Question

Pleaseeeeeee HELP❤️❤️❤️

Answer 1

C and b

Explanation:

First question:

The polynomial expression we want to factor is x^2-5x-6

Let's calculate the discriminant to find the roots. The discrminant is b^2-4ac

● b= -5

● a = 1

● c = -6

b^2-4ac= (-5)^2-4*1*(-6) = 25+24 = 49>0

So this polynomial expression has two roots since the discriminant is positive

Let x" and x' be the roots:

● x'= (-b-7)/2a = (5-7)/2= -1

● x"= (-b+7)/2a = (5+7)/2 =6

7 is the root square of the discrminant

The factorization of this pulynomial is:

● a(x - x') (x-x")

● 1*(x-(-1)) (x-6)

● (x+1)(x-6)

So the right answer is c

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Second question:

The expression is: (-20*p^(-5)*q*r^(6))/(16*p^(-2)*q^(-3)*r^3)

To make it easier we will simplify the similar terms one by one.

● Constant terms

-20/16 = (-5*4)/(4*4) = -5/4

● terms containing p

-p^(-5)/p^(-2) = p^(-5-(-2)) = p^(-3) =1/p^3

● terms containg q

q/q^(-3)= q(1-(-3)) = q^4

● terms containg r

r^6/r^4 = r^(6-4) = r^2

Multiply all terms together:

● -5/4 *1/p^3 *q^4 *r^2

● (-5*q^4*r^2)/(4p^3)

The right answer is b

Answer 2

1)
`\boxed{Option \ 3}`

2)
`\boxed{Option \ 2}`

Explanation:

A)
`x^2-5x+6`

Using mid term break formula

`x^2-6x+x-6\\x(x-6)+1(x-6)\\Taking \ (x+6) \ as \ common\\(x-6)(x+1)`

B)
`(-20p^(-5)qr^6)/(16p^(-2)q^(-3)r^4)`

Solving it using the two rules: =>
`(a^m)/(a^n) = a^(m-n) \ and \ a^m * a^n = a^(m+n)`

=>
`(-5p^(-3)q^4r^2)/(4)`

We need to put p in the denominator to cancel its negative sign

=>
`(-5q^4r^2)/(4p^3)`