Question

factor 7x^2+29x+4

Answer 1

\[7x^2 +29x +4\]\[=x^2 +29x +28\]\[=(x+28)(x+1)\]\[=\left(x+\frac{28}{7}\right)\left(x+\frac{1}{7}\right)\]Whichever fraction can reduce, reduce it. if it cannot reduce, take the denominator and multiply it to the variable \[=(x+4)(7x+1)\]

Answer 2

What I did was I multiplied to coefficient of the leading term to the constant at the end, this allowed me to simplify the quadratic function easier.

Answer 3

Whenever we have a 2nd degree polynomial, we are certain that it would have, two forms:
\[(x+a)^2\]
or:
\[(x-a_1)(x-a_2)\]
in order to know, we'd have to compare it with this form:
\[a^2 + 2ab+b^2\]
I'll guide you though it, let's take the polynomial given:
\[7x^2+29x+4\]
we can clearly see that it doesn't match, because it would be hard for me to find a number, that squared gave me a 7 and that number not being algebraically complex.
So we would have to choose another way.
What we can do is find the "roots" of the function by making it equal zero and then using the general formula to find "x":
\[7x^2+29x+4=0\]
we apply:
\[x=\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a }\]
so:
\[x=\frac{ -29 \pm \sqrt{29^{2}-4(7)(4)} }{ 2(7) }\]
\[x=\frac{ -29 \pm 27 }{ 14 }\]
\[x_1= -4\]
\[x_2= \frac{ -2 }{ 14 }\]
So therefore, the factored form is:
\[(x+4)(x+\frac{ 2 }{ 14 })\]
I did it a little quick but you can ask me anything if you have a question or confused in a step.

Answer 4

I wasn't looking for the quadratic formula