 u(g) be the third derivative of -g**7/11340 + g**6/540 - g**5/60 - g**4/6 - 4*g**2. Let i(j) be the second derivative of u(j). Let i(o) = 0. Calculate o.
3
Factor -38*a + 73*a**3 - 13*a**3 - 163*a**2 + 338*a - 67*a**2 - 125 - 5*a**4.
-5*(a - 5)**2*(a - 1)**2
Let c(v) be the third derivative of 1/270*v**5 - 1/27*v**3 + 1/108*v**4 + 0*v - v**2 - 1/540*v**6 + 0. Find g such that c(g) = 0.
-1, 1
Suppose -5*o = -h - 22, 4*o + h = 19 - 5. Suppose o*b - 2*q = 18, 0 = 2*b + 3*q + 6 - 3. Factor 0*g**2 + 2/5*g**b - 2/5*g + 0.
2*g*(g - 1)*(g + 1)/5
Let i(n) = n**2 + 15*n + 58. Let k be i(-9). Let q(z) be the second derivative of -z + 0 + 0*z**3 - 1/18*z**k + 1/3*z**2. Factor q(w).
-2*(w - 1)*(w + 1)/3
Let c be (-7 - (-3 - -4))*(-2)/28. Factor -c*p**2 + 0*p + 6/7*p**3 + 0 - 2/7*p**4.
-2*p**2*(p - 2)*(p - 1)/7
Suppose -c = 0, 7*o = 2*o + 4*c. Suppose o = w - 3. Factor -6/5*y**w - 2/5*y + 6/5*y**2 + 0 + 2/5*y**4.
2*y*(y - 1)**3/5
Let w(p) be the second derivative of 0 + 0*p**4 + 7*p + 1/4*p**3 - 1/40*p**5 + 1/2*p**2. Let w(l) = 0. Calculate l.
-1, 2
Factor 0 + 0*o**2 + 0*o - 3/7*o**5 + 0*o**3 + 3/7*o**4.
-3*o**4*(o - 1)/7
Solve 49*y**2 + 13*y**2 - 5*y - 37*y**2 = 0.
0, 1/5
Suppose -4*o = 5*n - 37, o - 5*n = 6*o - 50. Let l = o - 13. Find s, given that -2/7*s**2 + 2/7*s + l = 0.
0, 1
Let f = 24/17 + -134/119. Find o such that -f*o + 2/7*o**2 + 0 = 0.
0, 1
Let d = -43 - -62. Let b = d + -17. Factor 2*n**b + 14/5*n + 4/5.
2*(n + 1)*(5*n + 2)/5
Suppose -2 = -2*o + m, m + 8 - 21 = -3*o. Let w(l) be the first derivative of 2/3*l**o + 2*l**2 - 1 + 2*l. Suppose w(r) = 0. What is r?
-1
Let k(s) be the second derivative of -s**6/240 - s**5/60 + s**4/48 + s**3/6 - s**2 + 3*s. Let z(x) be the first derivative of k(x). Factor z(g).
-(g - 1)*(g + 1)*(g + 2)/2
Suppose -y + 4*w - 15 = 2*y, 20 = -5*y + 5*w. Let m(a) = a**2 - 3. Let h(u) be the third derivative of -u**3/6 - u**2. Let r(t) = y*m(t) + 2*h(t). Factor r(x).
-(x - 1)*(x + 1)
Let o(t) be the first derivative of t**6/10 - 3*t**5/5 + 5*t**4/4 - t**3 + 2*t + 2. Let g(j) be the first derivative of o(j). Suppose g(w) = 0. Calculate w.
0, 1, 2
Let w = -17 - -23. Let g be w/(-8) + (-5 - -6). Suppose -g*a + 0 + 1/4*a**2 + 9/4*a**3 + 11/4*a**4 + a**5 = 0. Calculate a.
-1, 0, 1/4
Let l(t) be the third derivative of t**7/350 + 3*t**6/200 + t**5/100 - 3*t**4/40 - t**3/5 - 15*t**2. Factor l(d).
3*(d - 1)*(d + 1)**2*(d + 2)/5
Let s(y) be the first derivative of y**6/4 - 3*y**4/2 + y**3 + 9*y**2/4 - 3*y + 6. Factor s(x).
3*(x - 1)**3*(x + 1)*(x + 2)/2
Let b(w) be the second derivative of -1/6*w**3 + 0 + 1/42*w**7 + 0*w**2 + 1/15*w**6 + 0*w**5 - 1/6*w**4 + w. Factor b(t).
t*(t - 1)*(t + 1)**3
Suppose 5/4*i**2 + 0 - i**5 + 1/4*i + 3/4*i**3 - 5/4*i**4 = 0. What is i?
