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3 years ago

Pre cal/cal master needed

1 answer:

5 0

Take x-2 and insert it into 2x^2 + 3x-2 where the x is located
2x^2 + 3x-2
2(x-2)^2 + 3(x-2)-2

Now work out 2(x-2)^2 + 3(x-2)-2 also follow PEMDAS
2(x-2)^2 + 3(x-2)-2
Since (x-2)^2 is an Exponent, lets work with that first and expand (x-2)^2.
(x-2)^2
(x -2)(x-2)
x^2 -4x + 4
Now Multiply that by 2 because we have that in 2(x-2)^2
(x-2)^2 = x^2 -4x + 4
2(x-2)^2 = 2(x^2 -4x + 4)
2(x^2 -4x + 4) = 2x^2 - 8x + 8
2x^2 - 8x + 8

Now that 2(x-2)^2 is done lets move on to 3(x-2).

Use the distributive property and distribute the 3
3(x-2) = 3x - 6

All that is left is the -2

Now lets put it all together
2(x-2)^2 + 3(x-2)-2

2x^2 - 8x + 8 + 3x - 6 - 2

Now combine all our like terms
2x^2 - 8x + 8 + 3x - 6 - 2
Combine: 2x^2 = 2x^2
Combine: -8x + 3x = -5x
Combine: 8 - 6 - 2 = 0

So all we have left is
2x^2 - 5x

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See explanation

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Step-by-step explanation:

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$2x^2+5x+3$

2. Decide if the three terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer.

In your case, coefficients 2, 5 and 3 do not have common factors, so go to the next step.

3. Multiply the leading coefficient and the constant, that is multiply the first and last numbers together:

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4. List all of the factors from step 3 and decide which combination of numbers will combine to get the number next to x:

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5. After choosing the correct pair of numbers, you must give each number a sign so that when they are combined they will equal the number next to x and also multiply to equal the number found in Step 3:

$2+3=5$

6. Rewrite the original problem with four terms by splitting the middle term into the two numbers chosen in step 5:

$2x^2+5x+3=2x^2+2x+3x+3$

7. Now that the problem is written with four terms, you can factor by grouping:

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