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How do you factor quadratic equations with a coefficient?

Answer 1

Savannah Anderson

Good question .

basically what are asking me to factor is :

#ax^2 + bx +c#

here is an eg.

#4x^2 – 15x + 9.#

First you need to make column like this

SUM = COEFFICIENT OF x =( -15) product = (COEFFICIENT of x^2 #*# COEFFICIENT of constant)= 36 Now you have to find factors which have a sum of -15 and a product of 36

THE FACTORS ARE (-12), (-3)

So now what we do is split the middle term in the equation and factor it out

#4x^2 – 12x– 3x +9.# #4x(x – 3)–3 (x-3).#

#(4x–3 )(x – 3).#

HENCE FACTORED

#f(4x^2 – 15x + 9.) = (4x–3 )(x – 3)#

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Answer 2

Eli Assouline

To factor quadratic equations with a coefficient, follow these steps:

Multiply the coefficient of (x^2) by the constant term.
Find two numbers that multiply to the result from step 1 and add up to the coefficient of (x).
Rewrite the quadratic equation using these two numbers to split the middle term.
Factor by grouping or using other appropriate factoring techniques.
Check if the factored expression can be simplified further.

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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.