Factor math problems.. please help?

Question

1. Factor completely: x^2 + 10x + 25
A) (x + 5)(x - 5)
B) (x + 5)(x + 5)
C) (x - 5)(x - 5)
D) (x + 25)(x + 1)

2. Factor completely: 3x^2 - 12
A) 3(x^2 - 4)
B) 3(x + 2)(x + 2)
C) 3(x + 2)(x - 2)
D) (x + 2)(x - 2)

3. Factor completely: 2x^2 - x - 10
A)(2x - 5)(x + 2)
B) (2x + 5)(x - 2)
C) (2x + 5)(x + 2)
D) (2x - 5)(x - 2)

4. Simplify completely: 4x -8 / x-2
A) 4(x-2) / (x-2)
B) 4
C) 8
D) 3x+4

could someone please help me with these math problems.. thanks you ..

Answer 1

x² + 10x + 25

The middle term is + 10x

Find the sum of the middle term

x = 1

Multiply the first term 1 times the last term 25 equals 25 and factor

Factors of 25 =

1 x 25
5 x 5. . .<= . .use these factors

+ 5 and + 5 satisft the sum of the middle term

insert + 5x and + 5x into the equation

x² + 10x + 25

x² + 5x + 5x + 25

x(x + 5) + 5(x + 5)

(x + 5)(x + 5)

- - - - - - - - -s-

Answer 2

1. Factor completely: x^2 + 10x + 25
A) (x + 5)(x - 5)
B) (x + 5)(x + 5)
C) (x - 5)(x - 5)
D) (x + 25)(x + 1)
Answer is B. x*x =x^2; 5*5=25; 5*x+5*x =10x
2. Factor completely: 3x^2 - 12
A) 3(x^2 - 4)
B) 3(x + 2)(x + 2)
C) 3(x + 2)(x - 2)
D) (x + 2)(x - 2)
Answer is C. A is correct but did not go far enough. x^2-4 can be factored to (x+4)(x-4).
3. Factor completely: 2x^2 - x - 10
A)(2x - 5)(x + 2)
B) (2x + 5)(x - 2)
C) (2x + 5)(x + 2)
D) (2x - 5)(x - 2)
Answer is A. 2x*x =2x^2; (-5)(2)=-10;(-5)x +(2x)2 = -x

4. Simplify completely: (4x -8) / (x-2)
A) 4(x-2) / (x-2)
B) 4
C) 8
D) 3x+4
Answer is B. A did not cancel the x-2 terms to get 4. It should that x cannot be equal to 2 or you would be dividing by zero which is a no-no

Answer 3

1. x^2 + 10x + 25 = (x+5)(x+5) = B

2. 3x^2 - 12 = x^2 - 4 = 3(x-2)(x+2) = C

3. 2x^2 - x - 10 = (2x-5)(x+2) = A

4. 4x -8 / x-2 = 4 = B

Answer 4

1. x^2 + 10x + 25
= x^2 + 5x + 5x + 25
= x(x+5) + 5(x+5)
= (x+5)^2
=> B

2. 3x^2 - 12
= 3(x^2 - 4)
= 3 (x^2 - 2^2)
= 3(x-2)(x+2)
=> C

3. B

4. A

Answer 5

1. B, cuz A=x^2-25, C=x^2-10x+25, D=x^2+26x+25
2. C, cuz A isn't completely factored, B=3x^2+12x+12, D=x^2-4
3. A, cuz B=2x^2+x-10, C=2x^2+9x+10, D=2x^2-9x+10
4. B, cuz A isn't completely simplified but when you divide out the (x-2)/(x-2) you are left with 4.

Answer 6

1.
x^2+10x+25
(x+5)(x+5)
The answer is B.

2.
3x^2-12
3(x^2-4)
3(x-2)(x+2)
The answer is C.

3.
2x^2-x-10
(2x-5)(x+2)
The answer is A.

4.
4x-8/x-2
4(x-2)/(x-2)=
4
The answer is B.

Answer 7

1. b
2. c
3. a
4. If it's (4x - 8) / (x - 2), it's b, because 4x - 8 can be expressed as 4 (x - 2)

Answer 8

1. B
2. C
3. A
4. B

Let me know if you need an explanation.

Answer 9

1. b
2. c
3. a
4. b