-1, -1/4, 0, 1
Let s = 42 - 292/7. Suppose 0*z + 0 + s*z**2 = 0. Calculate z.
0
Let u(o) = -o**3 + o**3 + 4*o**3 - 3*o**3 - o. Let x be u(-1). Factor 1/3*z**2 + z**3 + z**4 + 0*z + x + 1/3*z**5.
z**2*(z + 1)**3/3
Suppose 2*u - 14 = -10. Factor 0 - n**u - 2 + n**3 + 1 - 2*n**2 + 3*n.
(n - 1)**3
Let j(o) = 7 - o**2 - 4*o**2 - 5*o**3 - 2 + 5*o + 0*o. Let q(z) = -21*z**3 - 21*z**2 + 21*z + 21. Let x(s) = -9*j(s) + 2*q(s). What is v in x(v) = 0?
-1, 1
Let d(q) = 6*q + 48. Let y be d(-8). Let b(k) be the first derivative of -2 + y*k - 1/6*k**3 + 0*k**2 + 1/8*k**4. Factor b(r).
r**2*(r - 1)/2
Let z(f) = -f + 4. Let s be z(3). Let q be 26/6 - (s - -3). Let 1/3*r**3 + 0 + 2/3*r**2 + q*r = 0. Calculate r.
-1, 0
Let w be (-46)/(-6) - 2/(-6). Suppose -r = -w*r + 21. Factor -2/7*i**5 + 0 + 0*i - 6/7*i**4 - 6/7*i**r - 2/7*i**2.
-2*i**2*(i + 1)**3/7
Let x(m) be the third derivative of 0*m**3 + 3*m**2 + 0*m**5 - 1/420*m**7 + 1/120*m**6 - 1/672*m**8 + 0 + 0*m + 0*m**4. Factor x(u).
-u**3*(u - 1)*(u + 2)/2
Let s(j) be the third derivative of j**6/1140 - j**4/228 - 7*j**2. Let s(i) = 0. What is i?
-1, 0, 1
Let c(a) = -a**4 + a**3 - a. Let k(p) = -2*p**4 - 8*p**3 + 3*p. Let z(v) = -3*c(v) - k(v). Factor z(r).
5*r**3*(r + 1)
Let m(u) be the first derivative of 7*u**5/20 + u**4/6 - 5*u - 7. Let v(t) be the first derivative of m(t). Let v(q) = 0. Calculate q.
-2/7, 0
Let l = -46 - -46. Factor 0*d**2 + l*d + 2/11*d**3 + 0 + 2/11*d**4.
2*d**3*(d + 1)/11
Let a(s) be the third derivative of -s**8/336 - s**7/210 + 4*s**2. Solve a(r) = 0.
-1, 0
Let s(q) be the second derivative of q**7/168 + q**6/40 + q**5/40 + 9*q. Factor s(m).
m**3*(m + 1)*(m + 2)/4
Let l be (12/60)/((-1)/(-1)). Factor -2/5*j**3 + 1/5*j**5 + 0*j**2 + 0 + l*j + 0*j**4.
j*(j - 1)**2*(j + 1)**2/5
Let i(q) be the third derivative of q**7/6300 - q**6/600 + q**5/150 - q**4/24 + q**2. Let l(b) be the second derivative of i(b). Find k such that l(k) = 0.
1, 2
Suppose 6*s - 46 + 10 = 0. Let d(h) = -h + 1. Let g be (4/(-6))/(2/6). Let t(q) = q**2 - 5*q + 4. Let y(n) = g*t(n) + s*d(n). Factor y(w).
-2*(w - 1)**2
Let b be (-21)/70*(-2)/3. Let u be (2/(-15))/((-4)/6). Factor -b*s**3 + 0 + 2/5*s**2 - u*s.
-s*(s - 1)**2/5
Let t(m) = -2*m**4 - 35*m**3 - 36*m**2 - 3*m. Let c(x) = -20*x - 3*x**3 + 2*x**4 + 2*x**3 - x**4 + 21*x. Let f(v) = 10*c(v) - 2*t(v). Find o such that f(o) = 0.
-2, -2/7, 0
Let j be (1 + 34)*(-5)/((-1650)/12). Factor 0*k - j*k**3 + 4/11*k**2 + 0.
-2*k**2*(7*k - 2)/11
Let n(f) be the first derivative of f**5/40 + f**4/8 + f**3/6 + f - 3. Let v(c) be the first derivative of n(c). Find w, given that v(w) = 0.
-2, -1, 0
Let r(g) be the first derivative of -5*g**3/6 + 27*g**2/4 - 5*g - 3. What is w in r(w) = 0?
2/5, 5
Let f = -238 - -716/3. Factor f + 1/3*x - 1/3*x**2.
