Question

Multiply the following using the vertical multiplication method 3x2 - 5x +1 XX + 2x + 4 O A. 3x4 + x2 +10x7 - 18x + 4 O B. 3x4 +x+3x2 - 18x + 4 O C. 3x4 + x + 10x2 + x + 4 O D. 3x4 D. 3x4 - x2 + 3x2 + 18x + 4​

Answer 1

Answer:

ANSWER

C.

3 {x}^{4} - {x}^{3} + 3{x}^{2} + 18x + 43x

4

−x

3

+3x

2

+18x+4

EXPLANATION

We want to multiply;

(3 {x}^{2} + 5x + 1)( {x}^{2} - 2x + 4)(3x

2

+5x+1)(x

2

−2x+4)

We use the distributive property to obtain:

3 {x}^{2} ( {x}^{2} - 2x + 4) + 5x( {x}^{2} - 2x + 4) + 1( {x}^{2} - 2x + 4)3x

2

(x

2

−2x+4)+5x(x

2

−2x+4)+1(x

2

−2x+4)

We expand to get:

3 {x}^{4} - 6 {x}^{3} + 12 {x}^{2} + 5 {x}^{3} - 10 {x}^{2} + 20x + {x}^{2} - 2x + 43x

4

−6x

3

+12x

2

+5x

3

−10x

2

+20x+x

2

−2x+4

Regroup similar terms:

3 {x}^{4} - 6 {x}^{3} + 5 {x}^{3} + 12 {x}^{2} - 10 {x}^{2} + {x}^{2} + 20x - 2x + 43x

4

−6x

3

+5x

3

+12x

2

−10x

2

+x

2

+20x−2x+4

Combine similar terms:

3 {x}^{4} - {x}^{3} + 3{x}^{2} + 18x + 43x

4

−x

3

+3x

2

+18x+4

The correct choice is C.