(x + 1)(x + 3)(x - 5)
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
Factor it once, and then factor the factors.
True
Divide the GCF into each to get the other factors.
Too bad that's not a^2 - ab - 42b^2 That factors to (a + 6b)(a - 7b)
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
Suppose p(x) is a polynomial in x. Then p(a) = 0 if and only if (x-a) is a factor of p(x).
To determine which binomial is a factor of a given polynomial, you can apply the Factor Theorem. According to this theorem, if you substitute a value ( c ) into the polynomial and it equals zero, then ( (x - c) ) is a factor. Alternatively, you can perform polynomial long division or synthetic division with the given binomials to see if any of them divides the polynomial without a remainder. If you provide the specific polynomial and the binomials you're considering, I can assist further.
Factor it once, and then factor the factors.
x-a is a factor of the polynomial p(x),if p(a)=0.also,if x-a is a factor of p(x), p(a)=0.
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) ).
To determine which linear expression is a factor of a given polynomial function, you typically need to perform polynomial division or use the Factor Theorem. If you can substitute a root of the polynomial into the linear expression and obtain a value of zero, then that linear expression is indeed a factor. Alternatively, if you have the polynomial's roots, any linear expression of the form ( (x - r) ), where ( r ) is a root, will be a factor. Please provide the specific polynomial function for a more accurate response.
a
B
a
When a polynomial is divided by one of its binomial factors, the quotient is called the "reduced polynomial" or simply the "quotient polynomial." This resulting polynomial represents the original polynomial after removing the factor, and it retains the degree that is one less than the original polynomial.