Question

Examine the steps for finding the product of (224)(16) in the example shown.

Line 1:200+20+4
Line 2: ×10+6−−−−−−−−−−
Line 3: 1200+120+24
Line 4: +2000+200+40−−−−−−−−−−−−−−−−−−−−−−
Line 5: 2000+1400+160+24

What are the corresponding steps used to find the product of (2x^2+2x+4)(x+6)?

Select one correct answer for each step.

Line 2: 10x+6
Line 5: 2x^3+14x^2+16x+24
Line 2: x+6
Line 1: 200x^2+20x+4
Line 3: 1200x^2+120x+24
Line 4: 2x^3+2x^2+4x
Line 1: 2x^2+2x+4
Line 4: 2000x^3+200x^2+40x
Line 3: 12x^2+12x+24
Line 5: 2000x^3+1400x^2+160x+24

Answer 1

Line 1: 2x^2 +2x +4

Line 2: x +6

Line 3: 12x^2 +12x +24

Line 4: 2x^3 +2x^2 +4x

Line 5: 2x^3 +14x^2 +16x +24

Explanation:

Line 1 is the expanded form of the multiplicand. A polynomial is already in expanded form so this is simply the multiplicand.

Line 2 is the expanded form of the multiplier. It, too, is just the multiplier.

Line 3 is the sum of partial products of the least-degree term of the multiplier with each term of the multiplicand.

Line 4 is the sum of partial products of the highest-degree term of the multiplier with each term of the multiplicand.

Line 5 is the sum of lines 3 and 4.