Question

Subtract. Your answer should be a polynomial in standard form. (-4x^(4)+6x^(2)+3)-(5x^(2)-3)

Answer 1

To subtract the given polynomials, distribute the negative sign and combine like terms. The result is -4x^4+x^2+6.

Step-by-step explanation:

To subtract the given polynomials (-4x4+6x2+3)-(5x2-3), we can start by distributing the negative sign to each term inside the parentheses. This gives us -4x4+6x2+3-5x2+3. Then, we can combine like terms, which means we add or subtract the coefficients of the same degree terms. In this case, the like terms are the x4 terms, the x2 terms, and the constant terms.

1. The coefficient of x4 is -4 and there is no other x4 term, so it remains the same: -4x4.
2. The coefficient of x2 is 6, but there is a -5x2 term, so we subtract: 6x2-5x2=x2.
3. The constant term is 3 and there is a +3 term, so we add: 3+3=6.

Combining these simplified terms, the answer is -4x4+x2+6.

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