Q2 of 16 Page 153

What polynomial added to x2 + 4x – 5 gives 2x2 – 3x + 1?

Let the required polynomial p(x)

Now, according to the question


x2 + 4x – 5 + p(x) = 2x2 – 3x + 1


⇒ p(x) = 2x2 – 3x + 1 - x2 - 4x + 5


⇒ p(x) = x2 - 7x + 6


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Taking p(x) = 2x2 + 3x + 5, q(x) = x2 + 4x + 1 and s(x) = p(x) + q(x), calculate p(10), q(10), s(10), p(10) + q(10).

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What polynomial subtracted from x2 + 4x – 5 gives 2x2 – 3x + 1?

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Find polynomials p(x) and q(x) such that p(x) + q(x) = x2 – 4x + 1 and p(x) – q(x) = x2 + 5x –2.