QuestionSimplify: $3 x^{4}+2 x^{3}-5 x^{2}+4 x^{2}+6 x-2 x-3 x^{4}+7 x^{5}-3 x^{3}$ . Choose A, B, C, or D.

Studdy Solution

STEP 1

Assumptions1. We are given the expression $3 x^{4}+ x^{3}-5 x^{}+4 x^{}+6 x- x-3 x^{4}+7 x^{5}-3 x^{3}$ . . We need to simplify the expression by combining like terms.

STEP 2

First, we need to identify the like terms in the expression. Like terms are terms that have the same variable and exponent.In our expression, the like terms are- $x^{4}$ and $- x^{4}$ - $2 x^{}$ and $- x^{}$ - $-5 x^{2}$ and $4 x^{2}$ - $6 x$ and $-2 x$ - $7 x^{5}$

STEP 3

Now, we add or subtract the coefficients of the like terms to simplify the expression.
For the $x^{}$ terms $3 x^{} -3 x^{} =0 x^{}$

STEP 4

For the $x^{3}$ terms $2 x^{3} -3 x^{3} = -1 x^{3}$

STEP 5

For the $x^{2}$ terms $-5 x^{2} +4 x^{2} = -1 x^{2}$

STEP 6

For the $x$ terms $6 x -2 x =4 x$

STEP 7

The $x^{5}$ term remains as it is because it does not have any like terms.
$7 x^{5}$

STEP 8

Now, we combine all the simplified terms to get the simplified expression.
$7 x^{5} +0 x^{4} - x^{3} - x^{2} +4 x$

STEP 9

We can drop the $x^{4}$ term because it equals zero and does not affect the value of the expression.
So, the final simplified expression is $7 x^{5} - x^{3} - x^{2} +4 x$ The correct answer is D. $7 x^{5}-x^{3}-x^{2}+4 x$ .

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QuestionSimplify: $3 x^{4}+2 x^{3}-5 x^{2}+4 x^{2}+6 x-2 x-3 x^{4}+7 x^{5}-3 x^{3}$ . Choose A, B, C, or D.

Studdy Solution

STEP 1

Assumptions1. We are given the expression $3 x^{4}+ x^{3}-5 x^{}+4 x^{}+6 x- x-3 x^{4}+7 x^{5}-3 x^{3}$ . . We need to simplify the expression by combining like terms.

STEP 2

First, we need to identify the like terms in the expression. Like terms are terms that have the same variable and exponent.In our expression, the like terms are- $x^{4}$ and $- x^{4}$ - $2 x^{}$ and $- x^{}$ - $-5 x^{2}$ and $4 x^{2}$ - $6 x$ and $-2 x$ - $7 x^{5}$

STEP 3

Now, we add or subtract the coefficients of the like terms to simplify the expression.
For the $x^{}$ terms $3 x^{} -3 x^{} =0 x^{}$

STEP 4

For the $x^{3}$ terms $2 x^{3} -3 x^{3} = -1 x^{3}$

STEP 5

For the $x^{2}$ terms $-5 x^{2} +4 x^{2} = -1 x^{2}$

STEP 6

For the $x$ terms $6 x -2 x =4 x$

STEP 7

The $x^{5}$ term remains as it is because it does not have any like terms.
$7 x^{5}$

STEP 8

Now, we combine all the simplified terms to get the simplified expression.
$7 x^{5} +0 x^{4} - x^{3} - x^{2} +4 x$

STEP 9

We can drop the $x^{4}$ term because it equals zero and does not affect the value of the expression.
So, the final simplified expression is $7 x^{5} - x^{3} - x^{2} +4 x$ The correct answer is D. $7 x^{5}-x^{3}-x^{2}+4 x$ .

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QuestionSimplify: 3x4+2x3−5x2+4x2+6x−2x−3x4+7x5−3x33 x^{4}+2 x^{3}-5 x^{2}+4 x^{2}+6 x-2 x-3 x^{4}+7 x^{5}-3 x^{3}3x4+2x3−5x2+4x2+6x−2x−3x4+7x5−3x3. Choose A, B, C, or D.

Studdy Solution

STEP 1

Assumptions1. We are given the expression 3x4+x3−5x+4x+6x−x−3x4+7x5−3x33 x^{4}+ x^{3}-5 x^{}+4 x^{}+6 x- x-3 x^{4}+7 x^{5}-3 x^{3}3x4+x3−5x+4x+6x−x−3x4+7x5−3x3. . We need to simplify the expression by combining like terms.

STEP 2

STEP 3

Now, we add or subtract the coefficients of the like terms to simplify the expression.For the xx^{}x terms3x−3x=0x3 x^{} -3 x^{} =0 x^{}3x−3x=0x

STEP 4

For the x3x^{3}x3 terms2x3−3x3=−1x32 x^{3} -3 x^{3} = -1 x^{3}2x3−3x3=−1x3

STEP 5

For the x2x^{2}x2 terms−5x2+4x2=−1x2-5 x^{2} +4 x^{2} = -1 x^{2}−5x2+4x2=−1x2

STEP 6

For the xxx terms6x−2x=4x6 x -2 x =4 x6x−2x=4x

STEP 7

The x5x^{5}x5 term remains as it is because it does not have any like terms.7x57 x^{5}7x5

STEP 8

Now, we combine all the simplified terms to get the simplified expression.7x5+0x4−x3−x2+4x7 x^{5} +0 x^{4} - x^{3} - x^{2} +4 x7x5+0x4−x3−x2+4x

STEP 9

We can drop the x4 x^{4}x4 term because it equals zero and does not affect the value of the expression.So, the final simplified expression is7x5−x3−x2+4x7 x^{5} - x^{3} - x^{2} +4 x7x5−x3−x2+4xThe correct answer is D. 7x5−x3−x2+4x7 x^{5}-x^{3}-x^{2}+4 x7x5−x3−x2+4x.

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QuestionSimplify: $3 x^{4}+2 x^{3}-5 x^{2}+4 x^{2}+6 x-2 x-3 x^{4}+7 x^{5}-3 x^{3}$ . Choose A, B, C, or D.

Assumptions1. We are given the expression $3 x^{4}+ x^{3}-5 x^{}+4 x^{}+6 x- x-3 x^{4}+7 x^{5}-3 x^{3}$ . . We need to simplify the expression by combining like terms.

Now, we add or subtract the coefficients of the like terms to simplify the expression.
For the $x^{}$ terms $3 x^{} -3 x^{} =0 x^{}$

For the $x^{3}$ terms $2 x^{3} -3 x^{3} = -1 x^{3}$

For the $x^{2}$ terms $-5 x^{2} +4 x^{2} = -1 x^{2}$

For the $x$ terms $6 x -2 x =4 x$

The $x^{5}$ term remains as it is because it does not have any like terms.
$7 x^{5}$

Now, we combine all the simplified terms to get the simplified expression.
$7 x^{5} +0 x^{4} - x^{3} - x^{2} +4 x$

We can drop the $x^{4}$ term because it equals zero and does not affect the value of the expression.
So, the final simplified expression is $7 x^{5} - x^{3} - x^{2} +4 x$ The correct answer is D. $7 x^{5}-x^{3}-x^{2}+4 x$ .