# How do you factor by grouping x^2 + 7x + 5x + 35?

Apr 17, 2018

${x}^{2} + \left(7 + 5\right) \cdot x + 35 = \left(x + 5\right) \left(x + 7\right)$

#### Explanation:

${x}^{2} + \left(7 + 5\right) \cdot x + 35 =$
$= {x}^{2} + \left(7 + 5\right) \cdot x + \left(5 \cdot 7\right) =$
$= \left(x + 5\right) \left(x + 7\right)$

Remember:
${x}^{2} + \left(a + b\right) \cdot x + a \cdot b = \left(x + a\right) \left(x + b\right)$
For more click here. If you are interested in general polynomial: Vieta's formulas.

Apr 17, 2018

$\left(x + 7\right) \left(x + 5\right)$

#### Explanation:

$$


Grouping is a technique usually used when there is no factor common to all terms of a polynomial, but there are factors common to some of the terms, so I am not sure if this is the correct technique to answer this question.
Before we solve this problem, let me show you the FOIL method.
(x+a)(x+b)
Begin by multiplying the First terms ($x \cdot x$), then the Outer terms
($x \cdot b$), Inner terms ($a \cdot x$), and finnally Last terms ($a \cdot b$)
If we right that all out then we would have the equation
${x}^{2} + a x + b x + a b$ Now we apply this to your question..
${x}^{2} + 7 x + 5 x + 35$
Matching these equations side by side it is clear that $a = 7 \mathmr{and} b = 5$
When they are asking you to (group them) I assume that they are asking you to return them to the original format $\left(x + a\right) \left(x + b\right)$
Simply plug in 7 and 5 for "a" and "b" and you get your answer...
$\left(x + 7\right) \left(x + 5\right)$