48*y**4 - 5*y**2 + 0*y + 0*y**3 + x*y**5 + 1/240*y**6 + 0 - 1/420*y**7. Factor k(d).
-d*(d - 1)**2*(d + 1)/2
Suppose -5*s = 4*p + 245, -p - 7 = -2. Let w be ((-3)/s)/((-1)/(-8)). Factor w + 2/5*q - 2/15*q**2.
-2*(q - 4)*(q + 1)/15
Let d(f) be the second derivative of -f**4/36 + 6*f**2 + 4*f - 134. Factor d(w).
-(w - 6)*(w + 6)/3
Let a(k) = -88*k - 4. Let o be a(2). Let c = 182 + o. Factor 0 - 3/5*h**3 + 3/5*h - 3/5*h**c + 3/5*h**4.
3*h*(h - 1)**2*(h + 1)/5
Let s(b) = -4*b - 132. Let t be s(-34). Let x(a) be the second derivative of -5/48*a**4 + 0 + t*a - 1/3*a**3 + 1/2*a**2. Factor x(c).
-(c + 2)*(5*c - 2)/4
Let k(v) be the second derivative of 3/10*v**6 + 0*v**2 - 4*v + 3/2*v**5 - 2*v**3 + 0 - 9/4*v**4. Factor k(p).
3*p*(p - 1)*(p + 4)*(3*p + 1)
Let x(a) = 2*a**3 + 2*a - 1. Let i(b) = 3*b**3 - 17*b**2 - 26*b - 2. Let n(d) = -i(d) + 2*x(d). Let n(h) = 0. What is h?
-15, -2, 0
Suppose -17*z + 12 = -14*z. Find o such that -o**2 - 2 + 6*o - z*o**2 - o**2 + 2*o**3 = 0.
1
Let m(w) = -64*w**2 + 3140*w - 1231. Let j(o) = -17*o**2 + 785*o - 308. Let x(k) = 9*j(k) - 2*m(k). Solve x(u) = 0 for u.
2/5, 31
Let q(c) be the third derivative of 9/40*c**6 + 2*c**4 - 2*c**3 + 0 - 21/20*c**5 + 0*c + 55*c**2. Factor q(x).
3*(x - 1)*(3*x - 2)**2
Let k(g) be the third derivative of 0*g**4 - 16/525*g**7 + 0*g**3 - 1/120*g**8 + 0 + 0*g - 1/75*g**5 - 11/300*g**6 - 4*g**2. Suppose k(i) = 0. Calculate i.
-1, -2/7, 0
Let c(w) be the third derivative of -1/20*w**5 + 0*w + 0 + 1/4*w**4 - 5*w**2 - 1/2*w**3. Factor c(o).
-3*(o - 1)**2
Let i = 22/163 + -2698/15159. Let u = 85/186 - i. Factor -u*d**2 + 1/4*d + 0 + 1/4*d**3.
d*(d - 1)**2/4
Let y be ((-625)/15)/((-22)/33*3). Factor 1/6*b**3 - y + 25/2*b - 5/2*b**2.
(b - 5)**3/6
Let t = 98 - 96. Let q(s) = -6*s**2 + 13*s - 2. Let z be q(t). Factor z*l - 1/2*l**3 - 1/6*l**4 + 0 + 0*l**2.
-l**3*(l + 3)/6
Let x be (-5 - -11 - -2) + -8. Factor 12/5*l + 2/5*l**2 - 2/5*l**3 + x.
-2*l*(l - 3)*(l + 2)/5
Let t = -1040/7 - -148. Let m = 34/35 + t. Find d such that -2/5*d**2 + m*d**4 - 2/5*d**5 + 0 + 0*d + 2/5*d**3 = 0.
-1, 0, 1
Let s(p) = 5*p**3 - 11*p**2 - 19*p - 9. Let b(a) = -55*a**3 + 120*a**2 + 210*a + 100. Let v(u) = 6*b(u) + 65*s(u). Factor v(k).
-5*(k - 3)*(k + 1)**2
Let 33/4*y - 139/8*y**2 + 9*y**4 + 2*y**5 - 1 - 7/8*y**3 = 0. Calculate y.
-4, -2, 1/4, 1
Let k(t) be the third derivative of 0*t - 5/12*t**4 - 23*t**2 + 0 - 3/8*t**6 - 7/12*t**5 - 5/336*t**8 - 5/42*t**7 + 0*t**3. Determine q so that k(q) = 0.
-2, -1, 0
Let n(d) be the second derivative of -3/8*d**3 + 0*d**2 - 20*d - 1/80*d**5 + 0 + 1/8*d**4. Let n(c) = 0. What is c?
