. Let d be (-6)/8*(-24)/o. Factor 2/7*v**4 - 2/7*v**d + 0*v**3 + 0 + 0*v.
2*v**2*(v - 1)*(v + 1)/7
Let q(j) be the first derivative of -2*j**6/3 + 8*j**5/5 + 2*j**4 - 16*j**3/3 - 2*j**2 + 8*j - 40. Determine d so that q(d) = 0.
-1, 1, 2
Solve 5/2 - 2*u - 1/2*u**2 = 0.
-5, 1
Let m(z) be the first derivative of z**4 - 20*z**3/3 + 16*z**2 - 16*z - 55. Solve m(t) = 0 for t.
1, 2
Let t = 64 + -62. Let q(r) be the first derivative of -1/2*r**t + 1/3*r**3 - 3 + 1/3*r - 1/12*r**4. Suppose q(n) = 0. What is n?
1
Let h(o) be the second derivative of -1/45*o**6 - 3*o - 1/6*o**4 + 1/9*o**3 + 0*o**2 + 0 + 1/10*o**5. Factor h(x).
-2*x*(x - 1)**3/3
Let v = 7 + 1. Factor -15 + 4*o - 3 + 0*o - 2*o**2 + v*o.
-2*(o - 3)**2
Let r be 28/30 - 2/(-3). Find p such that 2/5*p**2 + 8/5 - r*p = 0.
2
Let t(y) be the second derivative of 3*y**6/10 + 6*y**5/5 + y**4 + y. Factor t(j).
3*j**2*(j + 2)*(3*j + 2)
Suppose -10*w = -12*w + 4. Suppose -c = -4*x + 11, 8 = 3*x + c - 2. Factor -3/4*y**w + 1/4*y**x + 3/4*y - 1/4.
(y - 1)**3/4
Suppose 4*m - 4 = -4*t, 12 = -2*t + 4*t - 3*m. Suppose 4*k = t*k + 7. Factor -1 - 5*i + k*i**2 - 6 + 5.
(i - 1)*(7*i + 2)
Let v(w) = -2*w**2 + 9*w + 11. Let u(t) be the third derivative of t**5/60 - 5*t**4/24 - t**3 + t**2. Let z(f) = -11*u(f) - 6*v(f). Factor z(x).
x*(x + 1)
Let i be -1 + 0 - (-6)/2. Factor -2*a**3 - 4*a**3 - 3*a**5 - 8*a**4 + a**i - a**2 + a.
-a*(a + 1)**3*(3*a - 1)
Factor -22*w + w**2 + 16 + 26*w - 12*w.
(w - 4)**2
Let p(o) be the second derivative of o**6/12 + o**5/2 + 5*o**4/6 - 33*o. Suppose p(s) = 0. Calculate s.
-2, 0
Let s(u) = u**2 + 3*u - 18. Let i be s(3). What is c in -2/17*c**2 + i - 2/17*c = 0?
-1, 0
Let f(u) be the first derivative of 1/4*u**4 + 5 + 3/8*u**6 + 3/5*u**5 + 0*u + 0*u**2 + 0*u**3. Let f(s) = 0. Calculate s.
-2/3, 0
Suppose 801*w - 12 = 797*w. Let 3/7*d**4 + 3*d + 6/7 + 27/7*d**2 + 15/7*d**w = 0. Calculate d.
-2, -1
Let a(h) be the first derivative of -1/2*h + 0*h**2 + 1/6*h**3 - 4. Let a(j) = 0. Calculate j.
-1, 1
Let c be ((-48)/20)/((-3)/10). Suppose 5*b + d - 6 = 4*d, b + 4*d = -c. Factor -3/2*t + b - 15/4*t**2.
-3*t*(5*t + 2)/4
Let h be 43 - 44 - (1 + -2)*1. Suppose 0 + 0*t + 2/13*t**4 + 2/13*t**3 + h*t**2 = 0. Calculate t.
-1, 0
Let t be (-32)/(-10) + (-4)/2 + -1. Find p such that 0*p - 1/5*p**2 - t*p**3 + 0 = 0.
-1, 0
Determine s, given that -2/3*s + 0 - 2/9*s**2 = 0.
-3, 0
Suppose -2*g + p + 2 = -2, 2*p = 0. Suppose 3*i - 20 = -8*b + 4*b, -g*i = b - 5. Factor 1/3*t**4 + 0*t**3 + i + 1/6*t**5 - 1/3*t**2 - 1/6*t.
t*(t - 1)*(t + 1)**3/6
Let k be (-105)/(-140)*2/3. Factor 1/2 - d**3 + 1/2*d**5 - d**2 + 1/2*d**4 + k*d.
(d - 1)**2*(d + 1)**3/2
Find a such that -7*a**3 - a**4 - 2*a - 6*a - 9*a**3 - 3*a**4 - 20*a**2 = 0.
