The area of a garden is given by the trinomial G second - 2G - 24 the gardens length is G + 4 what is the gardens width
To find the width of the garden, we need to first factor the trinomial G^2 - 2G - 24.
The factors of -24 that add up to -2 are -6 and 4:
G^2 - 6G + 4G - 24
G(G - 6) + 4(G - 6)
(G + 4)(G - 6)
Therefore, the width of the garden is G - 6. Since the garden's length is G + 4, we can set up an equation:
(G + 4)(G - 6) = G^2 - 2G - 24
Expanding the left side:
G^2 - 6G + 4G - 24 = G^2 - 2G - 24
Combining like terms on the left side:
G^2 - 2G - 24 = G^2 - 2G - 24
Since the equation is true, the width of the garden is G - 6.