Mathematics: P(x) = x3 - 2x2 - 13x - 10 one root of the polynomial above is 5. use synthetic division to factor out x - 5. enter the values for a, b, and c in the factored form

Step-by-step explanation:yee...

P(x) = x3 - 2x2 - 13x - 10 one root of the polynomial - id3221310571836, mirzakasumovic8926

cheyenne5201

11.03.2022

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

0,0(0 оценок)