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What is the difference multiplying binomials with factoring polynomials into binomial factors?
It's the difference between multiplication and division. Multiplying binomials is combining them. Factoring polynomials is breaking them apart.
How do you tell if a polynomial cannot be factored?
Try all the factoring techniques that you have been taught. If none work then it is prime (cannot be factored), try looking for (1) a greatest common factor (2) special binomials ... difference of squares, difference (or sum) of cubes (3) trinomal factoring techniques (4) other polymonials look for grouping techniques.
What does factoring a polynomial mean?
It means finding numbers (constant terms), or polynomials of the same or smaller order that multiply together to give the original polynomial.
What is an expression that completely divides a given polynomial?
An expression that completely divides a given polynomial without leaving a remainder is called a factor of the polynomial. This means that when the polynomial is divided by the factor, the result is another polynomial with no remainder. Factors of a polynomial can be found by using methods such as long division, synthetic division, or factoring techniques like grouping, GCF (greatest common factor), or special patterns.
How do you factor the polynomial 7x plus 49?
Factoring involves 'factoring out' the common numbers for each term. In a simple general form, a + ab = a(1+b). It's like "undistributing" factors: instead of multiplying both terms by a number, you essentially divide both terms by a number. In (7x + 49), both terms - 7x and 49 - have 7 as a factor. So, it can also be written: 7x + 49 = 7(x+7)
