Question 1: Monica wants to find the greatest common factor of the terms of the polynomial p(x)=12x3^y+6xy^2+18xy+24x. She sees that each term is divisible by 3x. She factors the polynomial as follows:

3x(4x^2y+2y^2+6y+8)

Did Monica correctly factor out the greatest common factor? Why or why not?

a. Monica is incorrect, the GCF should only include constants.
b. Monica is correct, 3x is the GCF and she factored it out correctly.
c. Monica is incorrect, the GCF should only include variables.
d. Monica is incorrect, there is a common factor larger than 3x.

Question 2: Lana uses factoring by grouping to factor the polynomial 8x^2y−10xy^2+12x−15y. Her work is shown below, but the last two lines of work are missing.

8x^2y−10xy^2+12x−15y
(8x^2y−10xy^2)+(12x−15y)
__[blank 1]__
__[blank 2]__

Select one statement for each blank to correctly complete Lana’s work.

a. blank 1: 2xy(4x−5y)+3(4x−5y)
a. blank 2: (2xy−3)(4x+5y)
b. blank 2: (2xy+3)(4x−5y)
b. blank 1: −2xy(4x+5y)−3(4x+5y)
c. blank 1: −4x(2xy+3)+5y(2xy+3)
c. blank 2: −(2xy+3)(4x−5y)

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)