# Math Help - Factoring

1. ## Factoring

im taking an online class and i just wanted to check my answers with someone...

1. (21x to the fifth - 14x to the fourth - 35xsquared) =
7xsquared (3x to the third - 2xsquared - 5)

is that all? or is there more to the answer??

2. (q squared +6q +9) =
(q+3)(q+3)

3. (t squared - 16t +64)=
(t-8) squared

and i have more...

2. Looks good to me, but another thing you can do with #2, is turn $(q+3)(q+3)\rightarrow(q+3)^2$, to be consistent with your #3 answer if you want; but your answers look perfectly fine to me!

3. Thanks :]

1. (x squared -x -20) =0
x=5,-4

2. 2x squared = 7x +15
x= -3/2, 5

3. (2x +1) (x+3) = 42
x= -13/2, 3

4. (x) (x-5) = 66
x= 11, -6

4. 1. (x squared -x -20) =0
x=5,-4
\begin{aligned}
x^2 - x - 20 &= 0 \\
(x - 5)(x + 4) &= 0 \\
x &= 5 \\
x &= -4
\end{aligned}

Correct!

2. 2x squared = 7x +15
x= -3/2, 5
\begin{aligned}
2x^2 = 7x + 15 \\
2x^2 - 7x - 15 &= 0 \\
(2x + 3)(x - 5) &= 0 \\
x &= -3/2 \\
x &= 5
\end{aligned}

Correct!

3. (2x +1) (x+3) = 42
x= -13/2, 3
\begin{aligned}
(2x +1) (x+3) &= 42 \\
2x^2 + 7x + 3 &= 42 \\
2x^2 + 7x - 39 &= 0 \\
(2x^2 + 13)(x - 3) &= 0 \\
x &= -13/2 \\
x &= 3
\end{aligned}

Correct!

4. (x) (x-5) = 66
x= 11, -6
\begin{aligned}
x(x - 5) &= 66 \\
x^2 - 5x &= 66 \\
x^2 - 5x - 66 &= 0 \\
(x - 11)(x + 6) &= 0 \\
x &= 11 \\
x &= -6
\end{aligned}

Correct!

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