Suatu suku banyak p(x) dibagi ( 2x – 1 ) dan dibagi ( 3x + 2 ) berturut turut bersisa 2 dan – 3 . suku banyak f(x) dibagi ( 2x – 1 ) dan dibagi ( 3x + 2 ) berturut turu bersisa – 2 dan 6 . sisa pembagian suku banyak h(x) = p(x). f(x) oleh ( 2x

Suatu suku banyak p(x) dibagi ( 2x – 1 ) dan dibagi ( 3x + 2 ) berturut turut bersisa 2 dan – 3 . suku banyak f(x) dibagi ( 2x – 1 ) dan dibagi ( 3x + 2 ) berturut turu bersisa – 2 dan 6 . sisa pembagian suku banyak h(x) = p(x). f(x) oleh ( 2x – 1 ) ( 3x + 2 ) adalah…

Jawab:

Penjelasan dengan langkah-langkah:

$H(x) = M(x)cdot L_1(x) cdot L_2(x) + boxed{A_1cdot x + B_1} to text{Sisa pembagian}\\ L_1(x) = a_1x + b_1, ; L_2(x) = a_2 x + b_2\\HBig(-dfrac{b_1}{a_1}Big) = MBig(-dfrac{b_1}{a_1}Big) cdot L_1Big(-dfrac{b_1}{a_1}Big) cdot L_2Big(-dfrac{b_1}{a_1}Big) - dfrac{A_1cdot b_1}{a_1}+B_1 to L_1Big(-dfrac{b_1}{a_1}Big) = 0\\HBig(-dfrac{b_1}{a_1}Big) = B_1 - dfrac{A_1cdot b_1}{a_1} = dfrac{a_1B_1-A_1b_1}{a_1}$

$HBig(-dfrac{b_2}{a_2}Big) = MBig(-dfrac{b_2}{a_2}Big) cdot L_1Big(-dfrac{b_2}{a_2}Big) cdot L_2Big(-dfrac{b_2}{a_2}Big) - dfrac{A_1cdot b_2}{a_2}+B_1 to L_2Big(-dfrac{b_2}{a_2}Big) = 0\\HBig(-dfrac{b_2}{a_2}Big) = B_1 - dfrac{A_1cdot b_2}{a_2} = dfrac{a_2B_1-A_1b_2}{a_1}$

$1) ; H(x) = P(x)cdot F(x)\\HBig(dfrac{1}{2}Big) = PBig(dfrac{1}{2}Big) cdot FBig(dfrac{1}{2}Big) \\HBig(dfrac{1}{2}Big) = 2cdot (-2) = -4\\\2); HBig(-dfrac{2}{3};Big) = PBig(-dfrac{2}{3};Big) cdot FBig(-dfrac{2}{3};Big) \\HBig(-dfrac{2}{3};Big) = (-3)cdot 6 = -18$

$3); HBig(dfrac{1}{2}Big) = -4 = dfrac{A_1}{2} + B_1\\A_1+2B_1 = -8\\2A_1+4B_1 = -16\\ HBig($-dfrac{2}{3}Big)$ = -18 = -dfrac{2A_1}{3} + B_1\\-2A_1+3B_1 = -54$

$begin{arranged}-2A_1+3B_1 = -54\ 2A_1+4B_1 = -16\noindentrule{4cm}{1pt} ;;boldsymbol{+}\B_1 = -10 to A_1 = -8+20 = 12end{arranged}$

sisa :

$boxed{text{Huge{$boldsymbol{S(x) = 12x-10}$}}}$