*u + 10*u**2 + 2/9*u**4.
2*(u - 7)**2*(u - 2)*(u + 2)/9
What is i in -82/13 + 84/13*i - 2/13*i**2 = 0?
1, 41
Let l(v) be the first derivative of v**6/18 + v**5/3 + 3*v**4/4 + 7*v**3/9 + v**2/3 - 179. Suppose l(q) = 0. Calculate q.
-2, -1, 0
Let 20/7*k - 2/7*k**2 + 22/7 = 0. Calculate k.
-1, 11
Let n(k) be the first derivative of k**6/345 + 3*k**5/230 + k**4/69 - 13*k - 15. Let j(r) be the first derivative of n(r). Find v such that j(v) = 0.
-2, -1, 0
Let r(z) be the third derivative of z**6/140 + 7*z**5/30 + 61*z**4/84 + 5*z**3/7 + 123*z**2 - 1. Factor r(f).
2*(f + 1)*(f + 15)*(3*f + 1)/7
Factor -1 - 12/11*y - 1/11*y**2.
-(y + 1)*(y + 11)/11
Let v(u) be the third derivative of -1/32*u**4 + 0*u + 0 - 1/12*u**3 - 1/240*u**5 - 4*u**2. Determine s, given that v(s) = 0.
-2, -1
Determine r so that -5404*r**2 + 5404*r**2 - 3*r**4 = 0.
0
Suppose -5*y = -3*b + 37, -3*y + 8 = 2*b + 2*y. Suppose -1 + b - 4 + 3*v**2 + 5 - 12*v = 0. What is v?
1, 3
Suppose -5*a = 5*o + 20, -8 = -4*o - o + 2*a. Suppose o = -3*z - 15, 5*z - 3 = -4*u + 2*u. Factor -4 + 4 - 12*t**4 - 2*t**2 + 2*t - 2*t**3 + u*t**4.
2*t*(t - 1)**2*(t + 1)
Suppose -3*a - 7*a + 20 = 0. Suppose -30 = -5*b - m - 10, a*b = -4*m + 26. Suppose 0*w**2 - 2/3*w**5 - 4/3*w**b - 2*w**4 + 0 + 0*w = 0. Calculate w.
-2, -1, 0
Let r be 1 - 20/(560/21). Find c such that -r*c**3 + 0 + 0*c + 1/4*c**4 - 1/2*c**2 = 0.
-1, 0, 2
Factor 0*l + 0 + 9*l**2 + 15/2*l**3.
3*l**2*(5*l + 6)/2
Suppose -68 - 338 = -58*y. Let i(m) be the second derivative of -7/225*m**6 + 0 - 8/45*m**3 - 3/25*m**5 - 2/9*m**4 - y*m - 1/315*m**7 + 0*m**2. Solve i(g) = 0.
-2, -1, 0
Suppose -w + 0 + 1 = 0. Let g(b) = -b**3 - 12*b**2 + b + 14. Let f be g(-12). Factor 54*q**3 - 7 + f - w + 2 - 84*q**2 + 34*q.
2*(q - 1)*(3*q - 1)*(9*q - 2)
Suppose -3*p - 6*p + 13*p = 0. Let a(u) be the third derivative of -1/240*u**5 + 1/32*u**4 + 0*u + p*u**3 + 9*u**2 + 0. Let a(w) = 0. What is w?
0, 3
Let u(s) = -s**3 - 16*s**2 + 18*s + 12. Let b be u(-17). Let p be b/4*(-64)/160. Suppose -1/4 + p*f - 1/4*f**2 = 0. What is f?
1
Let w(t) be the first derivative of 65*t**6/21 + 66*t**5/5 - 74*t**4/7 - 88*t**3/7 - 16*t**2/7 - 303. Find z such that w(z) = 0.
-4, -2/5, -2/13, 0, 1
Suppose -5*v + 9 = 2*y + 16, -3*v - 29 = -5*y. Let -3*h - 11/4*h**2 + 3*h**3 + 7/4*h**y + 1 = 0. What is h?
-2, -1, 2/7, 1
Let i(r) be the first derivative of 2*r**3/21 + 5*r**2/7 + 12*r/7 + 18. Factor i(q).
2*(q + 2)*(q + 3)/7
Let g be -2 + 20/12 + 5/15. Factor 3/2*r + g - 3/2*r**2.
-3*r*(r - 1)/2
Let m = 0 + -10. Let b = m + 50. Factor -2*j**2 - b*j**3 + 3*j**4 + 37*j**3 + j**5 - 3*j**4.
j**2*(j - 2)*(j + 1)**2
Suppose -12 = 10*j + 8. Let t be 31/62 + (j/(-8))/(-1). Let t*b**5 + 0*b + 1/4*b**4 - 1/4*b**3 - 1/4*b**2 + 0 = 0. What is b?
