Question

p(x)=x³-2x²-19x+20 g(x)=x²-6x+5​

Answer 1

Answer and explanation:

$g(x) = x^{2} - 6x + 5 = x^{2} - 5x - x + 5 = x(x-5) - 1(x-5)$

$g(x) = (x-5)(x-1)$

Therefore, zeroes of g(x) are 1 and 5. Hence, if p(1) and p(5) are equal to 0, then p(x) is divisible by g(x)

$p(1) = 1^{3} - 2(1^{2} ) - 19(1) + 20 = 1 - 2 - 19 + 20$

$p(1) = 0$

$p(5) = 5^{3} - 2(5^{2}) - 19(5) - 20 = 125 - 50 - 95 + 20$

$p(5) = 0$

Hence, g(x) is a factor of p(x).

Answer 2

Step-by-step explanation:

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