ตอนที่ 2 อัตนัย ข้อ \( 15-20 \) เขียนเติมเฉพาะคำตอบลงในกระดาษคำตอบ จงแยกตัวประกอบของพหุนามต่อไปนี้ (ข้อ \( 15-19) \) 15. \( 6 t^{2}-12 t+s t^{2}-2 s t \) 16. \( 9 y^{2}-15 y+6 \) 17. \( x^{2}-22 x+120 \) 18. \( (a+2)^{2}+14\left(a^{2}+2 a\right)+49 a^{2} \) 19. \( (4 y-5)^{2}-(3 y+7)^{2} \) 20. จากพหุนาม \( (-1)\left(10-53 y-36 y^{2}\right) \) เมื่อจัดอยู่ในรูปทั่วไป ค่าของ \( a, b \) และ \( c \) คือ จำนวนใด

Simplify the expression by following steps: - step0: : \(6t^{2}-12t+st^{2}-2st\) Solve the equation \( x^{2}-22 x+120=0 \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(x^{2}-22x+120=0\) - step1: Factor the expression: \(\left(x-12\right)\left(x-10\right)=0\) - step2: Separate into possible cases: \(\begin{align}&x-12=0\\&x-10=0\end{align}\) - step3: Solve the equation: \(\begin{align}&x=12\\&x=10\end{align}\) - step4: Rewrite: \(x_{1}=10,x_{2}=12\) Solve the equation \( -1(10-53 y-36 y^{2})=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(-\left(10-53y-36y^{2}\right)=0\) - step1: Multiply the terms: \(-10+53y+36y^{2}=0\) - step2: Rewrite in standard form: \(36y^{2}+53y-10=0\) - step3: Solve using the quadratic formula: \(y=\frac{-53\pm \sqrt{53^{2}-4\times 36\left(-10\right)}}{2\times 36}\) - step4: Simplify the expression: \(y=\frac{-53\pm \sqrt{53^{2}-4\times 36\left(-10\right)}}{72}\) - step5: Simplify the expression: \(y=\frac{-53\pm \sqrt{4249}}{72}\) - step6: Separate into possible cases: \(\begin{align}&y=\frac{-53+\sqrt{4249}}{72}\\&y=\frac{-53-\sqrt{4249}}{72}\end{align}\) - step7: Rewrite the fraction: \(\begin{align}&y=\frac{-53+\sqrt{4249}}{72}\\&y=-\frac{53+\sqrt{4249}}{72}\end{align}\) - step8: Rewrite: \(y_{1}=-\frac{53+\sqrt{4249}}{72},y_{2}=\frac{-53+\sqrt{4249}}{72}\) Expand the expression \( (a+2)^{2}+14(a^{2}+2 a)+49 a^{2} \) Simplify the expression by following steps: - step0: Add the terms: \(\left(a+2\right)^{2}+14\left(a^{2}+2a\right)+49a^{2}\) - step1: Expand the expression: \(a^{2}+4a+4+14\left(a^{2}+2a\right)+49a^{2}\) - step2: Expand the expression: \(a^{2}+4a+4+14a^{2}+28a+49a^{2}\) - step3: Add the terms: \(64a^{2}+32a+4\) Solve the equation \( 9 y^{2}-15 y+6=0 \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(9y^{2}-15y+6=0\) - step1: Factor the expression: \(3\left(y-1\right)\left(3y-2\right)=0\) - step2: Divide the terms: \(\left(y-1\right)\left(3y-2\right)=0\) - step3: Separate into possible cases: \(\begin{align}&y-1=0\\&3y-2=0\end{align}\) - step4: Solve the equation: \(\begin{align}&y=1\\&y=\frac{2}{3}\end{align}\) - step5: Rewrite: \(y_{1}=\frac{2}{3},y_{2}=1\) Solve the equation \( (4 y-5)^{2}-(3 y+7)^{2}=0 \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(\left(4y-5\right)^{2}-\left(3y+7\right)^{2}=0\) - step1: Expand the expression: \(7y^{2}-82y-24=0\) - step2: Factor the expression: \(\left(y-12\right)\left(7y+2\right)=0\) - step3: Separate into possible cases: \(\begin{align}&y-12=0\\&7y+2=0\end{align}\) - step4: Solve the equation: \(\begin{align}&y=12\\&y=-\frac{2}{7}\end{align}\) - step5: Rewrite: \(y_{1}=-\frac{2}{7},y_{2}=12\) ต่อไปนี้คือการแยกตัวประกอบของพหุนามตามที่ระบุในข้อ 15-19 และค่าของ \( a, b, c \) ในข้อ 20: 15. **พหุนาม:** \( 6 t^{2}-12 t+s t^{2}-2 s t \) **การแยกตัวประกอบ:** \( 6t^{2}-12t+st^{2}-2st \) 16. **พหุนาม:** \( 9 y^{2}-15 y+6 \) **ราก:** \( y_{1}=\frac{2}{3}, y_{2}=1 \) 17. **พหุนาม:** \( x^{2}-22 x+120 \) **ราก:** \( x_{1}=10, x_{2}=12 \) 18. **พหุนาม:** \( (a+2)^{2}+14(a^{2}+2 a)+49 a^{2} \) **การแยกตัวประกอบ:** \( 64a^{2}+32a+4 \) 19. **พหุนาม:** \( (4 y-5)^{2}-(3 y+7)^{2} \) **ราก:** \( y_{1}=-\frac{2}{7}, y_{2}=12 \) 20. **พหุนาม:** \( (-1)(10-53 y-36 y^{2}) \) **ค่าของ \( a, b, c \):** \( a = -36, b = 53, c = -10 \) กรุณาตรวจสอบคำตอบและหากมีข้อสงสัยเพิ่มเติมสามารถสอบถามได้!