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Find the difference.

[tex]\[
(x^3 + 4x^2 - 7x - 2) - (2x^2 - 9x + 4)
\][/tex]

[tex]\[
= x^3 + (4x^2 - 2x^2) + (-7x + 9x) + (-2 - 4)
\][/tex]

[tex]\[
= x^3 + 2x^2 + 2x - 6
\][/tex]

Sagot :

GinnyAnswer
To find the difference between the two given polynomials, we need to subtract the second polynomial from the first. Let's write down each polynomial clearly:

1. First polynomial: \( x^3 + 4x^2 - 7x - 2 \)
2. Second polynomial: \( 2x^2 - 9x + 4 \)

Now, perform the subtraction term-by-term:

1. Cubic term:
[tex]\[ x^3 - 0 = x^3 \][/tex]
(Note that the second polynomial has no \( x^3 \) term, so it is effectively \( 0 \) for the cubic term.)

2. Quadratic term:
[tex]\[ 4x^2 - 2x^2 = 2x^2 \][/tex]

3. Linear term:
[tex]\[ -7x - (-9x) = -7x + 9x = 2x \][/tex]

4. Constant term:
[tex]\[ -2 - 4 = -6 \][/tex]

Putting it all together, the resulting polynomial after subtraction is:
[tex]\[ x^3 + 2x^2 + 2x - 6 \][/tex]

So, the coefficients for each term from highest degree to the constant term are:
[tex]\[ [1, 2, 2, -6] \][/tex]

Thus, the difference between the given polynomials is:

[tex]\[ x^3 + 2x^2 + 2x - 6 \][/tex]
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