How do you write $7 x^{2} + 23 x + 6$ $7x^2+23x+6$ in factored form?

Question

4080 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-15T13:46:56

$(x + 3) (7 x + 2)$ $(x+3)(7x+2)$

Multiply the coefficients of #x^2 and the constant.

$+ 7 \times + 6 = + 42$ $+7 xx +6 = +42$

Find two numbers whose product (multiply) is $42$ $42$ and whose sum (add) is $+ 23$ $+23$ (the middle coefficient).

${: (bb"Pairs whose product is " 42," "" ",bb"Sums of the pairs"), (" "" "1xx42," "," "" "43),(" "" "2xx21," "," "" "23) :}$

STOP! We do not need to go any further.

Use these numbers to split the middle term

$7x^2+2x+21x+6$

Now factor by grouping:

$x(7x+2)+3(7x+2)$

$(x+3)(7x+2)$

Check the answer my multiplying (expanding).

How do you write 7x^2+23x+67x2+23x+67x^2+23x+6 in factored form?