-1, 0, 1
Let l(w) be the third derivative of -w**7/2520 - 7*w**6/1080 - w**5/60 + 5*w**3/2 + 18*w**2. Let m(v) be the first derivative of l(v). Factor m(d).
-d*(d + 1)*(d + 6)/3
Let i be (7 - 9)*((-192)/(-98) - 2). Let m = 139/98 + i. Factor -3*h**2 - 3/2*h + m*h**3 + 3.
3*(h - 2)*(h - 1)*(h + 1)/2
Let b(p) = 18*p**2 - 25*p - 495. Let k be b(6). Find a, given that -21/5*a + k*a**2 + 9/5 - 3/5*a**3 = 0.
1, 3
Suppose 5*f = 2*r + 105, 6 = 3*f + 4*r - 31. Factor -36*h + f*h - 60*h**2 - 55*h + 6 + 50*h**3 - 22.
2*(h - 2)*(5*h + 2)**2
Let q(y) be the third derivative of 0*y + 4/15*y**5 + 0*y**3 + 0 + 2/3*y**4 + 1/30*y**6 + 22*y**2. Solve q(l) = 0 for l.
-2, 0
Let x(c) be the second derivative of -c**4/6 + 13*c**3/3 - 40*c**2 + 24*c - 8. Solve x(s) = 0.
5, 8
Let b(d) = -d**3 + d**2 + d. Let j be (-6)/8 - (-3)/(-12). Let f(v) = -30*v**3 + 25*v**2 + 25*v. Let z(c) = j*f(c) + 25*b(c). Solve z(y) = 0 for y.
0
Let g(z) = -3*z**3 + 16*z**2 + 26*z + 14. Let j(t) = -t**3 + 5*t**2 + 8*t + 4. Let x(i) = 6*g(i) - 21*j(i). Suppose x(s) = 0. What is s?
-1, 0, 4
Let c(a) be the first derivative of a**4/20 + 7*a**3/3 - 494. Solve c(h) = 0.
-35, 0
Let d(w) be the first derivative of w**4/4 - 29*w**3/3 + w**2/2 - 29*w + 11. Let a be d(29). Factor a*j**2 + 2/5*j**3 - 2/5*j + 0.
2*j*(j - 1)*(j + 1)/5
Let h(q) be the third derivative of 2/105*q**7 + 0*q**3 - 1/30*q**6 + 0 + 0*q**4 - 25*q**2 + 0*q - 1/15*q**5 + 1/84*q**8. Factor h(v).
4*v**2*(v - 1)*(v + 1)**2
Let k(g) be the first derivative of -g**6/6 - 67*g**5/5 - 789*g**4/2 - 4914*g**3 - 41013*g**2/2 - 27783*g + 334. Suppose k(y) = 0. What is y?
-21, -3, -1
Let a(v) = 33*v**3 - 93*v**2 - 33*v + 402. Let y(m) = -8*m**3 + 23*m**2 + 8*m - 100. Let l(j) = -5*a(j) - 21*y(j). Factor l(b).
3*(b - 5)*(b - 3)*(b + 2)
Let f = -568 - -572. Let z(s) be the second derivative of -1/4*s**2 + 0 + s - 1/6*s**3 - 1/24*s**f. Solve z(i) = 0.
-1
Let g(w) be the second derivative of 1/10*w**5 + 0*w**3 + 7*w - 7/30*w**6 + 1/12*w**4 + 0 + 0*w**2 + 2/21*w**7. Factor g(m).
m**2*(m - 1)**2*(4*m + 1)
Let u be ((-20)/120)/(2/(-36)). Let s be 10*2/8 + (-6)/u. Factor -4*q**2 - s + 9/4*q + 1/4*q**5 + 7/2*q**3 - 3/2*q**4.
(q - 2)*(q - 1)**4/4
Let c(t) = t**3 - 6*t**2 - 5*t - 12. Let v be c(7). Let p = -10586/15 - -706. Factor -2/15*r**4 + 0*r**v - 4/15*r**3 + p*r + 2/15.
-2*(r - 1)*(r + 1)**3/15
Factor -13*o**2 - 16*o**2 + 3*o**3 + 5*o**2 + 132 + 119416*o - 119527*o.
3*(o - 11)*(o - 1)*(o + 4)
Suppose 4*i - 3*i - 13 = 0. Let b = i + -11. Factor -b - 3*j**3 - 2 - 15*j + 3*j**2 - 2 - 15*j**2.
-3*(j + 1)**2*(j + 2)
Let t(u) be the third derivative of -u**6/210 + u**5/35 + 5*u**4/21 - 16*u**3/7 + 88*u**2. Factor t(q).
