Factoring the gcf from the polynomial

[tex]Factoring the gcf from the polynomial[/tex]

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Factoring the gcf from the polynomial

[tex]Factoring the gcf from the polynomial[/tex]

It is A, C, and E

Step-by-step explanation:

B and E

There are no common variables among all three terms.

The resulting expression when factoring out the GCF is 7(4vw + 7v + 5w).

Step-by-step explanation:

Given Polynomial:

[tex]80b^4-32b^2c^3+48b^4c[/tex]

Factors of Coefficient of terms

80 = 5 × 16

32 = 2 × 16

48 = 3 × 16

Common factor of the coefficient of all term is 16.

Each term contain variable. So the Minimum power of b is common from all terms.

Common from all variable part comes b².

So, Common factor of the polynomial = 16b²

⇒ 16b² ( 5b² ) - 16b² ( 2c³ ) + 16b² ( 3b²c )

⇒ 16b² ( 5b² - 2c³ + 3b²c )

Therefore, Statements that are true about David's word are:

The GCF of the coefficients is correct.

The variable c is not common to all terms, so a power of c should not have been factored out.

In step 6, David applied the distributive property

I think its gonna be C

(1)the GCF for the polynomial [tex]4x^3 - 2x^2y[/tex]

4x^3 = 2*2* x* x* x

2x^2y = 2*x*x*y

Greatest common factor is [tex]2*x*x = 2x^2[/tex]

(2) the GCF for the polynomial [tex]8x^4y + 6x^2y^2[/tex]

[tex]8x^4y = 2*2*2*x*x*x*x*y[/tex]

[tex]6x^2y^2 = 3*2*x*x*y*y[/tex]

GCF is [tex]2*x*x*y=2x^2y[/tex]

(3) the GCF for the polynomial[tex]12x^3y^2 - 20x^5y^3[/tex]

[tex]12x^3y^2 = 2*2*3*x*x*x*y*y[/tex]

[tex]20x^5y^3=5*2*2*x*x*x*x*x*y*y*y[/tex]

GCF is [tex]2*2*x*x*x*y*y= 4x^3y^2[/tex]

(4) the GCF for the polynomial [tex]-10x^3y^4 - 16x^5y^2[/tex]

[tex]-10x^3y^4 =-2*5*x*x*x*y*y*y*y[/tex]

[tex]-16x^5y^2=-2*2*2*2*x*x*x*x*x*y*y[/tex]

GCF is [tex]-2*x*x*x*y*y= -2x^3y^2[/tex]

The correct answer is there are no common variables among all three terms and the resulting expression when factoring out the GCF is 7(4vw + 7v + 5w).

Step-by-step explanation:

We are given a polynomial (28vw + 49v + 35w) which has three terms: 28vw, 49v and 35w.

This polynomial can be simplified by taking 7 out of the equation, because it is common to all the three terms.

The simplified equation becomes: 7(4vw + 7v + 5w)

The greatest common factor is the constant which is common to all the terms of the polynomial and for this equation, the GCF is 7.

a,c,e

Step-by-step explanation:

given polynomial 80b^4 – 32b^2c^3 + 48b^4c.

to find: factor put gcf.

solution: in order to factor a gcf of ploynomial, we always look over coefficent of each term and factor out gcf of those coefficents .

then we choose first variable terms in all terms and find gcf of first variable terms.

then choose another variable and factor out gcf of those terms.

david choose 80, 32 and 48 and factored out gcf of those numbers as 16.

so first step is taken by david is correct.

then he choose b variable factors b^4,b^2, b^4 and found gcf b^2 which is correct.

then in third step he choose c^3, and c and found gcf c.

here devid mistaken. there are three terms and we need to take gcf of variable(s) that would be all terms.

variable c is not there in first term 80b^4.

therefore, final gcf would be just product of gcf found in first two steps.

that is 16 times b^2 = 16b^2.

therefore, following statements would be correct statements :

a)the gcf of the coefficients is correct.

b)the variable c is not common to all terms, so a power of c should not have been factored out.

c) in step 6, david applied the distributive property.

The correct statements are

The GCF of the coefficients is correct.

The variable c is not common to all terms, so a power of c should not have been factored out.

David applied the distributive property.

Step-by-step explanation:

GCF = Greatest common factor

1) GCF of coefficients : (80,32,48)

80 = 2 × 2 × 2 × 2 × 5

32 = 2 × 2 × 2 × 2 × 2

48 = 2 × 2 × 2 × 2 × 3

GCF of coefficients : (80,32,48) is 16.

2) GCF of variables :([tex]b^4,b^2,b^4[/tex])

[tex]b^4[/tex]= b × b × b × b

[tex]b^2[/tex] = b × b

[tex]b^4[/tex] =b × b × b × b

GCF of variables :([tex]b^4,b^2,b^4[/tex]) is [tex]b^2[/tex]

3) GCF of [tex]c^3[/tex]and c: c is not the GCF of the polynomial. The variable c is not common to all terms, so a power of c should not have been factored out.

4) [tex]80b^4-32b^2c^3+48b^4c[/tex]

[tex]=16b^2(5b^2-2c^3+3b^2c)[/tex]

David applied the distributive property.

1. 2x2

2. 2x2y

3. 4x3y2

4. -2x3y2

Step-by-step explanation:

1. 4x3 - 2x2y= GCF: 2x2

2. 8x4y + 6x2y2= GCF: 2x2y

3. 12x3y2 - 20x5y3= GCF: 4x3y2

4. -10x3y4 - 16x5y2= GCF: -2x3y2