Can u help me factor the expression?

Question

3. x^2-16
4. x^2+12x+36
5. x^2+10x+25
6. 3x^3+9x^2+2x
7. x^3-3x^2+2x-6
8. x^2-x^2+5x-5

Please i would appreciate it I really don't understand this Plez help me this is worth 50% of my finals

Answer 1

When your factoring, your looking for common terms so that you can simplify the expression down to its simpliest for form. Ill walk through each problem because each ahs a different situation:

X^2-16: we know that we need two numbers that will give us -16 when we multiply them, but because their no second X term, they also need to equal 0 when we add them. 4 and -4 are the answers because 4 times -4 equals 16 but 4+(-4)=0. So the factored form of this problem should look like (X+4)(X-4)

X^2+12X+36: Same scenario except now we need to find two numbers that will give us 36 when we multiply and 12 when we add them. 6 and 6 are the answers since 6 time 6=36 and 6+6=12. So the answers are (X+6)(X+6).

X^2+10X+25: Same scenario as the last problem; 2 numbers that give us 10 when add but 25 when we multiply. 5 and 5 are the answers since 5+5=10 and 5 times 5 =25. so the answer is (X+5)(X+5).

3X^3+9X^2+2x: You might have written this wrong because their is no defenitive answer. The closest you can get to factoring this one is by facotring out the common X in every term, so the problem reads X(3X^2+9X+2). That's as far as you can go by facotring.

X^3-3X^2+2X-6: Since there are 4 terms here, work only side of the problem at a time. First draw a line between 3X^2 and +2X. Now only worrying about the left side, factor out a common term in X^3 and -3X^2. Notice that each term can be factored by X^2. Now it should look like X^2(X-3). Now work on the other side. Now we see that the coefficient of 2x can be factored out. Now it should read 2(X-3). If youve done all the steps correctly, you should have X^2(X-3), then your line, 2(X-3). Now the last step is to combine the X^2 and the 2 that our outside the parenthesis, and because their are 2 (X-3)'s, we will only need one in the final product. So now your solution should be: (X^2+2)(X-3).

X^2-X^2+5X-5: Cross out the 2 X^2's because of one being negative and one positive. Now your left with 5x-5. Factor out 5 from the expression so that it reads 5(X-1).

Just remember the different rules for different expressions and youll be fine. Good luck on the Final

Answer 2

i attempted this stunt: pass the three from the front end to the back, giving x^2 + 5x -6. This tells us that we could like 2 numbers, whose distinction is 5 and product is 6. for sure, a million and 6 qualify. So, in case you progression the three back the place it started out, you land up with a million and a couple of, so which you have (3x -a million)(x + 2). If no longer the rest works, you could constantly equate the expression to 0, sparkling up the effect with the quadratic formulation, and if the roots are r1 and r2, the expression has aspects (x - r1)(x - r2). That performs whether the roots are complicated, even with the certainty that for the time of that case one many times says that the expression is top.

Answer 3

x^2-16

all the terms are squarred so you just find the square roots..
square foot of x^2 = x
square root of -16 = 4
since the sight *before* the constant (16) is negative, one of your fours should also be negative, both cannot be negative because two negatives make a positive
Ans:
(x+4)(x-4)

4...
factors of 36 with add to 12? (6+6)
since all the signs are positive, you keep it that way
(x+6)(x+6)

5....
factors of 25 which add up to 10? (5+5)
(x+5)(x+5)

6...
to make it easier first you factorise out the x
x(3x^2+9x+2)
now, do it normal like before though this one has a slight change
since the x^2 term has a 3 before it, you multiple the constant (2) by 3 before you start
factors of 6 (3x2) which...

GOOD LUCK :)

Answer 4

I'll do a couple

3. x^2-16
Think of it this way. What 2 numbers multiplied together equal 16, and added equal 0? -4, 4
Answer is (x-4)(x+4)

4. x^2+12x+36
What 2 numbers multiply to get 36 and add to get 12?
6, 6
(x+6)(x+6) or (x+6)^2


Hopefully you got the hang of it

Answer 5

3. (x+4)(x-4)
4. (x+6)(x+6)
5. (x+5)(x+5)
6.
7. (x+3)(x^2 +2)
8. 5(x-1)

Have you mistyped some of these?

Answer 6

3)

x² - 16 =

(x - 4)(x + 4)

4)

x² + 12x + 36 = 0

Group factor

x² + 6x + 6x + 36 = 0

x(x + 6) + 6(x + 6) = 0

(x + 6)(x + 6) = 0

- - - - - - - -s-

Answer 7

3. (x+4)(x-4)
4. (x+6)(x+6)
5. (x+5)(x+5)

sorry thats all i noe

good luck