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.
