Question 8, Review Exercise

Solutions of Question 8 of Review Exercise of Unit 05: Polynomials. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

If two linear factors of the polynomial y3+6y2y30 are (y2) and (y+3), find its third factor.

Solution.

Suppose p(y)=y3+6y2y30.

Since (y2) and (y+3) are factor of p(y), this gives 2 and 3 are zeros of p(y).

Using synthetic division: 21613021630318150315150

Thus p(y)=(y2)(y+3)(y+5).

Hence y+5 is the third factor. GOOD