How do you factor #12x^2+69x+45#?

Answer 1

The equation can be factorised to #3(4x+3)(x+5)#

Use the general formula #x = (-b +- sqrt(b^2 -4ac))/(2a)#
Substitute in the given values #x = (-69 +- sqrt(69^2 -4*12*45))/(24)#
simplify #x = (-69 +- 51)/(24)#
#x_"1" = -3/4# #x_"2" = -5#
Put those values back into #a(x-x_"1")(x-x_"2")#

gives

#12(x +3/4)(x+5)#
rearranging #3(4x+3)(x+5)#
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Answer 2

f(x) = 3(4x + 3)(x + 5)

#f(x) = 3y = 12x^2 + 69x + 45 = 3(4x^2 + 23x + 15)# Factor the trinomial y in parentheses. #y = 4x^2 + 23x + 15# Use the new AC Method to factor trinomials (Socratic Search) y = 4(x + p)(x + q) Converted trinomial: #y' = x^2 + 23x + 60 =# (x + p')(x + q') Find 2 numbers knowing sum (b = 23) and product (ac = 60). They are: 3 and 20. Back to y, we get: #p = (p')/a = 3/4#, and #q = (q')/a = 20/4 = 5# Factored form: y = 4(x + 3/4)(x + 5) = (4x + 3)(x + 5) f(x) = 3y = 3(4x + 3)(x + 5)
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Answer 3

To factor (12x^2+69x+45), you can first look for two numbers that multiply to (12 \times 45 = 540) and add up to (69). These numbers are (15) and (36).

Then, rewrite the middle term (69x) as (15x + 54x).

Next, group the terms: (12x^2 + 15x + 54x + 45).

Now, factor by grouping: (3x(4x + 5) + 9(4x + 5)).

Finally, factor out the common binomial factor ((4x + 5)): ((3x + 9)(4x + 5)).

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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.

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.

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.

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.

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