Question

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 1

$\large{\sf{\underline{\red{Correct\:Question:-}}}}$

• 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

$\sf{\orange{p(1)\:=\:0\:hence\:(x\:-\:1)\:is\:a\:factor\:of\:p(x)}}$