Question
Finish factoring by grouping. There are two more steps. \[ \begin{array}{l}8 x^{2}-64 x+x-8 \\ \left(8 x^{2}-64 x\right)+(1 x-8)\end{array} \]
Ask by Spencer Owen. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The factored form is \((x-8)(8x+1)\).
Solution
Factor the expression \( 8x^2-64x+x-8 \).
Factor the expression by following steps:
- step0: Factor:
\(8x^{2}-64x+x-8\)
- step1: Add the terms:
\(8x^{2}-63x-8\)
- step2: Rewrite the expression:
\(8x^{2}+\left(1-64\right)x-8\)
- step3: Calculate:
\(8x^{2}+x-64x-8\)
- step4: Rewrite the expression:
\(x\times 8x+x-8\times 8x-8\)
- step5: Factor the expression:
\(x\left(8x+1\right)-8\left(8x+1\right)\)
- step6: Factor the expression:
\(\left(x-8\right)\left(8x+1\right)\)
The factored form of the expression \(8x^2-64x+x-8\) is \((x-8)(8x+1)\).
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Simplify this solution The Deep Dive
To finish factoring by grouping, let's simplify each group separately. From the first group \(8x^2 - 64x\), we can factor out the greatest common factor, which is \(8x\): \[ 8x(x - 8) \] From the second group \(x - 8\), we see that it is already in its simplest form. Now, we can rewrite the expression as: \[ 8x(x - 8) + 1(x - 8) \] Next, we notice that both terms contain the common factor \((x - 8)\). Hence, we can factor that out: \[ (x - 8)(8x + 1) \] So the fully factored form of the original expression is: \[ (x - 8)(8x + 1) \] And there you have it, your expression is now completely factored!
