Question

The rectangular room is given by the trinomial x^2+4x-12. What are the possible dimensions of the rectangle? Use factoring. (1 point) (x-6) and (x-2) (x+6) and (x+2) (x-6) and (x+2) (x+6) and (x-2) 17. What is the factored form of the following expression? X^2+2xy-48y^2 (1 point) a. (x+6y)(x-8y) b. (x-6y)(x-8y) c. (x+6y)(x+8y) d. (x-6y)(x+8y) 18. The area of a rectangular art studio is given by the trinomial 24x^2-4x-8. What are the possible dimensions of the studio? Use factoring. a. (3x-2) and (8x-4) b. (3x-2) and (8x+4) (3x-2) and (8x-4) (3x+2) and (8x-4)

Answer 1

Given that the rectangle is x²+4x-12, the possible sides will be given by:
a]
x²+4x-12
=x²+6x-2x-12
=x(x+6)-2(x+6)
=(x-2)(x+6)
thus the dimensions are (x-2) units (x+6) units

b]
x²+2xy-48y²
factorizing the above is:
x²+8xy-6xy-48y²
=x(x+8y)-6y(x+8y)
=(x+8y)(x-6y)

c] 
24x²-4x-8
factoring the above we get:
=4(6x²-x-2)
=4(6x²+3x-4x-2)
=4(3x(x+2)-2(x+2))
=4(3x-2)(x+2)
=(12x-8)(4x+8)