# Factor each polynomial. x^{2}-4x-21

Factor each polynomial.
${x}^{2}-4x-21$
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Shannon Hodgkinson
Step 1
Consider the polynomial: ${x}^{2}-4x-21$
Assume that the above equation is in the form ${x}^{2}+bx+c$ where b is sum of factors and c is product of factors
Find a pair of numbers whose product is and whose sum is .
In this case, whose product is and whose sum is -7,3
Step 2
Write the factored form using these integers: (x-7)(x+3)
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William Appel
Step 1
Given polynomial is ${x}^{2}-4x-21$.
To factor the given polynomial.
Solution:
Factoring the given polynomial.
${x}^{2}-4x-21={x}^{2}-7x+3x-21$
=x(x-7)+3(x-7)
=(x-7)(x+3)
Therefore on factoring the given polynomial, we get
${x}^{2}-4x-21=\left(x-7\right)\left(x+3\right)$
Step 2
Hence, required factor is ${x}^{2}-4x-21=\left(x-7\right)\left(x+3\right)$.