Use the Factor Theorem to verify that each linear binomial is a factor of the given
polynomial. Then use synthetic division to write the polynomial as a product.
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I hope this answer helpful to you
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Step-by-step explanation:
factor theorem: (x-a) is a factor of f(x) only if the remainder f(a)=0
P(2)=2⁴-2×2³+5×2²-9×2-2 = 16-16+20-18-2 =0
hence (x-2) is a factor of P(x)
synthetic division:
1 -2 5 -9 -2
x=2 0 2 0 10 2
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1 0 5 1 (0)
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quotient = x³+0x²+5x+1 =x³+5x+1
P(x) = (x-2)(x³+5x+1)
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