use factor theorem to determine where X is a factor of PX where x is e

1.	use factor theorem to determine where X is a factor of PX where x is equal to x minus 1 and X is equal to 2 root 2 x cube + 5 root 2 x square - 7 root 2
Answer» <P> $\large{\sf{\underline{\red{Correct\:Question:-}}}}$ p(x) = 2√2x³ + 5√2x² -7√2 Use factor theorem and show that, (x - 1) is a factor of p(x) $\large{\sf{\underline{\red{Answer:-}}}}$ $\underline{\boxed{\bf{\blue{Factor\:theorem:}}}}$ Let p(x) be a polynomial. If p(a) = 0 then (x - a) is a factor of p(x) Conversely, we can SAY that if (x - a) is a factor of p(x), then p(a) is it's one zero. $\mathtt{\underline{HERE,}}$ Here we can see that the (x - a) term is equal to (x -1) So we can say that a = 1 We have to PROVE p(a) that is p(1) = 0, to show that (x - 1) is a factor. We know, p(x) = 2√2x³ + 5√2x² -7√2 $\underline{\green{\bf{finding\:p(1):-}}}$ p(1) = (2√2 * 1 * 1 * 1) + (5√2 * 1 * 1) - 7√2 $\implies$ p(1)= 2√2 + 5√2 - 7√2 $\implies$ p(1) = 7√2 - 7√2 $\implies$ p(1) = 0 $\sf{\orange{p(1)\:=\:0\:hence\:(x\:-\:1)\:is\:a\:factor\:of\:p(x)}}$