Answer:
The values are a=1, b=3 and c=2
Step-by-step explanation:
Given: [tex]P(x)=x^3-2x^2-13x-10[/tex]
One root of the polynomial above is 5.
(x-5) must be factor of P(x)
Using synthetic division to find another factor of P(x)
Synthetic Division:
5 | 1 -2 -13 -10 |
5 15 10
1 3 2 0
At last number we get 0. This show 5 is root of P(x)
We got three number 1 3 2
using this number write another factor of P(x)
[tex]\Rightarrow x^2+3x+2[/tex]
Factor of P(x)
[tex]P(x)=(x+5)(x^2+3x+2)[/tex]
[tex]P(x)=(x+5)(ax^2+bx+c)[/tex]
Compare the factored expression
[tex](x+5)(ax^2+bx+c)=(x+5)(x^2+3x+2)[/tex]
[tex]ax^2=x^2, a\rightarrow 1[/tex]
[tex]bx=3x, b\rightarrow 3[/tex]
[tex]c=2, c\rightarrow 2[/tex]
Hence, The values are a=1, b=3 and c=2
