Subtract. Express your answer as a polynomial in standard form. (1 point)

Question

(7x3−15x2+6x−2)−(4x2+9x−4) =

Answer 1

To subtract the polynomials \( (7x^3 - 15x^2 + 6x - 2) - (4x^2 + 9x - 4) \), we first distribute the negative sign across the second polynomial:

\[ 7x^3 - 15x^2 + 6x - 2 - 4x^2 - 9x + 4 \]

Next, we combine like terms:

1. The \( x^3 \) term: \( 7x^3 \)
2. The \( x^2 \) terms: \( -15x^2 - 4x^2 = -19x^2 \)
3. The \( x \) terms: \( 6x - 9x = -3x \)
4. The constant terms: \( -2 + 4 = 2 \)

Now we can write the resulting polynomial:

\[ 7x^3 - 19x^2 - 3x + 2 \]

Thus, the answer in standard form is:

\[ \boxed{7x^3 - 19x^2 - 3x + 2} \]