13) \( 4 m^{2}-9 m-9 \) 15) \( 6 p^{2}-11 p-7 \) 17) \( 4 r^{2}+3 r-7 \) 19) \( 3 x^{2}+10 x-8 \) 21) \( 2 y^{2}+15 y+7 \) 23) \( 4 x^{2}+16 x+16 \) 25) \( 10 x^{3}+15 x^{2}-10 x \) 27) \( 5 t^{2}+15 t+10 \) 29) \( 7 x^{2}-2 x y-5 y^{2} \)
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The Deep Dive
Got some quadratic polynomials and a cubic one to factor? Let's dive into the fun world of factorization! Remember, quadratic equations can often be simplified using techniques like completing the square or applying the quadratic formula. For instance, in \( 4 m^2 - 9 m - 9 \), look for two numbers that multiply to \( a*c \) (in this case, \(4 * -9\) = -36) while summing to \( b \) (-9). It's a puzzle waiting to be solved! Now, for polynomials like \( 10 x^3 + 15 x^2 - 10 x \), don't forget to factor out the greatest common factor first! Here, you can take out \( 5x \), leaving you with \( 2x^2 + 3x - 2 \). This step can make the rest of your factoring journey smoother and more manageable, just like finding the best route to a treasure in a pirate map!
