Question

without actually finding p(5), find whether (x-5) is a factor of x³-7x²+16x-12 justify your answer

​

Answer 1

Answer: NO, IT IS NOT A FACTOR

X-5 = 0

X=5

x^3 - 7x^2 + 16x -2

5^3 - 7 x 5^2 + 16 x 5 - 2

125 - 175 + 80 -2

-50 + 68 = 18

As the solution is not equal to zero, X -5 is not a factor of the equation.

Answer 2

To determine whether (x-5) is a factor of x³-7x²+16x-12, we can use the Remainder Theorem, which states that if we divide the polynomial by (x-a), then the remainder will be equal to p(a), where p(x) is the original polynomial. In this case, we want to find whether (x-5) is a factor, so a = 5.

We can use synthetic division to divide the polynomial by (x-5) as follows:

5 | 1 -7 16 -12

5 -10 30

1 -2 6 18

Since the remainder is not zero, this means that (x-5) is not a factor of the polynomial.
Additionally, we can see that the factorization of the polynomial is (x-2)(x-3)(x-4), which does not include (x-5). Therefore, we can conclude that (x-5) is not a factor of x³-7x²+16x-12.

for more such questions on factors
https://brainly.in/question/11538202
#SPJ3