Q4 of 16 Page 153

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

p(x) + q(x) = x2 – 4x + 1 – (1)

p(x) – q(x) = x2 + 5x –2 – (2)


by adding (1) and (2)


2 × p(x) = 2x2 + x –1


⇒


by (1)


q(x) = x2 – 4x + 1 – p(x)


⇒


⇒


More from this chapter

All 16 →
1

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).

 2

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

 3

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

 5

Taking p(x) = 3x2 – 2x + 4, write the following as polynomials:

i) (x + 1) p(x) + (x – 1) p(x)


ii) (x + 1) p(x) – (x – 1) p(x)


iii)