Question

Show that (x - √2) is a factor of 7x^2 - 2√8 x - 6​

Answer 1

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BY FACTOR THOREM,

The zero of the polynomial ( x - √2 ) is √2

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Substitute the zero of the polynomial in,

$7 {x}^{2} - 2 \sqrt{8} x - 6$

$7 {( \sqrt{2} )}^{2} - 2 \sqrt{8} ( \sqrt{2} ) - 6$

$7 \times 2 - 2 \sqrt{16} - 6$

$14 - 2 \times 4 - 6$

$14 - 8 - 6$

$14 - 14$

$0$

HENCE, PROVED