Answer :
Let's subtract the polynomials step-by-step:
We have two polynomials:
1. [tex]\( 6x^3 - 4x + 5 \)[/tex]
2. [tex]\( 3x^3 - 5x^2 + 6x - 2 \)[/tex]
Now, subtract the second polynomial from the first one:
1. Subtract the coefficients of the [tex]\(x^3\)[/tex] terms:
[tex]\[ 6x^3 - 3x^3 = 3x^3 \][/tex]
2. Subtract the coefficients of the [tex]\(x^2\)[/tex] terms:
- The first polynomial does not have an [tex]\(x^2\)[/tex] term, so treat it as [tex]\(0x^2\)[/tex].
[tex]\[ 0x^2 - (-5x^2) = 5x^2 \][/tex]
3. Subtract the coefficients of the [tex]\(x\)[/tex] terms:
[tex]\[ -4x - 6x = -10x \][/tex]
4. Subtract the constant terms:
[tex]\[ 5 - (-2) = 5 + 2 = 7 \][/tex]
Putting it all together, the result of the subtraction is:
[tex]\[
3x^3 + 5x^2 - 10x + 7
\][/tex]
Therefore, the correct answer is:
D. [tex]\(3x^3 - 5x^2 + 2x + 7\)[/tex]
We have two polynomials:
1. [tex]\( 6x^3 - 4x + 5 \)[/tex]
2. [tex]\( 3x^3 - 5x^2 + 6x - 2 \)[/tex]
Now, subtract the second polynomial from the first one:
1. Subtract the coefficients of the [tex]\(x^3\)[/tex] terms:
[tex]\[ 6x^3 - 3x^3 = 3x^3 \][/tex]
2. Subtract the coefficients of the [tex]\(x^2\)[/tex] terms:
- The first polynomial does not have an [tex]\(x^2\)[/tex] term, so treat it as [tex]\(0x^2\)[/tex].
[tex]\[ 0x^2 - (-5x^2) = 5x^2 \][/tex]
3. Subtract the coefficients of the [tex]\(x\)[/tex] terms:
[tex]\[ -4x - 6x = -10x \][/tex]
4. Subtract the constant terms:
[tex]\[ 5 - (-2) = 5 + 2 = 7 \][/tex]
Putting it all together, the result of the subtraction is:
[tex]\[
3x^3 + 5x^2 - 10x + 7
\][/tex]
Therefore, the correct answer is:
D. [tex]\(3x^3 - 5x^2 + 2x + 7\)[/tex]
