We won't be able to answer this accurately without knowing the polynomials.
Yes, if there is no remainder after division, the divisor is a factor.
(x + 11y)(x - 12y)
This polynomial doesn't factor. The only thing you can do is take out parts of some terms, e.g. 2(2x3 + 10x2 + x) - 3.
Yes, f(x) = 2 is a polynomial of degree 0 (because there are no x terms).
Take out the common factor, 3: 3x + 6 = 3(x + 2).
To determine the relationship between ( (x - 2) ) and the polynomial ( 2x^3 + x^2 - 3 ), we can perform polynomial division. If ( (x - 2) ) divides the polynomial evenly, then ( (x - 2) ) is a factor of the polynomial. Alternatively, we can evaluate the polynomial at ( x = 2 ); if the result is zero, it confirms that ( (x - 2) ) is a factor. In this case, substituting ( x = 2 ) gives ( 2(2)^3 + (2)^2 - 3 = 16 + 4 - 3 = 17 ), indicating that ( (x - 2) ) is not a factor of the polynomial.
(x-2)(x-3)
(x-2)(x+2)
To factor a polynomial expression, you identify common factors among the terms and express the polynomial as a product of simpler polynomials. For example, consider the polynomial ( x^2 - 5x + 6 ); it factors into ( (x - 2)(x - 3) ). Each factor is written in descending order, starting with the highest degree term. The specific steps to factor will depend on the polynomial you are working with.
x^2 + 5x - 24 = (x - 3)(x + 8)
Yes, that's correct. According to the Factor Theorem, if a polynomial ( P(x) ) is divided by ( (x - a) ) and the remainder is zero, then ( (x - a) ) is indeed a factor of the polynomial. This means that ( P(a) = 0 ), indicating that ( a ) is a root of the polynomial. Thus, the polynomial can be expressed as ( P(x) = (x - a)Q(x) ) for some polynomial ( Q(x) ).
Suppose p(x) is a polynomial in x. Then p(a) = 0 if and only if (x-a) is a factor of p(x).
(x+4)(x-2)
2(x + 4)(x - 10)
The coefficient of a factor in a polynomial is a numerical value that multiplies that factor within the expression. For example, in the polynomial (3x^2 + 5x + 2), the coefficient of the factor (x^2) is 3, while the coefficient of (x) is 5. Coefficients can represent various quantities, such as weights or scaling factors, depending on the context in which the polynomial is used.
X2 - X - 2(X + 1)(X - 2)===============(X + 1) is a factor of the above polynomial.
False