-4*(q - 4)*(q - 2)*(q + 3)/7
Let o(v) = v**3 + v**2 - 55*v - 55. Let q be o(-1). Factor -2/3 + q*f**2 + 2/3*f**4 + 4/3*f - 4/3*f**3.
2*(f - 1)**3*(f + 1)/3
Determine p so that 34225/4 + 1/4*p**2 + 185/2*p = 0.
-185
Let m(z) = 10. Let c(h) be the third derivative of h**5/60 + h**4/24 + 29*h**3/6 + h**2. Let l(x) = 2*c(x) - 7*m(x). Solve l(j) = 0 for j.
-3, 2
Factor -6/19*g**2 - 2/19*g**4 - 10/19*g**3 + 0 + 18/19*g.
-2*g*(g - 1)*(g + 3)**2/19
Let d = -218955499/60 + 7297761/2. Let v = d - -1515/4. Solve -4/15 - 2/3*c**2 - v*c = 0 for c.
-1, -2/5
Let s = 218 - 206. Let 3*d**4 + 3/2*d**5 - 21/2*d - 3 - s*d**2 - 3*d**3 = 0. Calculate d.
-1, 2
Let h(z) be the first derivative of z**5 + 5*z**4/4 - 5*z**3/3 - 5*z**2/2 + 11. Factor h(m).
5*m*(m - 1)*(m + 1)**2
Let a = -10 - -9. Let y = a - -1. Determine o so that 0*o + y*o**2 - 2*o**3 - 2*o - 4*o**2 = 0.
-1, 0
Suppose 4*k + 30 = 5*t, t + 2*k = 8 - 2. Let c be t/(-27) + 58/18. Factor -6*r**4 - 8*r**c + 2*r**5 + r**5 + 11*r**3.
3*r**3*(r - 1)**2
Let x = -46/61 + 199/183. Let t(z) be the first derivative of 6 + 40/27*z**3 - 4/9*z - x*z**2. Suppose t(n) = 0. Calculate n.
-1/4, 2/5
Factor 26*t**2 + 460 + 22*t + 34*t - 460 - t**3.
-t*(t - 28)*(t + 2)
Let b(c) = -5*c**4 + 38*c**3 - 62*c**2 - 2*c - 2. Let k(o) = 10*o**4 - 75*o**3 + 125*o**2 + 5*o + 5. Let g(v) = -5*b(v) - 2*k(v). Solve g(t) = 0.
0, 2, 6
Suppose 0 = 5*v - h + 4, 17*v - 20*v = 5*h - 20. Let p(i) be the second derivative of -3/10*i**2 + 0*i**3 - 2*i + v + 4/5*i**4. Factor p(a).
3*(4*a - 1)*(4*a + 1)/5
Let c(v) be the first derivative of -243*v**6/160 - 189*v**5/80 - 3*v**4/2 - v**3/2 + 9*v**2/2 + 11. Let j(s) be the second derivative of c(s). Factor j(q).
-3*(3*q + 1)*(9*q + 2)**2/4
Factor 63/4*g**2 + 0*g + 1/4*g**4 - 33/4*g**3 + 0 + 1/4*g**5.
g**2*(g - 3)**2*(g + 7)/4
Let w(j) be the third derivative of 5*j**5/12 + 5*j**4/12 - 40*j**3/3 + 788*j**2. Let w(u) = 0. What is u?
-2, 8/5
Let -2*g - 8/7 - 1/7*g**3 - g**2 = 0. What is g?
-4, -2, -1
Let q(v) be the second derivative of v**7/8400 + v**6/900 + v**5/240 + v**4/120 + v**3/3 + 10*v. Let d(u) be the second derivative of q(u). Factor d(h).
(h + 1)**2*(h + 2)/10
Let r(o) be the first derivative of 2*o**6/9 - 16*o**5/15 + 2*o**4/3 + 16*o**3/9 - 2*o**2 - 137. What is n in r(n) = 0?
-1, 0, 1, 3
Let b(w) be the first derivative of 3*w**5/4 - 3*w**4/4 - 13*w**3/2 - 15*w**2/2 - 9*w/4 - 112. Solve b(x) = 0.
-1, -1/5, 3
Let c be -4 + (-110)/(-5) - 3. Determine q, given that -8 + q - 4*q - 4*q**2 + c*q = 0.
1, 2
Factor 74/7*q**2 - 2/7*q**3 + 648/7 - 720/7*q.
-2*(q - 18)**2*(q - 1)/7
Let f(t) be the second derivative of -t**7/399 - t**6/285 + t**5/190 + t**4/114 + 4*t + 1. Determine c so that f(c) = 0.
-1, 0, 1
Determine w so that -14*w + 46*w + 13*w**2 - 28 - 17*w**2 = 0.
1, 7
Let u(c) be the third derivative of 0*c