Complete the statements to find the limit. lim x→3 x2 + 2x − 3 x2 + 4x − 5 = The numerator can be factored as . The denominator can be factored as . The common factor of can be divided out of the numerator and denominator. The limit is . ANSWERS:
1. C
2. D
3. B
4. A

Your choices are all correct.

Numerator: x ² + 2x - 3 = (x + 3) (x - 1)

Denominator: x ² + 4x - 5 = (x + 5) (x - 1)

Common factor: x - 1

Then

lim [x → 3] (x ² + 2x - 3) / (x ² + 4x - 5)

= lim [x → 3] (x + 3) / (x + 5)

= (3 + 3) / (3 + 5)

= 6/8 = 3/4

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step-by-step explanation:

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hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)