Joana solved the equation 4x^2−4x−3=0 . She followed the steps to solve a quadratic equation by grouping. However, in Step 3 she noticed that the two groupings did not share a common binomial, as shown in her work below. She concluded that the quadratic equation 4x^2−4x−3=0 has no solutions. Is Joana’s conclusion correct? Review Joana’s work to answer the question. Step 1: 4x^2+2x+(−6x)−3=0 Step 2: (4x^2+2x)+(−6x−3)=0 Step 3: x(4x+2)+(−3(2x+1))=0 (1 point) Responses No, because she did not factor out the GCF from the first grouping. No, because she did not factor out the GCF from the first grouping. Yes, because there are no factors of −12 that add up to −4 . Yes, because there are no factors of negative 12 that add up to negative 4 . No, because she can still continue the steps even if the two groupings have no shared binomial. No, because she can still continue the steps even if the two groupings have no shared binomial. Yes, because the two groupings do not share a common binomial.

Question

Joana solved the equation 4x^2−4x−3=0 . She followed the steps to solve a quadratic equation by grouping. However, in Step 3 she noticed that the two groupings did not share a common binomial, as shown in her work below. She concluded that the quadratic equation 4x^2−4x−3=0 has no solutions. Is Joana’s conclusion correct? Review Joana’s work to answer the question. Step 1: 4x^2+2x+(−6x)−3=0 Step 2: (4x^2+2x)+(−6x−3)=0 Step 3: x(4x+2)+(−3(2x+1))=0 (1 point) Responses No, because she did not factor out the GCF from the first grouping. No, because she did not factor out the GCF from the first grouping. Yes, because there are no factors of −12 that add up to −4 . Yes, because there are no factors of negative 12 that add up to negative 4 . No, because she can still continue the steps even if the two groupings have no shared binomial. No, because she can still continue the steps even if the two groupings have no shared binomial. Yes, because the two groupings do not share a common binomial.

Answer 1