Polynomial quesion (1 Viewer)

[enak]

From Patel textbook 5E

When a polynomial P(x) is divided by (x - 3), the remainder is 5 and when divided by (x - 4), the remainder is 9. Find the remainder when P(x) is divided by (x - 3)(x - 4).

I'm not quite sure how to do this.

 

[tonberry_kun]

When P(x) is divided by (x - 3)(x - 4) the remainder must be of the form ax + b
.'. P(x) = (x - 3)(x - 4)Q(x) + ax + b

By remainder theorem P(c) is the remainder when p(x) is divided by (x - c)
P(3) = 0 + 3a + b = 5
P(4) = 0 + 4a + b = 9

solving these 2
a = 4
.'. b = -7

.'. remainder is 4x - 7

 

[enak]

Ahh, me = stupid, thanks.