Answer:
[tex]x^2+ 4x - 21[/tex] =(x-3)(x+7)
Step-by-step explanation:
To factor the trimonial: [tex]x^2+ 4x - 21[/tex], we follow these steps:
Step 1: Multiply the first and last term
[tex]-21 \times x^2=-21x^2[/tex]
Step 2: List out product factors of the term derived above
[tex]-21=-1 \times 21\\ -21=-3 \times 7\\-21=3 \times -7\\-21=1 \times -21[/tex]
Step 3: Determine which of the factors sum up to the middle term 4x
The required product is: -3 and 7
Therefore: -3x+7x=4x
Step 4: Replace the middle term by the expression derived in step 3 and factorize.
[tex]x^2+ 7x -3x- 21\\=x(x+7)-3(x+7)\\=(x-3)(x+7)[/tex]