0, 3
Let p = 316 - 1798/5. Let q = p + 44. Factor 2/5*i - q*i**3 + 2/5*i**4 + 0 - 2/5*i**2.
2*i*(i - 1)**2*(i + 1)/5
Let m(z) be the second derivative of 5*z**6/6 + 21*z**5/4 + 95*z**4/12 + 5*z**3/2 + 20*z. What is v in m(v) = 0?
-3, -1, -1/5, 0
Let u(p) = p**3 - 2*p**2 - 6*p + 5. Let o be u(4). Factor 8*c + o*c**2 + c**3 - 4*c**2 - 5*c**2 - 5*c**3.
-4*c*(c - 2)*(c + 1)
Let c(k) be the third derivative of 0*k**4 + 1/2184*k**8 - 11*k**2 + 0*k**3 + 2/1365*k**7 - 1/195*k**5 - 1/780*k**6 + 0*k + 0. Suppose c(j) = 0. Calculate j.
-2, -1, 0, 1
Let x be -4 + (15/3 - 16/(-4)). Factor -3*m + 6*m**3 + 3*m**4 + m**x + 3 + 4*m**5 - 8*m**5 - 6*m**2.
-3*(m - 1)**3*(m + 1)**2
Let b(r) be the third derivative of 27*r**6/160 + 3*r**5/16 - r**4/3 + r**3/6 + 56*r**2. Find p, given that b(p) = 0.
-1, 2/9
Let s(q) be the second derivative of q**3/6 + q**2/2 - 7*q. Let b(h) = h**3 - 12*h**2 + 45*h - 67. Let y(f) = -2*b(f) - 6*s(f). Determine u so that y(u) = 0.
4
Let h(x) be the second derivative of -x**7/168 - x**6/60 + x**5/40 + x**4/6 + 7*x**3/24 + x**2/4 + 30*x - 2. Factor h(q).
-(q - 2)*(q + 1)**4/4
Let o(k) = 6*k + 16. Let g be o(-2). Find h such that 6/19*h**g + 0*h + 0 - 2/19*h**3 - 4/19*h**2 = 0.
-2/3, 0, 1
Let c(s) be the second derivative of 0 + 2/21*s**3 - 1/10*s**5 - 5/42*s**4 + 0*s**2 + 14*s. Factor c(o).
-2*o*(o + 1)*(7*o - 2)/7
Let d(g) be the third derivative of g**7/1050 + g**6/150 + g**5/60 + g**4/60 + 18*g**2 - 6. Factor d(o).
o*(o + 1)**2*(o + 2)/5
Suppose -5*v + 3*v = 0. Suppose n - 6*n + 25 = v. Solve -4*g**4 + n*g**2 + 10*g**3 + 4*g**3 - 14*g**5 - g**2 = 0.
-1, -2/7, 0, 1
Let a(h) = h**3 - 7*h**2 + 4*h + 14. Let v(r) = r**3 - 9*r**2 + 9*r - 2. Let c be v(8). Let j be a(c). Suppose 3 + 4*u - u + u**2 - u - 2*u**j = 0. What is u?
-1, 3
Suppose 4*t - 2*h - 15 = 3*h, -4*h = 2*t + 12. Let r(u) be the second derivative of t*u**2 - 1/2*u**4 + 0*u**3 + 0 - 9*u + 3/20*u**5. Factor r(v).
3*v**2*(v - 2)
Let a(k) be the third derivative of -18 - 3/32*k**4 - 7/12*k**3 + 0*k - 1/240*k**5 + k**2. Suppose a(f) = 0. Calculate f.
-7, -2
Let x(t) be the first derivative of -t**6/300 - t**5/50 - t**4/30 + 5*t**2 + 8. Let r(j) be the second derivative of x(j). Suppose r(n) = 0. Calculate n.
-2, -1, 0
Let w(p) be the first derivative of -p**4 - 184*p**3/3 + 166. Factor w(k).
-4*k**2*(k + 46)
Let l = -144 - -173. Let m be 14/(-4) - (l - 35). Let -m*n**2 + 0 + 15/2*n = 0. Calculate n.
0, 3
Let p(u) be the third derivative of -1/80*u**6 + 0*u**4 + 1/210*u**7 + 0*u + 0 + 0*u**3 + 1/120*u**5 - 8*u**2. What is l in p(l) = 0?
0, 1/2, 1
Let p(m) be the second derivative of 5*m**6/72 - m**5/6 - 5*m**4/24 - 3*m**3 - 9*m. Let o(f) be the second derivative of p(f). Factor o(h).
5*(h - 1)*(5*h + 1)
Let h(x) = -5*x**3 - 485*x**2 + 6245*x - 5770. Let d(p) = 4*p**3 + 242*p**2 - 3123*p + 2886. Let l(c) = -5*d(c) - 3*h(c). Factor l(v).
