Question

1) Why is it useful to factor out the GCF first when factoring? 2) How do you factor trinomials? How can we check the binomial factors to verify that they are truly factors? 3) What are the key features to graphing a polynomial function? Explain how to find these key features to sketch a rough graph 4) How do you recognize if a binomial is a difference of perfect? 5) What signals you that factoring by grouping is the best method to use when factoring a problem?

Answer 1

1. It's useful to divide out the GCF first because it makes factoring easier because the coefficients are smaller requiring less steps.  2. First, identify a,b, and c in the trinomial ax^2+bx+c.  Then, write down all factor pairs of c  Then, identify which factor pair from the previous step sums up to b.   Then, Substitute factor pairs into two binomials 3. Key features are the y-intercept the zeros and the end behavior. to graph these put a pont on the intercepts and draw a line through them that matches the end behavior. 4. A binomial that is the difference of perfect squares is in the form of a^2-b^2 And its factor form is a^2 - b^2=(a-b)(a+b)5. Factoring by grouping often works well with four-term polynomials but the last step of factoring the common binomial only works when both terms contain the exact same binomial.

Should be right