Question

check whether polynomial
$3 {x }^{2} - 5x + 2$
is the factor of polynomial
$3 {x}^{2} - 5 {x}^{2} - 10 {x}^{2} + 20x - 8$
Verify division algorithm
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Answer 1

p(x)=3x²-5x²-10x²+20x-8

p(x)= -12x²+20x-8

g(x)= 3x²-5x+2

Divide the polynomial p(x) by the polynomial g(x)

$\frac{ - 12 {x}^{2} + 20x - 8 }{3 {x}^{2} - 5x + 2} = - 4$

Since remainder is 0,

Therefore the Polynomial g(x) is a factor of Polynomial p(x)