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?\ntalia needs to leave the polynomial as is because it is prime and cannot be factored.\ntalia needs to factor out a (3x) from the first group and a (4x) from the second group.\ntalia needs to factor out a negative from one of the groups so the binomials will be the same.\ntalia 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?\ntalia needs to leave the polynomial as is because it is prime and cannot be factored.\ntalia needs to factor out a (3x) from the first group and a (4x) from the second group.\ntalia needs to factor out a negative from one of the groups so the binomials will be the same.\ntalia needs to apply the distributive property to get the expression ((3x + 4)(5x - 1)).

Answer

Explanation:

Step1: Analyze the factored form

We have (3x(5x - 1)+4(-5x + 1)). Notice that (-5x + 1=-(5x - 1)).

Step2: Rewrite the second term

Rewrite (4(-5x + 1)) as (-4(5x - 1)). So the expression becomes (3x(5x - 1)-4(5x - 1)).

Step3: Factor out the common binomial

Using the distributive property (a\times c - b\times c=(a - b)\times c) (where (a = 3x), (b = 4), and (c=(5x - 1))), we get ((3x - 4)(5x - 1)). This is equivalent to factoring out a negative from the second group.

Answer:

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