Solve 1+2^7b^7

$$1 + 2 ^ { 7 } b ^ { 7 }$$

Factor

$$\left(2b+1\right)\left(64b^{6}-32b^{5}+16b^{4}-8b^{3}+4b^{2}-2b+1\right)$$

Solution Steps

Multiply and combine like terms.

$$128b^{7}+1$$

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 1 and q divides the leading coefficient 128. One such root is -\frac{1}{2}. Factor the polynomial by dividing it by 2b+1. Polynomial 64b^{6}-32b^{5}+16b^{4}-8b^{3}+4b^{2}-2b+1 is not factored since it does not have any rational roots.

$$\left(2b+1\right)\left(64b^{6}-32b^{5}+16b^{4}-8b^{3}+4b^{2}-2b+1\right)$$

Evaluate

$$128b^{7}+1$$

Solution Steps

Calculate 2 to the power of 7 and get 128.

$$1+128b^{7}$$