Question

Which expressions are equivalent to the polynomial -12x^2-19x-5

Answer 1

$\bf (2x^2-11x-9)-(14x^2+8x-4)\implies (2x^2-11x-9)-14x^2-8x-4 \\\\\\ 2x^2-14x^2-11x-8x-9-4\implies -12x^2-19x-5~~\checkmark \\\\[-0.35em] ~\dotfill\\\\ 2(x-1)-3(4x^2+7x+1)\implies 2x-2-12x^2-21x-3 \\\\\\ -12x^2+2x-21x-2-3\implies -12x^2-19x-5~~\checkmark \\\\[-0.35em] ~\dotfill\\\\ 3(x-5)-2(6x^2+9x+5)\implies 3x-15-12x^2-18x-10 \\\\\\ -12x^2+3x-18x-15-10\implies -12x^2-15x-25~~\bigotimes \\\\[-0.35em] ~\dotfill\\\\ (4x^2-13x-7)-(16x^2+9x-5)\implies 4x^2-13x-7-16x^2-9x+5$

$\bf 4x^2-16x^2-13x-9x-7+5\implies -12x^2-22x-2~~\bigotimes \\\\[-0.35em] ~\dotfill\\\\ (-16x^2+10x-3)+(4x^2-29x-2)\implies -16x^2+10x-3+4x^2-29x-2 \\\\\\ -16x^2+4x^2+10x-29x-3-2\implies -12x^2-19x-5~~\checkmark \\\\[-0.35em] ~\dotfill\\\\ (-15x^2+9x-10)+(3x^2-10x-5)\implies -15x^2+9x-10+3x^2-10x-5 \\\\\\ -15x^2+3x^2+9x-10x-10-5\implies -12x^2-x-15~~\bigotimes$