-(x - 2)*(x + 1)/3
Let l be (6/4)/(39/637). Factor 0 - 12*d**2 - 2*d + l*d**4 - 21/2*d**3.
d*(d - 1)*(7*d + 2)**2/2
Solve 2*g**2 - 4/3*g + 0 - 2*g**4 + 2/3*g**5 + 2/3*g**3 = 0 for g.
-1, 0, 1, 2
Let p(c) be the first derivative of c**5/5 - 3*c**4/4 + c**3/3 + 3*c**2/2 - 2*c - 5. Factor p(r).
(r - 2)*(r - 1)**2*(r + 1)
Factor 6*f - 12*f**3 + 10*f**3 + 2*f**2 - 6*f**2.
-2*f*(f - 1)*(f + 3)
Let d(s) be the second derivative of -s**10/226800 + s**9/113400 + s**8/10080 + s**7/6300 - s**4/3 + 2*s. Let l(n) be the third derivative of d(n). Factor l(g).
-2*g**2*(g - 3)*(g + 1)**2/15
Let q = -136/3 - -46. Let c(y) be the first derivative of 0*y - 1/2*y**4 + 2 + 0*y**2 + q*y**3 + 1/3*y**6 - 2/5*y**5. Solve c(o) = 0 for o.
-1, 0, 1
Let o = -3 + 7. Let z(i) be the first derivative of -i**5/5 + i**2/2 + 8. Let v(l) = 5*l**4 + l**3 - l**2 - 5*l. Let h(a) = o*z(a) + v(a). Factor h(n).
n*(n - 1)*(n + 1)**2
Let x = 187/390 - 9/26. Let r(t) be the first derivative of -1/10*t**4 + 1 + 2/5*t - x*t**3 + 1/5*t**2. Factor r(d).
-2*(d - 1)*(d + 1)**2/5
Let q(i) be the second derivative of i**7/10080 + i**6/1440 + i**5/480 + i**4/4 + 2*i. Let b(n) be the third derivative of q(n). Determine a so that b(a) = 0.
-1
Let k(b) = 2*b**2 - b - 4. Let i be k(2). Factor -2/3*p**i - 2/3 - 4/3*p.
-2*(p + 1)**2/3
Let x(q) = 6*q + 4. Let z be x(-2). Let m(y) = y**3 + y**2. Let v(a) = -2*a**4 - 2*a**3 - 12*a**2. Let o(i) = z*m(i) - v(i). Factor o(n).
2*n**2*(n - 2)*(n - 1)
Let b be 20/(-16) - (-2)/8. Let a be (b/1)/((-2)/6). Factor -2 + 2*y**2 + 4*y**a - y**3 - y**3 - 2*y.
2*(y - 1)*(y + 1)**2
Let c(u) = -u**2 - 7*u + 10. Let k be c(-8). Suppose -2*f - k + 6 = 0. Determine l, given that -4*l**5 - 4*l**2 - f*l**4 + 2*l**3 + 2*l**5 + 6*l**2 = 0.
-1, 0, 1
Let r(a) be the third derivative of -2*a**7/105 + 2*a**5/15 - 2*a**3/3 - 14*a**2. Factor r(m).
-4*(m - 1)**2*(m + 1)**2
Let p = 2 - 4. Let y be (p/(-5))/((-7)/(-35)). Factor -25/2*s**y - 2 - 10*s.
-(5*s + 2)**2/2
Let u(r) = -r**2 + r - 2. Let i be u(0). Let h = i + 2. Factor h*o**3 + 0 + 0*o - 1/2*o**2 + 1/2*o**4.
o**2*(o - 1)*(o + 1)/2
Let i(u) be the third derivative of -u**7/420 - u**6/80 + u**4/12 - 10*u**2. Suppose i(t) = 0. What is t?
-2, 0, 1
Factor -d - 3*d**2 - 8*d + d - 4*d.
-3*d*(d + 4)
Suppose s + 2*c = c + 6, 2*s - 5*c = -2. Factor -2*h**4 + s*h**3 + 0 - 2*h**2 + 0.
-2*h**2*(h - 1)**2
Let b(h) = h**3 + h**2 - h + 45. Let y be b(0). Suppose -3*d + y = 15. Suppose 4 + d*t + 12*t**2 - 2 - 4*t**2 = 0. What is t?
-1, -1/4
Suppose 20*s = 12*s + 16. Determine y, given that -y**3 + 1/4*y**s + 0 + 0*y + y**4 = 0.
0, 1/2
Let q(m) be the second derivative of -m**6/150 + m**5/100 - 15*m. Factor q(z).
-z**3*(z - 1)/5
Let r(a) be the first derivative o