Solve 5x^{2}-7x^{2}+1/4x^2-8x^2-3/8x^2-x^2+9/8

$$5 x ^ { 2 } - 7 x ^ { 2 } + \frac { 1 } { 4 } x ^ { 2 } - 8 x ^ { 2 } - \frac { 3 } { 8 } x ^ { 2 } - x ^ { 2 } + \frac { 9 } { 8 }$$

Evaluate

$$\frac{9-89x^{2}}{8}$$

Solution Steps

Combine 5x^{2} and -7x^{2} to get -2x^{2}.

$$-2x^{2}+\frac{1}{4}x^{2}-8x^{2}-\frac{3}{8}x^{2}-x^{2}+\frac{9}{8}$$

Combine -2x^{2} and \frac{1}{4}x^{2} to get -\frac{7}{4}x^{2}.

$$-\frac{7}{4}x^{2}-8x^{2}-\frac{3}{8}x^{2}-x^{2}+\frac{9}{8}$$

Combine -\frac{7}{4}x^{2} and -8x^{2} to get -\frac{39}{4}x^{2}.

$$-\frac{39}{4}x^{2}-\frac{3}{8}x^{2}-x^{2}+\frac{9}{8}$$

Combine -\frac{39}{4}x^{2} and -\frac{3}{8}x^{2} to get -\frac{81}{8}x^{2}.

$$-\frac{81}{8}x^{2}-x^{2}+\frac{9}{8}$$

Combine -\frac{81}{8}x^{2} and -x^{2} to get -\frac{89}{8}x^{2}.

$$-\frac{89}{8}x^{2}+\frac{9}{8}$$

Factor

$$\frac{9-89x^{2}}{8}$$

Solution Steps

Factor out \frac{1}{8}. Polynomial -89x^{2}+9 is not factored since it does not have any rational roots.

$$\frac{40x^{2}-56x^{2}+2x^{2}-64x^{2}-3x^{2}-8x^{2}+9}{8}$$