the following is a polynomial?

• $4x^5-3x^4+2x^3-x^2+\ x\ +\ 2x^{\frac{1}{2}}+\ 6$

• $6x^3+2x^2+\ 5\ +\ 3x^{-2}$

• $\frac{2}{3}x^5-x^{2\ }+\ 2\sqrt{2}$

• $5x^7+3x^6-4\sqrt{x}-\ 7$

If the side of a square is (3x + 4y - z) cm, what is its area?

• $\left(9x^{2\ }+\ 16y^2+\ z^2\right)cm^2$

• $\left(9x^2+\ 16y^2+\ z^{2\ }+6x\ +\ 8y\ -\ 2z\right)\ cm^2$

• $\left(9x^2+\ 16y^2-z^2+24xy\ -\ 8yz\ -\ 6xz\right)cm^2$

• $\left(9x^2+16y^2+z^2+\ 24xy\ -\ 8yz-6xz\right)cm^2$

If the sum of (3x⁵ - 6x² + 8x + 5) and (3x⁴ + 7x³ - 7x² - 9x + 12) is subtracted from (3x⁵ + 8x⁴ - 8x + 15), the difference is...

• $5x^4+7x^{3\ }-\ 13x^{2\ }-\ 9x\ +\ 32$

• $5x^4+\ 7x^{3\ }-\ 13x^{2\ }-\ 7x\ -\ 2$

• $5x^4-7x^3+13x^2-7x\ -\ 2$

• $5x^4-\ 7x^{3\ }+\ 13x^{2\ }-\ 9x\ +\ 32$

What expression must be subtracted from 3x⁴ - 2x³ + 6x² + 8x - 5 to get x⁴ + 6x³ - x² + 16x - 12?

• $2x^{4\ }-\ 6x^{3\ }+\ 10x^{2\ }+\ 8x\ -\ 7$

• $2x^{4\ }-\ 8x^{3\ }+\ 7x^{2\ }-\ 8x\ +\ 7$

• $2x^{4\ }+\ 6x^{3\ }+\ 13x^{2\ }+\ 16x\ -\ 12$

• $2x^{4\ }+\ 6x^{3\ }-\ x^{2\ }+\ 16x\ -\ 12$

Find the surface area of a box whose side is (x + y + 7) cm.

• $\left(6x^{2\ }+\ 6y^2+\ 294\right)cm^2$

• $\left(6x^{2\ }+\ 6y^{2\ }+\ 6xy\ +\ 42x\ +\ 42\ y\ +\ 294\right)cm^2$

• $\left(6x^{2\ }+\ 6y^2+12xy\ +\ 84\ x\ +\ 84\ y\ +\ 294\right)cm^2$

• $\left(x^{2\ }+\ y^2+\ 2xy\ +\ 14x\ +\ 14y\ +\ 49\right)cm^2$

Find the product: (m + n - 9)(m + n + 9)

• $m^2+n^2-81$

• $m^2+2mn+n^{2\ }-\ 81$

• $m^2+n^2-18mn\ -\ 81$

• $m^2+\ n^2+18mn\ -\ 81$

Solve for x:  $x^3+6x^2-13x\ -\ 42=0$ 

•  $-7,\ 3,\ 2$  

•  $7,-3,\ 2$  

•  $7,\ 3,\ -2$  

•  $-\ 7,\ \ 3,\ -2$  

Determine the degree of the polynomial x⁵ - 2x⁴ - 7x³ + 6.

• $3$

• $4$

• $5$

• $6$

The length of a rectangle is (x⁴ + 3X³ - 7X² + 12X - 10) cm and its width is (x³ - 3x² + 15) cm. Find the perimeter of the rectangle.

• $\left(x^4\ +\ 8x^{3\ }-23x^{2\ }+\ 24x\ +\ 10\right)cm$

• $\left(x^4+8x^3-23x^2+24x\ -10\right)cm$

• $\left(2x^4+8x^{3\ }-23x^2+24x\ +\ 10\right)cm$

• $\left(2x^4+8x^3-23x^2+24x-10\right)cm$

Determine the difference of (8x³ - 3x² + 4x - 5) and (5x³ + 2x² - 6x + 7).

• $3x^3+x^2\ -10x\ -\ 2$

• $3x^3+x^2\ +10x\ +\ 2$

• $3x^3-5x^2\ +10x\ -12$

• $3x^3+5x^2\ +10x\ +12$