Q12 of 82 Page 130

Let us calculate and write the value of a for which x + a will be a factor of the polynomial x3 + ax2 – 2x + a – 12.

We have the polynomial as x3 + ax2 – 2x + a – 12.


Given that x + a is the factor of the polynomial, which means that x = -a is the root of the polynomial.


So f(-a) = 0.


(-a)3 + a(-a)2 - 2(-a) + a – 12 = 0


-a3 + a3 + 2a + a – 12 = 0


3a – 12 = 0


3a = 12


a = 4.


⸫ value of a is 4.


More from this chapter

All 82 →
11

(x + 1) is a factor of the polynomial xn + 1 when

 11

If n2 – 1 is a factor of the polynomial an4 + bn3 + cn2 + dn + e then

 12

Let us calculate and write the value of k for which x – 3 will be a factor of the polynomial k2x3 – kx2 + 3kx – k.

 12

Let us write the value of f(x) + f(–x) when f(x) = 2x + 5.