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Question
Which polynomial is to be subtracted from x2 + 13x + 7 to get the polynomial 3x2 + 5x − 4?
Solution
Let p(x) be the polynomial which is to be subtracted from x2 + 13x + 7 to get the polynomial 3x2 + 5x − 4.
∴ (x2 + 13x + 7) − p(x) = 3x2 + 5x − 4
⇒ p(x) = (x2 + 13x + 7) − (3x2 + 5x − 4)
⇒ p(x) = x2 + 13x + 7 − 3x2 − 5x + 4
⇒ p(x) = x2 − 3x2 + 13x − 5x + 7 + 4
⇒ p(x) = −2x2 + 8x + 11
Thus, the required polynomial is −2x2 + 8x + 11.
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