Question

Quadratic Functions Please help!! questions attached

Answer 1

Answers:

22) x^- 25 think about the 5 times table

(x-5)(x+5)

23) x^2+2x-8 think two numbers that equals to -8 and 2x

( x+4)(x-2)

24) x^2-2x+24 : not factorable because no numbers equal for 2x.

25) 9x^2-81 - use 9 times table

(3x-9)(3x+9)

26) 4x^2+8x-21

(2x-3)(2x+7)

27)2x^3+4x^ 2 -6x

2x(x-1)(x+3)

Answer 2

Question 1:

For this case we must factor the expression:

`x ^ 2-25`

Rewriting the expression:

`x ^ 2-5 ^ 2`

By definition, we have to fulfill that:

`(a ^ 2-b ^ 2) = (a + b) (a-b)`

So, we can factor the expression as:

`x ^ 2-25 = (x-5) (x + 5)`

Answer:

`(x-5) (x + 5)`

Question 2:

For this case we must factor the expression:

`9x ^ 2-81`

We take common factor 9 from the expression:

`9 (x ^ 2-9)`

By definition, we have to fulfill that:

`(a ^2 -b ^ 2) = (a + b) (a-b)`

Finally, rewriting the expression we have:

`9 (x-3) (x + 3)`

Answer:

`9 (x-3) (x + 3)`

Question 3:

For this case we must factor the expression:

`x ^ 2 + 2x-8`

To factor, we must find two numbers that, when multiplied, are obtained -8, and when added together, +2 is obtained. These numbers are +4 and -2:

`+ 4-2 = 2\\+ 4 * -2 = -8`

Thus, we can factor the expression as:

`(x + 4) (x-2)`

Answer:

`(x + 4) (x-2)`

Question 4:

For this case we must factor the expression:

`4x ^ 2 + 8x-21`

We rewrite the middle term as:

`4x ^ 2-14x + 6x-21`

We group:

`(4x ^ 2-14x) + (6x-21)`

We draw common factor from each group:

`2x (2x-7) +3 (2x-7)`

We take common factor
`(2x-7):`

`(2x + 3) (2x-7)`

Answer:

`(2x + 3) (2x-7)`

Question 5:

For this case we must factor the expression:

`x ^ 2-2x + 24`

To factor, we must find two numbers that, when multiplied, are obtained 24, and when added together, -2 is obtained. These numbers do not exist. Thus, the expression cannot be factored with rational numbers.

Answer:

The expression cannot be factorized with rational numbers.

Question 6:

For this case we must factor the expression:

`2x ^ 3 + 4x ^ 2-6x`

We take 2x common factor:

`2x (x ^ 2 + 2x-3)`

To factor the expression within the parenthesis, we must find two numbers that when multiplied are obtained -3, and when added together, +2 is obtained. These numbers are +3 and -1:

Thus, we can factor the complete expression as:

`2x (x + 3) (x-1)`

Answer:

`2x (x + 3) (x-1)`