Answer:
- [tex]x^{2} +12x+36[/tex] [tex]\\[/tex]----- factors [tex](x+6)^{2}[/tex]
- [tex]4x^{2} +24x+36[/tex] ----- factors [tex](2x+6)^{2}[/tex]
- [tex]2x^{2} +10x+8[/tex] ------ factors (2x+2)(x+4)
- [tex]y^{2} -4[/tex] --------- factor (y+2)(y-2)
Step-by-step explanation:
First bullet is called Perfect Square Trinomial (PST), the first and last is a perfect square and the middle is twice the product of the squared first and last term. To factor, just copy the middle sign and square the first and last term.
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2nd bullet is also a PST with a value on a. Likewise you just need to square the first and last term. Then, copy the middle sign.
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3rd bullet is a trinomial. To get the factor, get the prime factor of the value of a. Then, find the factors of 8 that when add up results to the value of b.
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4th bullet is a special case. First get the square root of the first and last term, and copy the sign, Then, copy the factors and change it to the opposite sign.
