Question

2. What must be taken away from the product (x – 3)(x2 + 4x – 1) to get 2x3 + x - 3?
22​

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{(x-3)(x^2+4x-1)}$

$\underline{\textsf{To find:}}$

$\textsf{The polynomial must be taken away from}\;\mathsf{(x-3)(x^2+4x-1)\;to\;get\;2x^3+x-3}$

$\underline{\textsf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{(x-3)(x^2+4x-1)}$

$\mathsf{=x^3+4x^2-x-3x^2-12x+3}$

$\mathsf{=x^3+x^2-13x+3}$

$\textsf{This can be written as}$

$\mathsf{=(2x^3+x-3)-(x^3-x^2+14x+6)}$

$\therefore\mathsf{x^3-x^2+14x+6\;must\be\;taken\;from\;the\;product\;to\;get\;2x^3+x-3}$

$\underrline{\textsf{Find more:}}$

What must be added to y cube minus y squared minus 3 Y - 22 get a square minus 5 Y + 6

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