Question

Factors of $(42–x–x²)$ are:

• A. $(x–7)(x–6)$
• B. $(x+7)(x–6)$
• C. $(x+7)(6–x)$
• D. $(x+7)(x+6)$

Answer 1

The correct option is C

$(x+7)(6–x)$

Explanation of correct option

Factorization

To find the factors $(42–x–x²)=\left(-x^2-x+42\right)$ we need to consider $p$and $q$ such that $p+q=-1$ and $p\times q=-42$

Certainly $p$and $q$ are $6$ and $-7$ respectively.

$$\begin{gathered} \Rightarrow -x^2-x+42=0 \\ \Rightarrow -x^2-7x+6x+42=0 \\ \Rightarrow -x\left(x+7\right)+6\left(x+7\right)=0 \\ \Rightarrow \left(x+7\right)\left(6-x\right)=0 \end{gathered}$$

Hence the two factors are $\left(x+7\right),\left(6-x\right)$

Hence, option C is correct.