Best Answer

Look for common factors. A common factor is a variable or number that can be factored out of each term in the equation. For example, in the polynomial 2x^3 + 6x + 10, all three terms are even and are therefore divisible by 2. Therefore, 2 is a factor of all 3 terms. In the polynomial 8x^4 + 2x^3 + x^2, x^2 is a factor of all three terms, since each of them contain at least an x^2 term.

- Step 2
Factor out the common factors. In the first example above, you can use the distributive property to factor out the 2:2x^3 + 6x + 10 = 2(x^3 + 3x + 5)In the second example, we can factor out the x^2:8x^4 + 2x^3 + x^2 = x^2(8x^2 + 2x + 1)Sometimes, you can factor out both a number and a variable. For example, in 3x^2 + 6x, you can factor out 3x:3x^2 + 6x = 3x(x + 2)

- Step 3
Look for a sum or difference of cubes. If, after factoring out your all the common factors, you only have a cubed variable and a cubed number left, you either have a difference of cubes or a sum of cubes. If one number is subtracted from another, it is a difference of cubes. If both numbers are added, it is a sum of cubes. For example, the polynomial equation x^4 + 8x can have an x factored out, resulting in x(x^3 + 8). x^3 is a cubed number, and 8 = 2^3. Therefore, you have a sum of cubes.

- Step 4
Plug in the formula for the sum or difference of cubes. The formula for a sum of cubes is:A^3 + B^3 = (A + B)(A^2 - AB + B^2)The formula for a difference of cubes is:A^3 - B^3 = (A - B)(A^2 + AB + B^2)So plugging in the problem from step 3, we get:x^4 + 8x =x(x^3 + 8)x(x^3 + 2^3)x(x + 2)(x^2 - 2x + 4)

- Step 5
Look for a difference of squares and apply the formula. A difference of squares is just like a difference of cubes, except that it involves a factorial with squared terms, such as x^2 - 4 = x^2 - 2^2. The formula is: A^2 - B^2 = (A + B)(A - B). So using that formula, we get:x^2 - 4 =x^2 - 2^2 = (x + 2)(x - 2)

- Step 6
Factor any remaining quadratic equations that can be factored. For example, in the expression x^2 + 7x +10, we need to find two numbers that multiply to 10 and add up to 7. Since 5 * 2 = 10, and 5 + 2 = 7, we get:x^2 + 7x + 10 =(x + 2)(x + 5)

Q: How do you factor polynomials completely?

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(x^2 + 1)(x^2 - 4x + 13)

There is no specific term for such polynomials. They may be referred to as are polynomials with only purely complex roots.

It is not possible to give a sensible answer to this question. The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers or polynomials. If you have only one number or polynomial there is nothing for it to have a factor in common with!

There is one way to determine weather each binomial is a factor of X-4. The division of polynomials is what determines each binomial.

how alike the polynomial and non polynomial

Related questions

12(b + 1)(b + 1)

x(x+3)(x+5)

9

Do you care weather a random stranger on their computer cares how to factor polynomials. P.S. i do in fact care how to factor polynomials, but i'm most likely in the minority on this one.

(x^2 + 1)(x^2 - 4x + 13)

There is no specific term for such polynomials. They may be referred to as are polynomials with only purely complex roots.

10

You can factor a polynomial using one of these steps: 1. Factor out the greatest common monomial factor. 2. Look for a difference of two squares or a perfect square trinomial. 3. Factor polynomials in the form ax^2+bx+c into a product of binomials. 4. Factor a polynomial with 4 terms by grouping.

We can't answer that without some polynomials to choose from.

The two things are completely unrelated.

(2a-3)(a-1)

We won't be able to answer this accurately without knowing the polynomials.