a \( x^{2}-5 x+4 \) \( (x)(x) \) b. \( -700+x^{2}+12 \) c \( 6 x^{2}+21+x-30 \) d. \( 20 x^{2}+33 x+10 \) \( -6 a^{2}+1 d a-4 \) If \( 00^{2}-6 x-8 \) \[ 9 \cdot 8 x^{2}+22 x+5 \]

Let's break down the problem step by step. It seems like you have several expressions and equations that need to be addressed. ### Known Conditions 1. **Expression a**: \( x^{2} - 5x + 4 \) 2. **Expression b**: \( -700 + x^{2} + 12 \) 3. **Expression c**: \( 6x^{2} + 21 + x - 30 \) 4. **Expression d**: \( 20x^{2} + 33x + 10 \) 5. **Expression involving a and d**: \( -6a^{2} + 1da - 4 \) 6. **Expression involving x**: \( 00^{2} - 6x - 8 \) (likely a typo, assuming it should be \( 0^{2} - 6x - 8 \)) 7. **Expression**: \( 9 \cdot 8x^{2} + 22x + 5 \) ### Step 1: Simplifying Each Expression Let's simplify each expression where applicable. 1. **Expression a**: \( x^{2} - 5x + 4 \) is already in its simplest form. 2. **Expression b**: Simplifying \( -700 + x^{2} + 12 \): \[ x^{2} - 688 \] 3. **Expression c**: Simplifying \( 6x^{2} + 21 + x - 30 \): \[ 6x^{2} + x - 9 \] 4. **Expression d**: \( 20x^{2} + 33x + 10 \) is already in its simplest form. 5. **Expression involving a and d**: \( -6a^{2} + 1da - 4 \) needs clarification on what \( a \) and \( d \) represent. 6. **Expression involving x**: Assuming \( 0^{2} - 6x - 8 \) simplifies to: \[ -6x - 8 \] 7. **Expression**: \( 9 \cdot 8x^{2} + 22x + 5 \) simplifies to: \[ 72x^{2} + 22x + 5 \] ### Step 2: Further Analysis If you need to solve any of these expressions or equations, please specify which ones you would like to focus on. For example, if you want to solve for \( x \) in any of the quadratic expressions, we can use the quadratic formula or factorization methods. Please clarify your request so I can assist you further!