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If z ≠ −1, then (4z^2-12z-16)/2z+2 is equivalent to which of the

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If z ≠ −1, then (4z^2-12z-16)/2z+2 is equivalent to which of the [#permalink] New post   24 Nov 2020, 02:15
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If \(z ≠ −1\), then \(\frac{4z^2-12z-16}{2z+2}\) is equivalent to which of the following?

(A) \(z − 4\)

(B) \(2z − 8\)

(C) \(4z − 16\)

(D) \(2z+8\)

(E) \(4z+16\)
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B
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Re: If z ≠ −1, then (4z^2-12z-16)/2z+2 is equivalent to which of the [#permalink] New post   24 Nov 2020, 07:13
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Sajjad1994 wrote:
If \(z ≠ −1\), then \(\frac{4z^2-12z-16}{2z+2}\) is equivalent to which of the following?

(A) \(z − 4\)

(B) \(2z − 8\)

(C) \(4z − 16\)

(D) \(2z+8\)

(E) \(4z+16\)


Take: \(\frac{4z^2-12z-16}{2z+2}\)

Factor out the greatest common factors: \(\frac{4(z^2-3z-4)}{2(z+1)}\)

Factor the quadratic expression: \(\frac{4(z-4)(z+1)}{2(z+1)}\)

Simplify: \(2(z-4)\)

Expand: \(2z-8\)

Answer: B
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Re: If z ≠ −1, then (4z^2-12z-16)/2z+2 is equivalent to which of the [#permalink] New post   28 Nov 2020, 03:18
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Solution



Given
In this question, we are given that
    • The number z is not equal to 1

To find
We need to determine
    • The value of the given expression \(\frac{4z^2-12z-16}{2z+2}\)

Approach and Working out
Simplifying the numerator and the denominator individually,
    • \(4z^2 – 12z – 16 = 4(z^2 – 3z – 4) = 4(z^2 – 4z + z – 4) = 4 (z – 4) (z + 1)\)
    • 2z + 2 = 2 (z + 1)

Hence, the value = \(\frac{4 (z – 4) (z + 1)}{2 (z + 1)}\) = 2 (z – 4) = 2z – 8
[here, we can cancel (z + 1) as we already know z is not equal to 1]

Thus, option B is the correct answer.

Correct Answer: Option B
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Re: If z 1, then (4z^2-12z-16)/2z+2 is equivalent to which of the [#permalink] New post   25 Mar 2024, 05:36
We can also just plug in plausible value Like z=0 and see which option fits.
(4z^2-12z-16)/(2z+2)
= -16/2 = -8

For Z=0, Only Option B fits as
2(0)-8= -8
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Re: If z 1, then (4z^2-12z-16)/2z+2 is equivalent to which of the [#permalink] New post   28 Mar 2024, 07:25
­Why it's answer can't by (A)? 

If we take common (2) at the starting from numerator and denominator, then it cancels out. 

We solved the numerator and got values (z+1) and (z-4)

So the equation becomes- (z+1) (z-4)/(z+1), from here we cancel out (z+1) and left with (z-4). 

Is this approach wrong?, please let me know. 
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Re: If z 1, then (4z^2-12z-16)/2z+2 is equivalent to which of the [#permalink] New post   28 Mar 2024, 08:00
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The approach fits but you seem to have made a calculation error here.

Even when you take 2 common in numerator and denominator you will still be left with a 2 in the numerator.
Here see.

2(2z^2-6z-8)/2(z+1)
= (2z^2-8z+2z-8)/(z+1)
=(2z+2)(z-4)/(z+1)
=2(z+1)(z-4)/(z+1)

Ans: 2z-8, Option(B)
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Re: If z 1, then (4z^2-12z-16)/2z+2 is equivalent to which of the [#permalink]
28 Mar 2024, 08:00
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