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) $$ 7 x^{2}-2 x y-5 y^{2} $$

Question

UpStudy AI · Accepted Answer

Factor the expression by following steps:
- step0: Factor:
  $$6p^{2}-11p-7$$
- step1: Rewrite the expression:
  $$6p^{2}+\left(-14+3\right)p-7$$
- step2: Calculate:
  $$6p^{2}-14p+3p-7$$
- step3: Rewrite the expression:
  $$2p\times 3p-2p\times 7+3p-7$$
- step4: Factor the expression:
  $$2p\left(3p-7\right)+3p-7$$
- step5: Factor the expression:
  $$\left(2p+1\right)\left(3p-7\right)$$
Factor the expression $$ 7 x^{2}-2 x y-5 y^{2 $$.
Factor the expression by following steps:
- step0: Factor:
  $$7x^{2}-2xy-5y^{2}$$
- step1: Rewrite the expression:
  $$7x^{2}+\left(-7+5\right)xy-5y^{2}$$
- step2: Calculate:
  $$7x^{2}-7xy+5yx-5y^{2}$$
- step3: Rewrite the expression:
  $$7x\times x-7xy+5yx-5y\times y$$
- step4: Factor the expression:
  $$7x\left(x-y\right)+5y\left(x-y\right)$$
- step5: Factor the expression:
  $$\left(7x+5y\right)\left(x-y\right)$$
Factor the expression $$ 3 x^{2}+10 x-8 $$.
Factor the expression by following steps:
- step0: Factor:
  $$3x^{2}+10x-8$$
- step1: Rewrite the expression:
  $$3x^{2}+\left(-2+12\right)x-8$$
- step2: Calculate:
  $$3x^{2}-2x+12x-8$$
- step3: Rewrite the expression:
  $$x\times 3x-x\times 2+4\times 3x-4\times 2$$
- step4: Factor the expression:
  $$x\left(3x-2\right)+4\left(3x-2\right)$$
- step5: Factor the expression:
  $$\left(x+4\right)\left(3x-2\right)$$
Factor the expression $$ 4 m^{2}-9 m-9 $$.
Factor the expression by following steps:
- step0: Factor:
  $$4m^{2}-9m-9$$
- step1: Rewrite the expression:
  $$4m^{2}+\left(3-12\right)m-9$$
- step2: Calculate:
  $$4m^{2}+3m-12m-9$$
- step3: Rewrite the expression:
  $$m\times 4m+m\times 3-3\times 4m-3\times 3$$
- step4: Factor the expression:
  $$m\left(4m+3\right)-3\left(4m+3\right)$$
- step5: Factor the expression:
  $$\left(m-3\right)\left(4m+3\right)$$
Factor the expression $$ 4 x^{2}+16 x+16 $$.
Factor the expression by following steps:
- step0: Factor:
  $$4x^{2}+16x+16$$
- step1: Factor the expression:
  $$4\left(x+2\right)^{2}$$
Factor the expression $$ 4 r^{2}+3 r-7 $$.
Factor the expression by following steps:
- step0: Factor:
  $$4r^{2}+3r-7$$
- step1: Rewrite the expression:
  $$4r^{2}+\left(7-4\right)r-7$$
- step2: Calculate:
  $$4r^{2}+7r-4r-7$$
- step3: Rewrite the expression:
  $$r\times 4r+r\times 7-4r-7$$
- step4: Factor the expression:
  $$r\left(4r+7\right)-\left(4r+7\right)$$
- step5: Factor the expression:
  $$\left(r-1\right)\left(4r+7\right)$$
Factor the expression $$ 2 y^{2}+15 y+7 $$.
Factor the expression by following steps:
- step0: Factor:
  $$2y^{2}+15y+7$$
- step1: Rewrite the expression:
  $$2y^{2}+\left(1+14\right)y+7$$
- step2: Calculate:
  $$2y^{2}+y+14y+7$$
- step3: Rewrite the expression:
  $$y\times 2y+y+7\times 2y+7$$
- step4: Factor the expression:
  $$y\left(2y+1\right)+7\left(2y+1\right)$$
- step5: Factor the expression:
  $$\left(y+7\right)\left(2y+1\right)$$
Factor the expression $$ 5 t^{2}+15 t+10 $$.
Factor the expression by following steps:
- step0: Factor:
  $$5t^{2}+15t+10$$
- step1: Rewrite the expression:
  $$5t^{2}+5\times 3t+5\times 2$$
- step2: Factor the expression:
  $$5\left(t^{2}+3t+2\right)$$
- step3: Factor the expression:
  $$5\left(t+1\right)\left(t+2\right)$$
Factor the expression $$ 10 x^{3}+15 x^{2}-10 x $$.
Factor the expression by following steps:
- step0: Factor:
  $$10x^{3}+15x^{2}-10x$$
- step1: Rewrite the expression:
  $$5x\times 2x^{2}+5x\times 3x-5x\times 2$$
- step2: Factor the expression:
  $$5x\left(2x^{2}+3x-2\right)$$
- step3: Factor the expression:
  $$5x\left(x+2\right)\left(2x-1\right)$$
Here are the factorizations for the given expressions:

1. **For $$ 4 m^{2}-9 m-9 $$**:
   $$
   4 m^{2}-9 m-9 = (m-3)(4m+3)
   $$

2. **For $$ 6 p^{2}-11 p-7 $$**:
   $$
   6 p^{2}-11 p-7 = (2p+1)(3p-7)
   $$

3. **For $$ 4 r^{2}+3 r-7 $$**:
   $$
   4 r^{2}+3 r-7 = (r-1)(4r+7)
   $$

4. **For $$ 3 x^{2}+10 x-8 $$**:
   $$
   3 x^{2}+10 x-8 = (x+4)(3x-2)
   $$

5. **For $$ 2 y^{2}+15 y+7 $$**:
   $$
   2 y^{2}+15 y+7 = (y+7)(2y+1)
   $$

6. **For $$ 4 x^{2}+16 x+16 $$**:
   $$
   4 x^{2}+16 x+16 = 4(x+2)^{2}
   $$

7. **For $$ 10 x^{3}+15 x^{2}-10 x $$**:
   $$
   10 x^{3}+15 x^{2}-10 x = 5x(x+2)(2x-1)
   $$

8. **For $$ 5 t^{2}+15 t+10 $$**:
   $$
   5 t^{2}+15 t+10 = 5(t+1)(t+2)
   $$

9. **For $$ 7 x^{2}-2 x y-5 y^{2} $$**:
   $$
   7 x^{2}-2 x y-5 y^{2} = (7x+5y)(x-y)
   $$

These factorizations simplify the expressions into products of binomials or polynomials. If you have any further questions or need additional assistance, feel free to ask!
Here are the factorizations: 1. $$ 4 m^{2}-9 m-9 = (m-3)(4m+3) $$ 2. $$ 6 p^{2}-11 p-7 = (2p+1)(3p-7) $$ 3. $$ 4 r^{2}+3 r-7 = (r-1)(4r+7) $$ 4. $$ 3 x^{2}+10 x-8 = (x+4)(3x-2) $$ 5. $$ 2 y^{2}+15 y+7 = (y+7)(2y+1) $$ 6. $$ 4 x^{2}+16 x+16 = 4(x+2)^{2} $$ 7. $$ 10 x^{3}+15 x^{2}-10 x = 5x(x+2)(2x-1) $$ 8. $$ 5 t^{2}+15 t+10 = 5(t+1)(t+2) $$ 9. $$ 7 x^{2}-2 x y-5 y^{2} = (7x+5y)(x-y) $$

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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