How do you factor the trinomial #x^2+2x-4=0#?

Answer 1

#y = (x + 1 + sqrt5)(x + 1 - sqrt5)#

Method 1. Apply the formula of quadratic function in intercept form (Google Search): #y = (x +b/(2a) + d/(2a))(x + b/(2a) - d/(2a))#, with #b/(2a )= 1# #D = d^2 = 4 + 16 = 20# --> #d = +- 2sqrt5# We get: #y = (x + 1 + sqrt5)(x + 1 - sqrt5)# Method 2. Solve the quadratic equation. #D = d^2 = 4 + 16 = 20# --> #d = +- 2sqrt5# 2 real roots: #x1 = (- 1 - sqrt5)# and #x2 = (- 1 + sqrt5)# Therefor, the factored form is: #y = (x - x1)(x - x2) = (x + 1 + sqrt5)(x + 1 - sqrt5) #
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Answer 2

To factor the trinomial ( x^2 + 2x - 4 = 0 ), you can use the factoring method:

  1. Identify the coefficients of the quadratic equation: ( a = 1 ), ( b = 2 ), and ( c = -4 ).
  2. Find two numbers that multiply to ( a \times c = 1 \times -4 = -4 ) and add to ( b = 2 ). The numbers are 4 and -1.
  3. Rewrite the quadratic equation using these numbers: ( x^2 + 4x - 2x - 4 = 0 ).
  4. Group the terms: ( (x^2 + 4x) + (-2x - 4) = 0 ).
  5. Factor out the common terms from each group: ( x(x + 4) - 2(x + 4) = 0 ).
  6. Factor out the common factor of ( x + 4 ): ( (x + 4)(x - 2) = 0 ).

Therefore, the factored form of ( x^2 + 2x - 4 = 0 ) is ( (x + 4)(x - 2) = 0 ).

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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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