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ozzi
2 years ago
10

Is X +3 a factor of 2X squared minus 2X -12

Mathematics
1 answer:
Fantom [35]2 years ago
3 0

Answer: No, x+3 is not a factor of 2x^2-2x-12

========================================================

Explanation:

Let p(x) = 2x^2 - 2x - 12

If we divide p(x) over (x-k), then the remainder is p(k). I'm using the remainder theorem. A special case of the remainder theorem is that if p(k) = 0, then x-k is a factor of p(x).

Compare x+3 = x-(-3) to x-k to find that k = -3.

Plug x = -3 into the function

p(x) = 2x^2 - 2x - 12

p(-3) = 2(-3)^2 - 2(-3) - 12

p(-3) = 12

We don't get 0 as a result so x+3 is not a factor of p(x) = 2x^2 - 2x - 12

----------------------------------------

Let's see what happens when we factor p(x)

2x^2 - 2x - 12

2(x^2 - x - 6)

2(x - 3)(x + 2)

The factors here are 2, x-3 and x+2

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Scrat [10]

Let's solve your equation step-by-step.

Question 1:   −2(6−2x) =4(−3+x)

 

Step 1: Simplify both sides of the equation.

−2(6−2x) =4(−3+x)

(−2) (6) +(−2) (−2x) =(4)(−3)+(4)(x)(Distribute)

−12+4x=−12+4x

4x−12=4x−12

 

Step 2: Subtract 4x from both sides.

4x−12−4x=4x−12−4x

−12=−12

 

Step 3: Add 12 to both sides.

−12+12=−12+12

0=0

Answer: All real numbers are solutions.

Question 2:  

Let's solve your equation step-by-step.

5−1(2x+3) =−2(4+x)

 

Step 1: Simplify both sides of the equation.

5−1(2x+3) =−2(4+x)

5+(−1) (2x) +(−1) (3) =(−2) (4)+(−2)(x)(Distribute)

5+−2x+−3=−8+−2x

(−2x) +(5+−3) =−2x−8(Combine Like Terms)

−2x+2=−2x−8

−2x+2=−2x−8

 

Step 2: Add 2x to both sides.

−2x+2+2x=−2x−8+2x

2=−8

 

Step 3: Subtract 2 from both sides.

2−2=−8−2

0=−10

 

Answer: There are no solutions.

 

8 0
3 years ago
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Step-by-step explanation:

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35.6 = the square root of 15.3^2 + the square root of x^2. Find x.​
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