Exercise Zone : Polinom (Suku Banyak)
Tipe:
No.
JikaALTERNATIF PENYELESAIAN
Substitusikan x = 0,
\(\begin{aligned} 2(0)^4+3(0)^3-9(0)+4&=\left(2(0)^2-3(0)+1\right)\left(0^2+p(0)+q\right)\\ 4&=\left(1\right)\left(q\right)\\ q&=4 \end{aligned}\)
Substitusikanx = −1,
\(\begin{aligned} 2(-1)^4+3(-1)^3-9(-1)+4&=\left(2(-1)^2-3(-1)+1\right)\left((-1)^2+p(-1)+4\right)\\ 2-3+9+4&=(2+3+1)(1-p+4)\\ 12&=6(-p+5)\\ 2&=-p+5\\ p&=3 \end{aligned}\)
\(\begin{aligned} p^2-q&=3^2-4\\ &=9-4\\ &=\color{blue}\boxed{\boxed{\color{black}5}} \end{aligned}\)
\(\begin{aligned} 2(0)^4+3(0)^3-9(0)+4&=\left(2(0)^2-3(0)+1\right)\left(0^2+p(0)+q\right)\\ 4&=\left(1\right)\left(q\right)\\ q&=4 \end{aligned}\)
Substitusikan
\(\begin{aligned} 2(-1)^4+3(-1)^3-9(-1)+4&=\left(2(-1)^2-3(-1)+1\right)\left((-1)^2+p(-1)+4\right)\\ 2-3+9+4&=(2+3+1)(1-p+4)\\ 12&=6(-p+5)\\ 2&=-p+5\\ p&=3 \end{aligned}\)
\(\begin{aligned} p^2-q&=3^2-4\\ &=9-4\\ &=\color{blue}\boxed{\boxed{\color{black}5}} \end{aligned}\)
Jadi, p2 − q = 5 .
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