Factor. 2p^2 + 9p + 9 ____

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Identify a, b, c: Identify a, b, and c in the quadratic expression 2p^2 + 9p + 9. Compare 2p^2 + 9p + 9 with ax^2 + bx + c. a = 2 b = 9 c = 9Find numbers multiply add: Find two numbers that multiply to a*c (2*9 = 18) and add up to b (9). We need to find two numbers that multiply to 18 and add up to 9. After checking possible pairs that multiply to 18 (1 and 18, 2 and 9, 3 and 6), we see that 3 and 6 add up to 9. Two numbers: 3, 6Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in Step 2. 2p^2 + 9p + 9 can be expressed as 2p^2 + 3p + 6p + 9.Factor by grouping: Factor by grouping. Group the terms: (2p^2 + 3p) + (6p + 9). Factor out a common factor from each group. From the first group, we can factor out p: p(2p + 3). From the second group, we can factor out 3: 3(2p + 3).Write factored form: Write the factored form of the expression. Since both groups contain the common factor (2p + 3), we can factor this out: p(2p + 3) + 3(2p + 3) = (p + 3)(2p + 3).Verify factored form: Verify the factored form by expanding it to ensure it matches the original expression. (p + 3)(2p + 3) = 2p^2 + 3p + 6p + 9 = 2p^2 + 9p + 9. The expanded form matches the original expression, so the factoring is correct.

Factor. $\newline$ $2p^2 + 9p + 9$

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Factor. $\newline$ $2p^2 + 9p + 9$