-5*(v - 24)**2*(v - 1)
Let c(x) = -6*x**2 - 14*x - 28. Let h(z) = 4*z**2 + 10*z + 19. Let a(v) = 5*c(v) + 8*h(v). Suppose a(n) = 0. What is n?
-3, -2
Let w(u) = -10*u + 5. Let i be w(-2). Let r be (-2 - -6) + i/(-7). Suppose r*p**4 + 0 + 15/7*p**2 - 6/7*p - 12/7*p**3 = 0. What is p?
0, 1, 2
Let f be 30/26 + 0 - 1. Let x be (1431/(-795))/((-6)/10). Determine g, given that -f*g**x - 10/13*g**2 - 6/13 - 14/13*g = 0.
-3, -1
Let s(f) be the third derivative of -f**7/504 - f**6/36 - f**5/8 - f**4/2 - 7*f**2. Let v(m) be the second derivative of s(m). Factor v(l).
-5*(l + 1)*(l + 3)
Let f be (115/506)/((147/36 - 4)*15). Solve -f*p**2 + 0*p + 8/11 = 0.
-2, 2
Factor 30 + u + 505*u**3 - 251*u**3 - 30*u**2 - 255*u**3.
-(u - 1)*(u + 1)*(u + 30)
Let i(w) = -116505*w**2 - 6255*w - 120. Let f(j) = -6853*j**2 - 368*j - 7. Let x(b) = -35*f(b) + 2*i(b). Suppose x(p) = 0. Calculate p.
-1/37
Suppose -14*n + 15*n = 5. Solve -10*y - 3*y + 3*y - n*y**2 = 0.
-2, 0
Factor -2/5*j**3 + 0 - 4/5*j - 6/5*j**2.
-2*j*(j + 1)*(j + 2)/5
Let f(j) be the first derivative of j**6/45 + 14*j**5/75 + 2*j**4/15 - 8*j**3/15 - 423. Let f(s) = 0. What is s?
-6, -2, 0, 1
Let l(u) = u**2 - 421*u - 22469. Let q(d) = -2*d**2 + 420*d + 22468. Let s(h) = 4*l(h) + 3*q(h). Factor s(k).
-2*(k + 106)**2
Let n(m) = -m**4 + 8*m**2 + 12*m + 5. Let d(h) = h**3 + h**2 - h - 1. Suppose 6*t - 3*t - 3 = 0. Let p(r) = t*n(r) + d(r). Determine v so that p(v) = 0.
-1, 4
Let q(p) be the third derivative of p**5/150 - 23*p**4/30 + 529*p**3/15 - 3*p**2 + 81*p. Suppose q(y) = 0. What is y?
23
Factor 24*q + 15*q**4 - 12*q + 35*q**3 - 32*q.
5*q*(q + 1)*(q + 2)*(3*q - 2)
Let a = 2392 + -2392. Determine o so that -2/15*o**5 + 0*o + a*o**4 + 2/15*o**3 + 0 + 0*o**2 = 0.
-1, 0, 1
Let y(k) be the first derivative of -4/3*k**3 - 9*k**2 - 8*k - 17. What is h in y(h) = 0?
-4, -1/2
Let l be 24/3 - 4 - (1 + 38). Let c = -35 - l. Find v such that 0 + c*v + 3/2*v**4 - 3/2*v**3 - 1/2*v**5 + 1/2*v**2 = 0.
0, 1
Let q(z) be the second derivative of z**4/30 + 4*z**3/5 + 11*z**2/5 - 279*z + 2. Factor q(v).
2*(v + 1)*(v + 11)/5
Let b(g) be the first derivative of -7*g**6/660 + 13*g**5/165 - 5*g**4/33 - 8*g**3/33 + 17*g**2/2 + 3. Let q(u) be the second derivative of b(u). Factor q(w).
-2*(w - 2)**2*(7*w + 2)/11
Let p = -3152 - -34641/11. Let h = p + 250/77. Solve -2/7 + h*a - 1/7*a**2 = 0 for a.
1, 2
Let f be 5244/(-36)*(-7)/30. Let s = f + -296/9. Factor 0 + s*d**2 + 7/10*d**4 - 1/5*d - 8/5*d**3.
d*(d - 1)**2*(7*d - 2)/10
Let y(v) be the first derivative of v**5/20 + 9*v**4/16 + 9*v**3/4 + 27*v**2/8 + 145. Suppose y(x) = 0. Calculate x.
-3, 0
Solve 60/7 + 9/7*t**2 + 183/7*t = 0 for t.
-20, -1/3
Let y = 129 - 126. Let l(b) be the second derivative of 0 + 0*b**2 - 1/60*b**4 + 1/10*b**y - b. Factor