Question

The area of a rectangular garden is given by the trinomial `x^2+6x-27`. What are the possible dimensions of the rectangle?

Answer 1

`x=3, -6`

Explanation:

This needs to be double checked but I'm guessing you just solve the quadratic formula to find values for `x` and it's as simple as that.

If so, then all you do is factorise and solve, factorising a quadratic involves two rules the numbers in the brackets have to sum to make `b` and multiply to make `c` of the formula `ax^2+bx+c`

9 and -3 multiply to make -27 and add to make 6 therefore

`(x-3)(x+6)`

since this is a quadratic and equals zero that tells you that either one of the brackets are equal to zero (as anything multiplied by zero is zero)

`x-3=0 therefore x=3`
`x+6 = 0 therefore x=-6`

Answer 2

`A=lw=x^2+6x-27` so the dimensions are `l times w` with any `l>0` and

`w=A/l={x^2+6x-27}/l.`

Explanation:

This is probably just supposed to be a question about factoring:

`A = x^2 + 6 x - 27 = (x + 9)(x - 3)`

But the factors don't really constrain the rectangle so this isn't a very good question.