Question

1. factor: $x^{2}-17x + 70$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to 70 and add up to 17. The numbers are 10 and 7 since \(10\times7 = 70\) and \(10 + 7=17\).

Step2: Rewrite the middle - term

Rewrite \(-17x\) as \(-10x-7x\). So \(x^{2}-17x + 70=x^{2}-10x-7x + 70\).

Step3: Group the terms

Group the terms: \((x^{2}-10x)+(-7x + 70)\).

Step4: Factor out the common factors from each group

From \(x^{2}-10x\), we can factor out \(x\) to get \(x(x - 10)\). From \(-7x + 70\), we can factor out \(-7\) to get \(-7(x - 10)\).

Step5: Factor out the common binomial factor

\(x(x - 10)-7(x - 10)=(x - 10)(x - 7)\).

Answer:

\((x - 10)(x - 7)\)