i need help i don't know how to do the next step.
factor by grouping
x^3-3x^2+4x-12
so what i have so far is this
=(x^3-3x^2)+(4x-12)
=x(x^2-3x)+4(x-3)
from here i don't know...
and then this one is driving me insane this next one...
Rewrite the middle term as the sum of two terms and then factor by grouping.
x^2-14x+45
i'd figure out problem #1
these are the steps I did:
factor by grouping
x^3-3x^2+4x-12
so what i have so far is this
=(x^3-3x^2)+(4x-12)
=x^2(x-3)+4(x-3)
= (x-3)(x^2+4)
I AM STILL HAVING TROUBLE WITH PROBLEM NUMBER 2
to your second question
wouldnt it be-
(x-5)(x-9)
You have to find 2 numbers to multiply to bed 45 BUT add to be negative 14.
yes,thank you......
For the first problem, you are on the right track with factor by grouping. Let's continue from where you left off:
Rewrite the expression as:
=(x^2(x-3)) + 4(x-3)
Now, take the common factor out:
=(x-3)(x^2 + 4)
That's the final factored form.
For the second problem, you need to rewrite the middle term as the sum of two terms. The coefficient of the middle term, -14x, is negative, so you need to find two numbers that multiply to be 45 and add up to be -14. Based on your answer, it seems like you found the correct pair of numbers, which are -5 and -9.
So, the expression can be rewritten as:
x^2 - 5x - 9x + 45
Now, you can factor by grouping. Take the common factors from the first two terms and the last two terms separately:
= (x^2 - 5x) + (-9x + 45)
Take the common factor out from each group:
= x(x - 5) - 9(x - 5)
Notice that now we have a common factor, which is (x - 5). We can factor it out:
= (x - 5)(x - 9)
That's the final factored form.
I hope these explanations help you with your problems! Let me know if you have any more questions.