Question

Write quotient and remainder (y²+6y+5)÷(y+5)
explanation and solution please
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Answer 1

Answer:

remainder =0

quotient=(y+1)

Step-by-step explanation:

p(y)=y²+6y+5

f(y)=y+5

by remainder theorem,

if x-a is divisor p(a)=remainder

therfore,

comparing (y+5) with X-a,

we get,

a=-5

p(-5)=remainder

=(-5)²+6*(-5)+5

=25-30+5

=0

let other factor be(y-a)

by factor theorem,

p(a)=0,

=>a²+6a+5=0

=>a²+a(5+1)+5=0

=>a²+5a+1a+5=0

=>a(a+5)+1(a+5)=0

=>(a+1)(a+5)=0

so, a=-1,a=-5;

factors are

(y+1)and(y+5)