Answer: [tex]2x^{2} + 5x -3[/tex]
Step-by-step explanation:
Find the quotient of [tex]\frac{16x^4+40x^3-24x^2}{8x^2}[/tex]
Step 1: Break down the polynomial equation
[tex]\frac{16x^4}{8x^2}[/tex] + [tex]\frac{40x^3}{8x^2}[/tex] - [tex]\frac{24x^2}{8x^2}[/tex]
Step 2: Divide each piece by dividing the coeffients and subtracting the variables.
16 ÷ 8 = 2
[tex]x^{4}[/tex] - [tex]x^{2}[/tex] = [tex]x^{2}[/tex] → 2[tex]x^{2}[/tex]
40 ÷ 8 = 5
[tex]x^{3}[/tex] - [tex]x^{2}[/tex] = [tex]x[/tex] → 5[tex]x[/tex]
- 24 ÷ 8 = - 3
[tex]x^{2}[/tex] - [tex]x^{2}[/tex] = 1 → - 3
Step 3: Put the polynomial together
2[tex]x^{2}[/tex] + 5[tex]x[/tex] - 3
