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1 answer:
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Answer:
YES
NO
NO
Step-by-step explanation:
The given polynomial is:
(x - a) is a factor of a polynomial iff x = a is a solution to the polynomial.
To check if (x - 5) is a factor of the polynomial f(x), we substitute x = 5 and check if it satisfies the equation.
∴ f(5) = 5³ + 4(5)² - 25(5) - 100
= 125 + 100 - 125 - 100
= 225 - 225
= 0
We see, x = 5 satisfies f(x). So, (x - 5) is a factor to the polynomial.
Now, to check (x + 2) is a factor.
i.e., to check x = - 2 satisfies f(x) or not.
f(-2) = (-2)³ + 4(-2)² - 25(-2) - 100
= -8 + 16 + 50 - 100
= -108 + 66
≠ 0
Therefore, (x + 2) is not a factor of f(x).
To check (x - 4) is a factor.
∴ f(4) = 4³ + 4(4)² - 25(4) - 100
= 64 + 64 - 100 - 100
= 128 - 200
≠ 0
Therefore, (x - 4) is not a factor of f(x).
The other polynomial addend, when the sum of two polynomials is 10a2b2 – 8a2b 6ab2 – 4ab is 15a²b²- 20a²b + 6ab² - 4ab + 7.
<h3>What is polynomial?</h3>Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).
The sum of two polynomials is,
The one polynomial addend is,
Let suppose the other polynomial addend is f(a,b). Thus,
Isolate the second polynomial as,
Arrange the like terms as,
Hence, the other polynomial addend, when the sum of two polynomials is 10a2b2 – 8a2b 6ab2 – 4ab is 15a²b²- 20a²b + 6ab² - 4ab + 7.
Learn more about polynomial here;