16. Given that (x - 1) is a factor of the polynomial fix)= ax + x3 - 12x2- x+ 2.Find the value of the constant a and verify thatf(-1)3D0

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Solve Q15, & 16 showing clearly all steps involved

14. (iThe polynomial f(x) where f(x) x'- ax + bx + 8 leaves a remainder of 6 when divided by x-1
and a remainder of -70 when divided by x +3. Find the values of the constants a and b. Hence
factorise f(x) completely.
(ii) Given that the equation (k- 3)x +4x+k= 0 has real roots, find
The range of values of k.
6 The set of values ofk for which the roots have the same sign.
5. When a polynomia! P(x) is divided by x- 3and x+ 2, the remainders are 5 and -5 respectively.
Given that P(x) = (x - x - 6)Q()+ ax +b, find the values of a and b
16. Given that (x- 1) is a factor of the polynomial fix)= ax + x³ – 12x? - x+ 2.Find the value of the
constant a and verify thatf(-1)= 0
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Transcribed Image Text:14. (iThe polynomial f(x) where f(x) x'- ax + bx + 8 leaves a remainder of 6 when divided by x-1 and a remainder of -70 when divided by x +3. Find the values of the constants a and b. Hence factorise f(x) completely. (ii) Given that the equation (k- 3)x +4x+k= 0 has real roots, find The range of values of k. 6 The set of values ofk for which the roots have the same sign. 5. When a polynomia! P(x) is divided by x- 3and x+ 2, the remainders are 5 and -5 respectively. Given that P(x) = (x - x - 6)Q()+ ax +b, find the values of a and b 16. Given that (x- 1) is a factor of the polynomial fix)= ax + x³ – 12x? - x+ 2.Find the value of the constant a and verify thatf(-1)= 0 | |
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