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How do you factor #6x^2 - 25x + 14#?

Answer 1

Hazel Anglin

#6x^2-25x+14=(3x-2)(2x-7)#

Given:

#6x^2-25x+14#

Use an AC Method:

Look for a pair of factors of #AC=6*14=84# which sum to #B=25#.

The pair #21, 4# works.

Use this pair to split the middle term and factor by grouping:

#6x^2-25x+14#

#=6x^2-21x-4x+14#

#=(6x^2-21x)-(4x-14)#

#=3x(2x-7)-2(2x-7)#

#=(3x-2)(2x-7)#

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Answer 2

Ethan Adkins

To factor the quadratic expression (6x^2 - 25x + 14), you need to find two binomials that multiply together to give you the original expression. First, check if the quadratic can be factored using the AC method. Find two numbers that multiply to give you (6 \times 14 = 84) and add to give you (-25). These numbers are (-6) and (-14). Rewrite the middle term using these numbers: (6x^2 - 6x - 14x + 14). Now, group the terms: ((6x^2 - 6x) + (-14x + 14)). Factor out the greatest common factor from each group: (6x(x - 1) - 14(x - 1)). Factor out the common binomial factor (x - 1): ((6x - 14)(x - 1)). Simplify: ((2x - 7)(x - 1)). So, (6x^2 - 25x + 14) factors into ((2x - 7)(x - 1)).

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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.