-2, -1, 0
Solve -55/3*q**2 - 20*q + 35/3*q**4 + 20/3 + 20*q**3 = 0.
-2, -1, 2/7, 1
Let l(q) = q**2 - 11*q. Let c be l(11). Let g(t) be the third derivative of 2*t**4 + 0 + 3*t**2 + 4/3*t**3 + 7/10*t**5 + c*t - 49/60*t**6. Factor g(r).
-2*(r - 1)*(7*r + 2)**2
Factor -1 + 3/4*q + 1/4*q**2.
(q - 1)*(q + 4)/4
Suppose -v**3 - 1/2 - 1/2*v**5 - v**2 + 3/2*v + 3/2*v**4 = 0. What is v?
-1, 1
Let n(j) be the first derivative of j**4/8 - j**3/3 - 3*j**2/4 + 31. Solve n(g) = 0.
-1, 0, 3
Let q(r) be the first derivative of r**6/21 - 2*r**5/35 - 3*r**4/14 + 2*r**3/21 + 2*r**2/7 + 5. Suppose q(x) = 0. Calculate x.
-1, 0, 1, 2
Let a(f) be the third derivative of 1/12*f**4 + 0*f**6 + 0*f**3 + 5*f**2 + 0 - 1/15*f**5 - 1/168*f**8 + 2/105*f**7 + 0*f. Factor a(y).
-2*y*(y - 1)**3*(y + 1)
Let x(p) = 2*p**2 - 20*p - 18. Let k be x(11). Let u(s) be the third derivative of -1/30*s**5 + 1/6*s**k + 0*s + 0*s**3 - 3*s**2 + 0. What is r in u(r) = 0?
0, 2
Suppose 3*b - 4 = -4. Find q such that 0*q - q**3 - 1/2*q**2 - 1/2*q**4 + b = 0.
-1, 0
Let j(u) be the second derivative of 2*u**6/15 - 2*u**5/5 + 4*u**3/3 - 2*u**2 + 16*u. Determine h, given that j(h) = 0.
-1, 1
Suppose f - 3 = -h, -5*f + h + 4 = -11. Factor 1/4*c + 1/4 - 1/4*c**2 - 1/4*c**f.
-(c - 1)*(c + 1)**2/4
Let s(m) be the first derivative of m**7/210 + m**6/120 + 2*m**2 - 3. Let i(y) be the second derivative of s(y). Suppose i(u) = 0. What is u?
-1, 0
Let i(k) = 8*k**3 + 3*k**2 + 5. Let y(q) = 33*q**3 + 12*q**2 + 21. Suppose 0 = 2*p + 2*t + 12, 4*p + 5*t + 21 = -4. Let g(s) = p*y(s) + 21*i(s). Solve g(a) = 0.
-1, 0
Let d(h) be the first derivative of -h**5/10 - h**4/3 - h**3/3 - 3*h**2/2 + 3. Let y(i) be the second derivative of d(i). What is r in y(r) = 0?
-1, -1/3
Let a(q) = 2*q**3 - 1. Let v(y) = -3*y**3 - y**2 - y + 1. Let p(h) = 4*a(h) + 3*v(h). Factor p(m).
-(m + 1)**3
Factor -4 + 2*t**4 + 6*t - 3*t**3 - 12*t + 9*t**3 + 2*t**2.
2*(t - 1)*(t + 1)**2*(t + 2)
Let b(k) = k**3 + 12*k**2 - 15*k - 22. Let a be b(-13). Factor 4/7*p**a + 0 + 2/7*p**3 - 2/7*p**2 + 0*p.
2*p**2*(p + 1)*(2*p - 1)/7
Let y(a) be the first derivative of -2/3*a**6 - 13/3*a**3 - 4*a - 4*a**4 + 17/5*a**5 - 3 + 10*a**2. Determine o so that y(o) = 0.
-1, 1/4, 1, 2
Factor -2*j + j**4 - 1/2*j**5 - 2*j**2 + 0 + 3/2*j**3.
-j*(j - 2)**2*(j + 1)**2/2
Let p(a) = -8*a**4 + 20*a**3 - 24*a**2 + 4*a - 4. Let i(m) = -9*m**4 + 21*m**3 - 25*m**2 + 3*m - 5. Let s(j) = 4*i(j) - 5*p(j). Factor s(h).
4*h*(h - 2)*(h - 1)**2
Let m(n) be the first derivative of -n**3/9 - n**2/6 - 2. Suppose m(v) = 0. What is v?
-1, 0
Let b = 26 - 22. Let f(n) be the second derivative of 0*n**2 + 2/21*n**3 + 0 + 1/14*n**b + 5/147*n**7 + n - 1/35*n**6 - 1/10*n**5. Determine p so that f(p) = 0.
