How do you factor #14x^2 + 29x - 15#?

Answer 1

If #14x^2+29x-15# #=(ax+b)(cx-d) color(white)("XXXXX")#we know there needs to be a 'minus' on the #d# because of the 'minus' on #15#

then, we're trying to find

Fortunately there are not a lot of factor pairs for #14 and 15# so we can quickly come up with #(2x+5)(7x-3)#

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Answer 2

Abigail Allen

To factor the quadratic expression 14x^2 + 29x - 15, we can use the AC method or trial and error:

Multiply the coefficient of the quadratic term (14) by the constant term (-15): 14 * (-15) = -210
Find two numbers that multiply to -210 and add up to the coefficient of the linear term (29): The pair of numbers is 35 and -6 (35 * (-6) = -210 and 35 + (-6) = 29).
Rewrite the middle term using these two numbers: 14x^2 + 35x - 6x - 15
Group the terms: (14x^2 + 35x) + (-6x - 15)
Factor out the greatest common factor from each group: 7x(2x + 5) - 3(2x + 5)
Factor out the common binomial factor: (2x + 5)(7x - 3)

So, the factored form of the expression 14x^2 + 29x - 15 is (2x + 5)(7x - 3).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.