Question

A solar panel has an area of x2 + 13x + 42. Find the possible dimensions of the solar panel.

Answer 1

Answer: (x + 6) and (x + 7)

Step-by-step explanation: Determine if the polynomial terms contain a common factor. In this case, there's no common factor. Next, find two numbers whose product is 42 and whose sum is 13. The only pair of numbers that satisfies these conditions is 6 and 7. Finally, write the polynomial in factored form as (x + 6)(x + 7). Therefore, the possible dimensions of the rectangle are (x + 6) by (x + 7).

Answer 2

Answer: x+6 and x+7

Explanation:

`x^(2) +13x + 42 = 0\\D = b^(2) - 4ac = 169 - 4*42 = 169 - 168 = 1\\x_(1) = (-13 + 1)/2 = -6\\x_(2) = (-13 -1)/2 = -7\\\\So, x^(2) + 13x + 42 = (x+6)(x+7) \\\\\\`

Hence, the possible dimensions are x+6 and x+7.