Use polynomial long division to rewrite the following fraction in the form q(x)+r(x)d(x), where d(x) is the denominator of the original fraction, q(x) is the quotient, and r(x) is the remainder.
2x^2+8x-12/x+1

Step-by-step explanation:

p(x) = 2x^2+8x-12

d(x) = x + 1

r(x) = -13

q(x) = 2x + 6

q(x)+r(x)d(x)

= 2x + 6 + (-13) * x + 1

= 2x + 6 -13 * x + 1

= 2x + 6 - 13x + 1

= (- 11x + 7)

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

where is the option given