Math, asked by HALLOOBRAINLYYHRU, 6 hours ago

1. Consider P(x) = x3 + 8x2 + 17x + 10.
a. List the integer divisors of 1, the leading coefficient (d).
b. List the integer divisors of 10, the constant term (c).
c. Give all the possible ratios of a divisor of 10 to a divisor of 1, which is ).
d. Find a root of P(x) = 0 from the rational numbers obtained in letter c.
e. Use synthetic division to find the remaining factors.
f. Give the three roots of the equation.
g. Write P(x) as a product of linear factors.
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Answers

Answered by ItsInnocentGirl
4

Answer:

P(x) = x3 + 8x2 + 17x + 10.

Step-by-step explanation:

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Answered by pavanadevassy
2

Answer:

The roots of the equation are -1, -5 and -2.

Step-by-step explanation:

Given the polynomial

P(x)=x^3+8x^2+17x+10

a) Integer divisors of 1 are 1 and -1.

b) Integer divisors of 10 are 1,-1,2,-2,5,-5,10 and -10.

c) All possible ratios of a divisor of 10 to a divisor of 1 are 1,-1,2,-2,5,-5,10 and -10.

d) We can now find a root of P(x) from the above set of numbers.

x=1\implies P(x)=10

x=-1\implies P(x)=-1+8-17+10=0.

So x=-1 is root of the given polynomial.

e) Now using synthetic division, we get

x^3+8x^2+17x+10=(x+1)(x^2+7x+10)=(x+1)(x+5)(x+2)

f) Roots of the equation are x=-1,-5,-2

g) P(x)=(x+1)(x+5)(x+2)

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