Answer:
Choice b.
.
Step-by-step explanation:
The highest power of the variable
in this polynomial is
. In other words, this polynomial is quadratic.
It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to
.)
After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.
Apply the quadratic formula to find the two roots that would set this quadratic polynomial to
. The discriminant of this polynomial is
.
.
Similarly:
.
By the Factor Theorem, if
is a root of a polynomial, then
would be a factor of that polynomial. Note the minus sign between
and
.
- The root
corresponds to the factor
, which simplifies to
. - The root
corresponds to the factor
, which simplifies to
.
Verify that
indeed expands to the original polynomial:
.
Answer:
f(x)=x(x-5)(x+2)
Step-by-step explanation:
Since the steps of the factorization of the polynomial f(x) is not given, I will proceed to give the correct factorization of f(x).
f(x)=x³-3x²-10x
First, we factor out x since it is a common term.
f(x)=x(x²-3x-10)
Next, we factorize the quadratic expression x²-3x-10.
f(x)=x(x²-5x+2x-10)
f(x)=x(x(x-5)+2(x-5))
f(x)=x(x-5)(x+2)
The correct factorization of the polynomial f(x)=x³-3x²-10x is: f(x)=x(x-5)(x+2)
Probably true
you can test it too
Your answer is no solution (because a negative square root doesn't exist)
first, you divide all sides by five and then take b, half it then square it