-1, -2/5, 0, 1
Let h be -2*3/15*-5. Suppose -h*d = -4*d + 6. Find o, given that d*o**5 - 1/3*o - 2*o**2 + 0 + 2*o**4 - 8/3*o**3 = 0.
-1, -1/3, 0, 1
Let v(j) be the first derivative of 2*j**5/25 + j**4/10 + 10. Factor v(f).
2*f**3*(f + 1)/5
Factor 2/7*r**2 + 0 + 2/7*r.
2*r*(r + 1)/7
Suppose 0 = 189*o - 196*o. Let n(i) be the third derivative of 1/105*i**7 - 1/30*i**5 + 1/336*i**8 - 1/24*i**4 - i**2 + 0*i + 0*i**3 + o*i**6 + 0. Factor n(r).
r*(r - 1)*(r + 1)**3
Let t(b) = b**2 + 16*b - 34. Let m be t(-18). Factor -1/4*i**4 + 0*i + 0*i**3 + 1/2*i**m - 1/4.
-(i - 1)**2*(i + 1)**2/4
Let c(b) be the third derivative of -b**6/90 + 14*b**5/45 - 49*b**4/18 + 28*b**2. Factor c(l).
-4*l*(l - 7)**2/3
Determine c, given that 1/2*c**3 + 7/2*c + 3/2 + 5/2*c**2 = 0.
-3, -1
Let u(g) = 2*g**2 + 5*g + 4. Let q be u(-2). Solve 2/3*v**2 + 0 + 2*v**3 + q*v**4 + 2/3*v**5 + 0*v = 0 for v.
-1, 0
Let s(q) be the second derivative of -q**8/315 - 2*q**7/315 - q**6/180 - q**5/360 - q**4/6 + q. Let h(w) be the third derivative of s(w). Solve h(p) = 0 for p.
-1/4
Let y be (-18)/(-8) - (-12)/16. Factor -h + h - h + h**2 - 1 + 4*h**3 - 3*h**y.
(h - 1)*(h + 1)**2
Suppose -12*f + 20*f = 11*f. Let v(b) be the third derivative of 1/210*b**6 - 1/42*b**4 + f*b + 1/735*b**7 + 0 + 3*b**2 - 1/21*b**3 + 0*b**5. Factor v(s).
2*(s - 1)*(s + 1)**3/7
Let a(j) be the first derivative of -j**4/14 - 2*j**3/7 + 6*j**2/7 + 16*j/7 + 27. Let a(b) = 0. Calculate b.
-4, -1, 2
Let a(b) be the first derivative of -1/15*b**3 + 1/5*b**2 + 3/5*b + 4. Let a(y) = 0. Calculate y.
-1, 3
Let o(l) be the second derivative of -l**6/40 + l**5/10 + 7*l**4/8 + 2*l**3 - l**2 + 7*l. Let i(p) be the first derivative of o(p). What is h in i(h) = 0?
-1, 4
Suppose -5*o - 4*u + 5*u = 22, 3*o + 5*u + 30 = 0. Let g = 9 + o. Factor n**4 - 2*n + 2*n**4 - 6*n**2 - 5*n**g - 6*n**3.
-2*n*(n + 1)**3
Let r be -2 + (-10)/(-5 + 3). Let w = r - 1. Solve -10*k + 4*k - 8*k - 4*k**w + 14*k**3 + 4 = 0.
-1, 2/7, 1
Let r(h) be the second derivative of -h**5/140 + 11*h**4/28 - 121*h**3/14 + 1331*h**2/14 + 23*h. Find k, given that r(k) = 0.
11
Let o(n) be the third derivative of -n**8/896 + n**6/160 - n**4/64 - 15*n**2. Let o(r) = 0. Calculate r.
-1, 0, 1
Factor 0 + 4/7*x - 2/7*x**2.
-2*x*(x - 2)/7
Let o(x) be the second derivative of x**7/630 + x**6/180 - x**4/36 - x**3/18 + x**2/2 - 5*x. Let g(a) be the first derivative of o(a). Let g(k) = 0. What is k?
-1, 1
Factor -g + 1/2*g**5 - 1/2*g**4 - 3/2*g**3 + 0 + 5/2*g**2.
g*(g - 1)**3*(g + 2)/2
Let u(n) be the second derivative of -1/3*n**2 + 0 + 1/18*n**4 + 1/9*n**3 + n - 1/30*n**5. Suppose u(j) = 0. Calculate j.
-1, 1
Find g, given that 45 + 9*g - 45 - 3*g**2 = 0.
0, 3
Let o(q) be the third derivative of q**6/180 - q**4/12 - 2*q**3/9 - 13*q**2. Find m, given that o(m) = 0.
-1, 2
