(x⁴ + 8x³ - 45x + 30) ÷ (x + 7) Topic is Polynomials. Find the answer using long division. Please, provide detailed steps.

Step-by-step explanation:

I added 3 images labelled Synthetic division 1 , 2 , 3 . I hope you understand this. It's really hard to type the method in the format so I used an online calculator symbolab.

The quotient is:

The remainder is: 2

Step-by-step explanation:

We need to solve the polynomials

by using long division.

The long division is done in figure attached.

The quotient is:

The remainder is: 2

i belive those are the ones that are under 90 degreese.

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)