h(x)= 3x^(5) + 2x^(4) + 15x^(3) + 10x^(2) - 528x - 352
for this equation how would I know to use the square root of 11 in synthetic division to be a factor?
I used the p / q list but I did not get sqt root of 11 as a possible factor.
could someone help please.
you can group factor
(3x^5+2x^4)=x^4(3x+2)
(15x^3+10^2)=5x^2(3x+2)
(-528x-352)=-176(3x+2)
(3x+2)(x^4+5x^2+176)and continue from here
How do I solve 2x-4=x-10?
bro what
To determine if the square root of 11 is a possible factor of the given equation h(x), you need to apply the Rational Root Theorem. The Rational Root Theorem provides a list of possible rational roots of a polynomial equation, which can help you in finding factors.
The Rational Root Theorem states that if a polynomial equation with integer coefficients has a rational root, it will be of the form p/q, where p is a factor of the constant term (in this case, -352) and q is a factor of the leading coefficient (in this case, 3).
To find the factors of -352, you can begin by listing all the positive and negative divisors of 352. Some of the divisors include: 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, -1, -2, -4, -8, -11, -16, -22, -32, -44, -64, -88, -176, -352.
Next, you need to determine which of these factors satisfy the Rational Root Theorem, which states that p (the factor of the constant term) must divide evenly into -352, and q (the factor of the leading coefficient) must divide evenly into 3. In this case, p can be any of the divisors of 352 that we just listed, and q can only be 1 or 3.
Using this information, you can generate a list of all possible rational roots by forming fractions with p/q. However, it is vital to simplify these fractions to determine if the square root of 11 is a possible factor.
After simplification, you will see that the square root of 11 does not appear as a rational root in the simplified form. Therefore, the square root of 11 is not a possible factor of the given equation, h(x).
Note that the Rational Root Theorem only provides a list of possible rational roots. It does not guarantee that these roots will be the actual factors of the equation. To verify if a number is a factor, you can use synthetic division or polynomial long division to check.