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When a polynomial is divided by one of its binomial factors what is the quotient called?
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How do you know if you have simplified a polynomial correctly?
I suppose you mean factoring the polynomial. You can check by multiplying the factors - the result should be the original polynomial.
What are prime polynomials?
A polynomial that can't be separated into smaller factors.
What are the solutions of the equation x3 plus 3x2-x-3 equals 0?
the solutions to this equation are -1,+1 and -3. you can solve this equation by using the polynomial long division method. we basically want to factorize this and polynomial and equate its factors to zero and obtain the roots of the equation. By hit and trial , it clear that x=1 i.e is a root of this equation. So (x-1) should be a factor of the given polynomial (LHS). Divide the polynomial by x-1 using long division method and you will get the quotient as x2+4x+3 and remainder would be 0 ( it should be 0 as we are dividing the polynomial with its factor. Eg when 8 is divided by any of its factor like 4,2 .. remainder is always zero ) Now, we can write the given polynomial as product of its factors as x3+3x2-x-3 = (x-1)(x2+4x+3) =(x-1)(x+1)(x+3) [by splitting middle term method] so the solutions for the given polynomial are obtained when RHS = 0, Hence x=-1 , X = +1, x=-3 are the solutions for this equation.
If the factors of a polynomial are x plus 2 and x plus 6 what values of x make that polynomial 0?
-2 and -6
Are a polynomial's factors the values at which the graph of a polynomial meets the y-axis?
Not quite. The polynomial's linear factors are related - not equal to - the places where the graph meets the x-axis. For example, the polynomial x2 - 5x + 6, in factored form, is (x - 2) (x - 3). In this case, +2 and +3 are "zeroes" of the polynomial, i.e., the graph crosses the x-axis. That is, in an x-y graph, y = 0.
What is a number written as a product of its factors called?
two factors is a binomial three factors is a trinomial four of more is a polynomial the product of any of these is just a polynomial
Why does 72000 divided by 9 have the same quotient as 40000 divided by 5?
72000 shares a factor with 40000. This factor is 8000. By having one factor be the same, both of these equations, when divided by the factors NOT shared, will have the same quotient.
How does knowing one linear factor of a polynomial help find the other factors?
If you know one linear factor, then divide the polynomial by that factor. The quotient will then be a polynomial whose order (or degree) is one fewer than that of the one that you stared with. The smaller order may make it easier to factorise.
How are factors and quotients related?
In the sentence 6 times 9 equals 54, 6 and 9 are factors of the product 54. In the sentence 54 divided by 9 equals 6, 6 is the quotient. In the sentence 54 divided by 6 equals 9, 9 is the quotient. The result of a multiplication sentence is the product of factors; the result of a division sentence is the quotient.
Are a polynomial's factors the values at which the graph of a polynomial meets the x-axis?
false
How is quotients and factors related?
In the sentence 3 times 6 equals 18, 3 and 6 are factors of 18. In the sentence 18 divided by 6 equals 3, 3 is the quotient. In the sentence 18 divided by 3 equals 6, 6 is the quotient. Same numbers, same relationships, different processes, different words.
How do you know if you have simplified a polynomial correctly?
I suppose you mean factoring the polynomial. You can check by multiplying the factors - the result should be the original polynomial.
Why might it be useful to know the linear factors of a polynomial function?
It is useful to know the linear factors of a polynomial because they give you the zeros of the polynomial. If (x-c) is one of the linear factors of a polynomial, then p(c)=0. Here the notation p(x) is used to denoted a polynomial function at p(c) means the value of that function when evaluated at c. Conversely, if d is a zero of the polynomial, then (x-d) is a factor.
How do you find a degree of a graphed polynomial?
Factors
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - a is a factor?
B
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - b is a factor?
a
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - c is a factor?
a
