talia grouped the terms and factored out the gcf of the groups of the polynomial $15x^2 - 3x - 20x + 4$. her…

talia grouped the terms and factored out the gcf of the groups of the polynomial $15x^2 - 3x - 20x + 4$. her work is shown below.\n1. $(15x^2 - 3x) + (-20x + 4)$\n2. $3x(5x - 1) + 4(-5x + 1)$\ntalia noticed that she does not have a common factor. what should she do?\n○ talia needs to leave the polynomial as is because it is prime and cannot be factored.\n○ talia needs to factor out a 3x from the first group and a 4x from the second group.\n○ talia needs to factor out a negative from one of the groups so the binomials will be the same.\n○ talia needs to apply the distributive property to get the expression $(3x + 4)(5x - 1)$.

talia grouped the terms and factored out the gcf of the groups of the polynomial $15x^2 - 3x - 20x + 4$. her work is shown below.\n1. $(15x^2 - 3x) + (-20x + 4)$\n2. $3x(5x - 1) + 4(-5x + 1)$\ntalia noticed that she does not have a common factor. what should she do?\n○ talia needs to leave the polynomial as is because it is prime and cannot be factored.\n○ talia needs to factor out a 3x from the first group and a 4x from the second group.\n○ talia needs to factor out a negative from one of the groups so the binomials will be the same.\n○ talia needs to apply the distributive property to get the expression $(3x + 4)(5x - 1)$.

Answer

Brief Explanations:

When factoring by grouping, if the resulting binomials are additive inverses (like $5x-1$ and $-5x+1$), factoring out a negative from one group will make them identical, allowing further factoring. The polynomial is not prime, and the other options either repeat incorrect steps or skip the necessary adjustment.

Answer:

Talia needs to factor out a negative from one of the groups so the binomials will be the same.