Question

P(x) = x3 - 2x2 - 13x - 10 one root of the polynomial above is 5. Use synthetic division to factor out x - 5.

Answer 1

a = 1 , b = 3 , c = 2

Answer 2

Answer:

The values are a=1, b=3 and c=2

Step-by-step explanation:

Given: $P(x)=x^3-2x^2-13x-10$

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)

$\Rightarrow x^2+3x+2$

Factor of P(x)

$P(x)=(x+5)(x^2+3x+2)$

$P(x)=(x+5)(ax^2+bx+c)$

Compare the factored expression

$(x+5)(ax^2+bx+c)=(x+5)(x^2+3x+2)$

$ax^2=x^2, a\rightarrow 1$

$bx=3x, b\rightarrow 3$

$c=2, c\rightarrow 2$

Hence, The values are a=1, b=3 and c=2