Factor by Grouping.please show me the steps!!!!!!!
1.) y2+11y+30
2.) x2+4x-5
3.) a2-a-56
what multiples to the last term, and add to the second?
1) 6,5
2) 5,-1
3) -8,7 Notice when signs are different, you place the sign of the middle term on the larger
So, on 3, for instance...the answer is..
(x-8)(x+7)
you do the others, I will check if you need it.
Sure, I'd be happy to explain the steps for factoring by grouping. Factoring by grouping is a method used to factorize quadratic expressions that have four terms.
Let's go through the steps for each expression you provided:
1.) y^2 + 11y + 30:
To factor this expression, we look for two numbers that multiply to give us 30 and add up to 11 (the coefficient of y in this case). The numbers that meet this criteria are 5 and 6.
So, we can begin by splitting the middle term as follows:
y^2 + 5y + 6y + 30
Now, we group the terms together:
(y^2 + 5y) + (6y + 30)
Next, we factor out the greatest common factor from each group:
y(y + 5) + 6(y + 5)
Notice that now we have a common factor, which is (y + 5). So, we can factor out this common factor:
(y + 5)(y + 6)
Thus, the factored form of y^2 + 11y + 30 is (y + 5)(y + 6).
2.) x^2 + 4x - 5:
To factor this expression, we look for two numbers that multiply to give us -5 and add up to 4 (the coefficient of x in this case). The numbers that meet this criteria are 5 and -1.
So, we can rewrite the middle term as:
x^2 + 5x - x - 5
Now, we can group the terms together:
(x^2 + 5x) + (-x - 5)
Next, we factor out the greatest common factor from each group:
x(x + 5) - (x + 5)
Again, we can see that we have a common factor, which is (x + 5). So, we factor out this common factor:
(x + 5)(x - 1)
Therefore, the factored form of x^2 + 4x - 5 is (x + 5)(x - 1).
3.) a^2 - a - 56:
To factor this expression, we look for two numbers that multiply to give us -56 and add up to -1 (the coefficient of a in this case).
The numbers that meet this criteria are -8 and 7.
So, we rewrite the middle term as:
a^2 - 8a + 7a - 56
Next, we can group the terms together:
(a^2 - 8a) + (7a - 56)
We factor out the greatest common factor from each group:
a(a - 8) + 7(a - 8)
Finally, we have a common factor of (a - 8), so we can factor it out:
(a - 8)(a + 7)
Therefore, the factored form of a^2 - a - 56 is (a - 8)(a + 7).
I hope this step-by-step explanation helps you understand how to factor by grouping.