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)
Question 1:
For this case we must factor the expression:
[tex]x ^ 2-25[/tex]
Rewriting the expression:
[tex]x ^ 2-5 ^ 2[/tex]
By definition, we have to fulfill that:
[tex](a ^ 2-b ^ 2) = (a + b) (a-b)[/tex]
So, we can factor the expression as:
[tex]x ^ 2-25 = (x-5) (x + 5)[/tex]
Answer:
[tex](x-5) (x + 5)[/tex]
Question 2:
For this case we must factor the expression:
[tex]9x ^ 2-81[/tex]
We take common factor 9 from the expression:
[tex]9 (x ^ 2-9)[/tex]
By definition, we have to fulfill that:
[tex](a ^2 -b ^ 2) = (a + b) (a-b)[/tex]
Finally, rewriting the expression we have:
[tex]9 (x-3) (x + 3)[/tex]
Answer:
[tex]9 (x-3) (x + 3)[/tex]
Question 3:
For this case we must factor the expression:
[tex]x ^ 2 + 2x-8[/tex]
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:
[tex]+ 4-2 = 2\\+ 4 * -2 = -8[/tex]
Thus, we can factor the expression as:
[tex](x + 4) (x-2)[/tex]
Answer:
[tex](x + 4) (x-2)[/tex]
Question 4:
For this case we must factor the expression:
[tex]4x ^ 2 + 8x-21[/tex]
We rewrite the middle term as:
[tex]4x ^ 2-14x + 6x-21[/tex]
We group:
[tex](4x ^ 2-14x) + (6x-21)[/tex]
We draw common factor from each group:
[tex]2x (2x-7) +3 (2x-7)[/tex]
We take common factor [tex](2x-7):[/tex]
[tex](2x + 3) (2x-7)[/tex]
Answer:
[tex](2x + 3) (2x-7)[/tex]
Question 5:
For this case we must factor the expression:
[tex]x ^ 2-2x + 24[/tex]
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:
[tex]2x ^ 3 + 4x ^ 2-6x[/tex]
We take 2x common factor:
[tex]2x (x ^ 2 + 2x-3)[/tex]
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:
[tex]2x (x + 3) (x-1)[/tex]
Answer:
[tex]2x (x + 3) (x-1)[/tex]
