Question

The area of a rectangular garden is given by the trinomial x2 + x – 42. What are the possible dimensions of the rectangle? Use factoring.

Answer 1

Answer:

$\boxed{ \boxed{ \bold{ \sf{(x + 7) \: and \: (x - 6)}}}}$

Step-by-step explanation:

$\sf{ {x}^{2} + x - 42}$

Here, we have to find two numbers which subtracts to 1 and multiplies to 42

⇒$\sf{ {x}^{2} + (7 - 6)x - 42}$

⇒$\sf{ {x}^{2} + 7x - 6x - 42}$

Factor out x from the expression

⇒$\sf{x(x + 7) - 6x - 42}$

Factor out 6 from the expression

⇒$\sf{x(x + 7) - 6(x + 7)}$

Factor out x + 7 from the expression

⇒$\sf{(x + 7)(x - 6)}$

So, the possible dimensions of the rectangle are x + 7 and x - 6 .

Hope I helped!

Best regards!

Answer 2

Answer:

Step-by-step explanation:

Hello, please consider the following.

$x^2+x-42\\\\\text{The sum of the zeroes is -1=-7+6 and the product is -42=-7*6.}\\\\\text{So, we can factorise.}\\\\x^2+x-42\\\\=x^2+7x-6x-42\\\\=x(x+7)-6(x+7)\\\\=(x+7)(x-6)$

So, the possible dimensions of the rectangle are (x+7) and (x-6).

Thank you.