Question

Factor. x2+5x−14 polynomials and binomials

Answer 1

These are a lot easier when they r like this...no coefficient in front of ur x^2.

x^2 + 5x - 14....u see ur last sign, the -.....this tells me that in ur 2 factors, both signs will be different....one is positive and one is negative. U see ur first sign, the +, this tells me that ur bigger number will be positive.
Now we just have to find 2 numbers, that when added = 5 and when multiplied = 14, So ur 2 numbers are 7 and 2.

(x^2 + 5x - 14) = 
(x + 7)(x - 2) <===

Answer 2

Answer:

$x^{2}+5x-14=(x-2)(x+7)$

Step-by-step explanation:

The given expression is

$x^{2}+5x-14$

To factor this expression, we need to use the quadratic formula

$x_{1,2} =\frac{-b\±\sqrt{b^{2}-4ac} }{2a}$

Where $a=1, b=5, c=-14$

Replacing this values, we have

$x_{1,2} =\frac{-(5)\±\sqrt{(5)^{2}-4(1)(-14)} }{2(1)}\\x_{1,2} =\frac{-5\±\sqrt{25+56} }{2}=\frac{-5\±\sqrt{81} }{2}=\frac{-5\±9}{2}$

This expression represents two solutions

$x_{1}=\frac{-5+9}{2}=2\\ x_{1}=\frac{-5-9}{2}=-7$

If we express these solutions as binomials, they would be

$(x-2)(x+7)$

Therefore, the answer is

$x^{2}+5x-14=(x-2)(x+7)$