High School

Subtract \((3x + 2x^7 + 5x^5) - (12x^5 + 8x^7 - 13x)\).

1) \(-6x^7 - 7x^5 - 10x\)
2) \(-6x^7 + 13x^5 - 10x\)
3) \(3x^{13}\)
4) \(-6x^7 - 7x^5 + 16x\)

Answer :

The subtraction of the two polynomials [tex](3x+2x⁷+5x⁵)-(12x⁵+8x⁷-13x[/tex]) results in -6x⁷ - 7x⁵ + 16x, which is the fourth option. 4) -6x⁷-7x⁵+16x is correct.

To subtract two polynomials: ([tex]3x+2x⁷+5x⁵)-(12x⁵+8x⁷-13x).[/tex] We start by distributing the negative sign across the second polynomial and then combine like terms.

  • Subtract coefficients of [tex]x⁷: 2x⁷ - 8x⁷ = -6x⁷[/tex]
  • Subtract coefficients of [tex]x⁵: 5x⁵ - 12x⁵ = -7x⁵[/tex]
  • [tex]x: 3x - (-13x) = 3x + 13x = 16x[/tex]

Combining the terms, we get -6x⁷ - 7x⁵ + 16x , option 4 is correct.