When the polynomial \( 6 x-5 x^{2}+x^{3}-7 \) is added to \( 10+4 x^{2}-x-5 x^{3} \) the resulting polynomial has which of the following as its leading coefficient?

To find the leading coefficient of the resulting polynomial when \( 6x - 5x^2 + x^3 - 7 \) is added to \( 10 + 4x^2 - x - 5x^3 \), we first combine the like terms. The polynomials are: 1. \( 6x - 5x^2 + x^3 - 7 \) 2. \( 10 + 4x^2 - x - 5x^3 \) Now, let's add them together: \[ (6x - 5x^2 + x^3 - 7) + (10 + 4x^2 - x - 5x^3) \] Combine the constant terms: \[ -7 + 10 = 3 \] Combine the \( x \) terms: \[ 6x - x = 5x \] Combine the \( x^2 \) terms: \[ -5x^2 + 4x^2 = -x^2 \] Combine the \( x^3 \) terms: \[ x^3 - 5x^3 = -4x^3 \] Now the resulting polynomial is: \[ -4x^3 - x^2 + 5x + 3 \] The leading term is \(-4x^3\), so the leading coefficient is \(-4\). Thus, the leading coefficient of the resulting polynomial is \(-4\).