Guide :

# what is the gcf of this polynomial?

a^8b^6-a^5b^4+a^4b^7-a^4b^4

## Research, Knowledge and Information :

### Try Factor a Polynomial by Finding Its Greatest Common Factor ...

Try Factor a Polynomial by Finding Its Greatest Common Factor ... For a polynomial, the GCF is the largest polynomial that will divide evenly into that polynomial.

### How to Find a Greatest Common Factor in a Polynomial

No matter how many terms a polynomial has, you always want to check for a greatest common factor (GCF) ... How to Find a Greatest Common Factor in a Polynomial;

### Factoring Polynomials - Using GCF

In this lesson we will study polynomials that can be factored using the Greatest Common Factor. ... The greatest common factor (GCF)for a polynomial is the largest ...

### Factor polynomials: common factor (practice) | Khan Academy

Khan Academy is a nonprofit with the mission of providing a free, ... Factoring polynomials: common binomial factor. Practice: Factor polynomials: ...

### Simple Polynomial Factoring - Purplemath

Simple Polynomial Factoring (page 1 of 3) Sections ... Some books teach this topic by using the concept of the Greatest Common Factor, or GCF. In ...

### Factoring the Greatest Common Factor of a Polynomial ...

Factoring the Greatest Common Factor of a Polynomial. ... The greatest common factor (GCF) of polynomials is the largest polynomial that divides evenly into the ...

### Algebra Examples | Factoring Polynomials | Factoring Out ...

Factoring Polynomials. Factor. Factor out of . Tap for more steps... Factor out of . Factor out of . Factor out of . Enter YOUR Problem. About; Examples; Worksheet ...

### Polynomial greatest common divisor - Wikipedia

In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both ...

### How to Factor a Polynomial Expression - dummies

How to Factor a Polynomial Expression. ... No matter how many terms a polynomial has, it is always important to check for a greatest common factor (GCF) first.

### Polynomial Factoring The Greatest Common Factor (GCF ...

Feb 24, 2011 · how to factor the greatest common factor (gcf) from a polynomial.

## Suggested Questions And Answer :

### How do you factor the sum of terms as a product of the GCF and a sum?

It took me a while to interpret your question, and I came up with a polynomial that had a GCF, but it doesn't have to be a polynomial: 36x^2+45x+63 simplifies when we note that the GCF of the numbers 36, 45 and 63 is 9. That means 9 is the largest integer to divide into the numbers: 36=9*4, 45=9*5 and 63=9*7. This means we can rewrite the polynomial as the product of a GCF and a sum: 9(4x^2+5x+7). It utilises the distributive property of numbers. Another example: abc+ace-ca^2. In this case the GCF is algebraic: ac, because all the terms contain ac, so we can factorise: ac(b+e-a). This is the product of the GCF ac and the sum b+e-a. Another example: 4x^2+2xy+6x=2x(2x+y+3). This time the GCF is 2x because the GCF of the numbers is 2 and of the algebraic quantities is x, so we just combine the two GCFs to make 2x. Does this help you in time? If you still don't understand send me a private message explaining your difficulties and providing examples.

### Write each rational expression in lowest terms(20 r+10)/(30r+15)

(20r+10)/(30r+15) Factor out the GCF of 10 from each term in the polynomial. (10(2r)+10(1))/(30r+15) Factor out the GCF of 10 from 20r+10. (10(2r+1))/(30r+15) Factor out the GCF of 15 from each term in the polynomial. (10(2r+1))/(15(2r)+15(1)) Factor out the GCF of 15 from 30r+15. (10(2r+1))/(15(2r+1)) Reduce the expression (10(2r+1))/(15(2r+1)) by removing a factor of 5 from the numerator and denominator. (2(2r+1))/(3(2r+1)) Reduce the expression by canceling out the common factor of (2r+1) from the numerator and denominator. (2(2r+1))/(3(2r+1)) Reduce the expression by canceling out the common factor of (2r+1) from the numerator and denominator. (2)/(3)

### GCF of 43 and 387

43 is a prime, so its only factors are 1 and 43. If 387 is not divisible by 43, then the GCF has to be 1. 387 / 43 = 9, which means that 387 is divisible by 43. Hence, the GCF of 43 and 387 is 43.

### I need to factor this

-x^(3)-3x^(2)+4x+12 Factor the greatest common factor (GCF) from each group. (-x^(2)(x+3)+4(x+3)) Factor the polynomial by grouping the first two terms together and finding the greatest common factor (GCF).  Next, group the second two terms together and find the GCF.  Since both groups contain the factor (x+3), they can be combined. (-x^(2)+4)(x+3)

### What is a miss on this?Example: Removing the GCF from the PolynomialFigure each term totally3•x•x + 3•3•x

3 x^2 + 9 x    The greatest common factor is 3x 3x(x + 3)      The miss would be x+3?  I think that is what is left over...   (x-2)       5 ------- - ------- (x + 1)   (x - 5)   (x-2)(x-5) - 5(x+1) ---------------------      (x+1)(x-5)

### 16c^16-16 (factored)

16c^(16)-16 Factor out the GCF of 16 from each term in the polynomial. 16(c^(16))+16(-1) Factor out the GCF of 16 from 16c^(16)-16. 16(c^(16)-1) The binomial can be factored using the difference of squares formula, because both terms are perfect squares. 16(c^(8)+1)(c^(8)-1) The binomial can be factored using the difference of squares formula, because both terms are perfect squares. 16(c^(8)+1)(c^(4)+1)(c^(4)-1) The binomial can be factored using the difference of squares formula, because both terms are perfect squares. 16(c^(8)+1)(c^(4)+1)(c^(2)+1)(c^(2)-1) The binomial can be factored using the difference of squares formula, because both terms are perfect squares.  The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b). 16(c^(8)+1)(c^(4)+1)(c^(2)+1)(c-1)(c+1)

### Factoring polynomials?

Alright so now you group them. 2( (12x^3+20x^2) (-27x-45) ) Next you find the GCF of each group of numbers. 2( 4x^2(3x+5) -9(3x+5) ) Next you put the outside numbers in one bracket and the matching numbers as another. 2( (4x^2-9) (3x+5) ) Then you use difference of squares method on the first group of numbers because they are both perfect squares and they are separated by a minus sign. So (4x^2-9) becomes: (2x-3) (2x+3) So your final equation will be (2x-3) (2X+3) (3x+5)

### can someone help me solv; 100t² - 25t.

from all em werds, me thank the portant part is "fakter polynominal" 100x^2 -25x=25x*(4x-1) ???? "gratest kommon fakter ????? maebee sumwon want 25x ????

### 36x3 y2 z3 + 18x2 y2 z

36x^(3)y^(2)z^(3)+18x^(2)y^(2)z Factor out the GCF of 18x^(2)y^(2)z from each term in the polynomial. 18x^(2)y^(2)z(2xz^(2))+18x^(2)y^(2)z(1) Factor out the GCF of 18x^(2)y^(2)z from 36x^(3)y^(2)z^(3)+18x^(2)y^(2)z. 18x^(2)y^(2)z(2xz^(2)+1)