contestada

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

Respuesta :

Alfpfeu

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]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)[/tex]

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

Thank you.

TheAnimeGirl

Answer:

[tex] \boxed{ \boxed{ \bold{ \sf{(x + 7) \: and \: (x - 6)}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ {x}^{2} + x - 42}[/tex]

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

⇒[tex] \sf{ {x}^{2} + (7 - 6)x - 42}[/tex]

⇒[tex] \sf{ {x}^{2} + 7x - 6x - 42}[/tex]

Factor out x from the expression

⇒[tex] \sf{x(x + 7) - 6x - 42}[/tex]

Factor out 6 from the expression

⇒[tex] \sf{x(x + 7) - 6(x + 7)}[/tex]

Factor out x + 7 from the expression

⇒[tex] \sf{(x + 7)(x - 6)}[/tex]

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

Hope I helped!

Best regards!

Otras preguntas