Question

This is an practice assignment. The topic is factoring quadratics for algebra.

Answer 1

`\begin{gathered} \text{when we have a polynomial in the form} \\ x^2+bx+c \\ we\text{ factor it by looking two numbers }h\text{ and k such that} \\ \text{hk}=c,\text{ h+k=b} \end{gathered}`
`\begin{gathered} 1.x^2+7x+12 \\ we\text{ must find two numbers such that a}\cdot b=12\text{ and a+b=7} \\ 12=3\cdot4 \\ \text{and 3+4=7} \end{gathered}`
`\begin{gathered} \text{ thus } \\ x^2+7x+12=(x+3)(x+4) \end{gathered}`
`\begin{gathered} m^2+10m+21,\text{ } \\ 21=3\cdot7 \\ 3+7=10 \\ \\ m^2+10m+21=(m+7)(m+3) \end{gathered}`
`\begin{gathered} x^2-7x-8 \\ -8=(-8)\cdot1 \\ -7=-8+1 \\ \\ x^2-7x-8=(x-8)(x+1) \end{gathered}`
`\begin{gathered} x^2-6x+5 \\ 5=(-5)(-1) \\ -6=-5-1 \\ \\ x^2-6x+5=(x-5)(x-1) \end{gathered}`