Question

Question 4 I need help to solve all 3

Answer 1

• 
  `x^(2) +12x+36`
  `\\`----- factors
  `(x+6)^(2)`
• 
  `4x^(2) +24x+36` ----- factors
  `(2x+6)^(2)`
• 
  `2x^(2) +10x+8` ------ factors (2x+2)(x+4)
• 
  `y^(2) -4` --------- factor (y+2)(y-2)

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.