Question

if (2x-1) 2x⁴-ax³+4x²-x+2

Answer 1

2x-1= 0
x=1/2
2 (1/2)^4-a (1/2)^3+4 (1/2)^2-(1/2)+2
2 (1/16)-a(1/8)+4 (1/4)-1/2+2
(1/8)-a/8+1-(2+4/4)
1-a/8+1-6/4
1-a/8+1-3/2=0
1-a/8+2-3/2=0
1-a/8-1/2=0
1-a/8=1/2
1-a=1/2×8
1-a=4
-a=4-1
-a=3
a=3
HOPE IT HELPS! !

Answer 2

By remainder theorem we have,
2x-1=0
2x=1
x=1/2
$f(x) = {2x}^{4} - a {x}^{3} + 4 {x}^{2} - x \: + 2$
$f( \frac{1}{2} ) = 2 \times ({ \frac{1}{2} })^{4} - a \times ({ \frac{1}{2} })^{3} + 4 \times ( { \frac{1}{2} })^{2} + 2 = 0$
$2 \times \frac{1}{16} - a \times \frac{1}{8} + 4 \times \frac{1}{4} - \frac{1}{2} + 2 = 0$
$\frac{1}{8} - \frac{a}{8} - \frac{1 + 4}{2} = 0$
$\frac{1}{8} + \frac{3}{2} = \frac{a}{8}$
$\frac{1 + 12}{8} = \frac{a}{8} \\ \frac{13}{8} = \frac{a}{8} \\ 13 \times 8 = a8 \\ a = \frac{13 \times 8}{8} \\ a = 13$