help please

Question

factor these polynomials:

 

A) 3x^2-75

 

B) x^2-3x+5x-15

 

C) x^2-7x+12

Answer 1

If you have a polynomial in standard form, ax²+bx+c, if a≠1 then you need to find the numbers that multiples to a*c and adds to b. Then you need to do factor by grouping. If a=1 then you need to find the numbers that multiples to c and adds to b and go from there. 

 

Note: Always try and factor out common terms first!! It will make everything easier.

 

Here is my work for A, B, and C. Let me know if you need clarification on anything.

 

A) 3x²-75

 

So here a=3, b=0, and c=-75. We can notice that both terms have a common term of 3 thus we can factor it out.

3(x²-25)

 

Now we are just left with factoring the expression x²-25. In this case, a=1,b=0, and c=-25. What numbers multiply together to equal -25 and add to 0? The numbers -5 and 5 will satisfy.

 

Thus the expression 3x²-75 factors too 3(x-5)(x+5)

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B) x²-3x+5x-15

 

First join like terms, so now we have x²+2x-15

 

So now what numbers multiply to -15 and add to 2? -3 and 5 will do the trick.

 

Thus we factor the expression to (x-3)(x+5)

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C) x²-7x+12

 

So what numbers multiply to 12 and add to -7?

Yep, -3 and -4.

 

So we can factor the expression to, (x-3)(x-4)

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Hope this helps!!!

Answer 2

3x² - 75

3(x² - 25)

From here we have "The difference of two squares. That means that the factorization will be the square roots with a positive and negative sign:

3(x + 5)(x - 5)

 

x² - 3x + 5x - 15

x(x - 3) + 5(x - 3)

Careful you don't accidentally add them together to make 5x(x-3) because distributing that back out will give a totally different answer.

 

x² - 7x + 12

let's look at the m and n to see how they can create -7 and 12:

-3 * -4 = 12

-3 - 4 = -7

(x - 3)(x - 4)