Question

(5x^4-2x^3-7x^3 - 39) + (x-4) divide using polynomial long divison

(4x^4+5x-4)÷(x-2) divide using polynomial long division

please help ​

Answer 1

I assume the third term in the first problem should be -7x², not -7x³.

5x⁴ = 5x³•x, and

5x³ (x - 4) = 5x⁴ - 20x³

Subtract this from the dividend to get an initial remainder of

(5x⁴ - 2x³ - 7x² - 39) - (5x⁴ - 20x³) = 18x³ - 7x² - 39

Next, 18x³ = 18x²•x, and

18x² (x - 4) = 18x³ - 72x²

Subtract this from the previous remainder to get a new one of

(18x³ - 7x² - 39) - (18x³ - 72x²) = 65x² - 39

Next, 65x² = 65x•x, and

65x (x - 4) = 65x² - 260x

which gives a new remainder of

(65x² - 39) - (65x² - 260x) = 260x - 39

Next, 260x = 260•x, and

260 (x - 4) = 260x - 1040

which gives a final remainder of

(260x - 39) - (260x - 1040) = 1001

1001 does not divide x, so we're done, and we've shown that

`(5x^4-2x^3-7x^2-39)/(x-4)=\boxed{5x^3+18x^2+65x+260+(1001)/(x-4)}`

A similar process can be used to show

`(4x^4+5x-4)/(x-2)=\boxed{4x^3+8x^2+16x+37+(70)/(x-2)}`