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.
Question 8
If two linear factors of the polynomial y3+6y2−y−30 are (y−2) and (y+3), find its third factor.
Solution.
Suppose p(y)=y3+6y2−y−30.
Since (y−2) and (y+3) are factor of p(y), this gives 2 and −3 are zeros of p(y).
Using synthetic division: 216−1−30↓21630−318150↓−3−15150
Thus p(y)=(y−2)(y+3)(y+5).
Hence y+5 is the third factor.
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