Using factoring by grouping, how would you factor these out.
4t^2+3t-4t-3
3t^2-1t-3t+1
Thank you
To factor these quadratics using factoring by grouping, you need to group the terms in a way that allows you to factor out a common factor.
Let's start with the first quadratic: 4t^2 + 3t - 4t - 3.
Step 1: Group the terms.
Group the first two terms, 4t^2 + 3t, and the last two terms, -4t - 3.
(4t^2 + 3t) + (-4t - 3)
Step 2: Factor out the common factors from each group.
From the first group, factor out the common factor of t: t(4t + 3).
From the second group, factor out the common factor of -1: -1(4t + 3).
Step 3: Factor out the common binomial.
Now, you have (t - 1)(4t + 3).
So, the factored form of 4t^2 + 3t - 4t - 3 is (t - 1)(4t + 3).
Let's move on to the second quadratic: 3t^2 - 1t - 3t + 1.
Step 1: Group the terms.
Group the first two terms, 3t^2 - 1t, and the last two terms, -3t + 1.
(3t^2 - 1t) + (-3t + 1)
Step 2: Factor out the common factors from each group.
From the first group, factor out the common factor of t: t(3t - 1).
From the second group, factor out the common factor of -1: -1(3t - 1).
Step 3: Factor out the common binomial.
Now, you have (t - 1)(3t - 1).
So, the factored form of 3t^2 - 1t - 3t + 1 is (t - 1)(3t - 1).
I hope this explanation helps you understand how to use factoring by grouping to factor quadratics.