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------------------------------------------------ factor out by grouping 7. x^(2)-2x-8 8. z^(2)-10z+21 9. y^(2)+16y+60 10. 5x^(2)+14x-3 11. 6t^(2)-19t-7 12. 4z^(2)+19z+12

7.(x2-2x-8) - We can't factor this any further since there's no common factor between the terms.
8.We can factor this into (z-7)(z-3).
9.We can factor this into (y+6)(y+10).
10. We can factor this into (x+3)(5x-1).
11. We can factor this into (3t+1)(2t-7).
12. We can factor this into (2z+3)(2z+4).

To factor by grouping, look for common factors in pairs of terms and factor them out. Each of the given polynomials can be factored using this method.

We need to group the terms in pairs and look for a common factor to factor out.

Let's go through each problem:

7.(x2-2x-8) - We can't factor this any further since there's no common factor between the terms.
8.(z2-10z+21) - We can factor this into (z-7)(z-3).
9.(y2+16y+60) - We can factor this into (y+6)(y+10).
10.5x2+14x-3 - We can factor this into (x+3)(5x-1).
11.6t2-19t-7 - We can factor this into (3t+1)(2t-7).
12.4z2+19z+12 - We can factor this into (2z+3)(2z+4).

Learn more about the topic of Factoring by grouping here:

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