 3*m**2 + 27*m. Determine s, given that l(s) = 0.
-4, -3
Let r(o) be the third derivative of o**7/420 + o**6/10 + 26*o**5/15 + 16*o**4 + 256*o**3/3 + 6*o**2 + 20*o. Find c, given that r(c) = 0.
-8, -4
Factor 2/5*n**3 - 192/5*n**2 + 6144/5*n - 65536/5.
2*(n - 32)**3/5
Let w(s) = -s**2 - 7*s - 2. Let n be w(-7). Let q be n + -4*(-4 - -3). Factor 8*r**q - 12*r**4 + 47*r**4 - 52*r**3 + 37*r**4.
4*r**2*(2*r - 1)*(9*r - 2)
Suppose 49/4*v**5 - 4761 - 362185/4*v**2 + 6685/4*v**4 + 37950*v + 222695/4*v**3 = 0. Calculate v.
-69, 2/7, 1
Let b(h) be the third derivative of h**5/40 - 7*h**4/8 + 49*h**3/4 - 5*h**2. Find t such that b(t) = 0.
7
Let s(i) be the third derivative of 16/3*i**3 - 52*i**2 + 0*i + 2/5*i**5 - 2*i**4 - 1/30*i**6 + 0. Factor s(h).
-4*(h - 2)**3
Let s be (-4)/((-24)/(-15))*-2. Suppose 5 = -s*u + 20. Determine g so that 29*g + 18*g**2 - g**4 + 4*g**4 - 41*g + 3 - 12*g**u = 0.
1
Let j(f) be the first derivative of 4*f + 1/10*f**5 + 10 + 3*f**3 - 7/8*f**4 - 5*f**2. Let j(d) = 0. What is d?
1, 2
Suppose -5*w = -f + 63, f - 4*w - 23 - 40 = 0. Find q, given that -22 - f*q**3 - 17*q**3 - 23 + 58*q**2 - 258*q**2 - 165*q = 0.
-1, -3/4
Let c(z) be the first derivative of z**4/10 - 4*z**3/15 - 7*z**2/5 - 8*z/5 - 238. Solve c(k) = 0 for k.
-1, 4
Let y(h) = 2*h**3 - 2*h**2 - 4*h + 4. Let i be y(2). Let j = 18 - 15. Suppose 643*v**j - 9*v**2 - 643*v**3 - 6*v + 3*v**i = 0. What is v?
-1, 0, 2
Let r(a) = -5*a**3 + 202*a**2 - 694*a + 692. Let p(z) = 5*z**3 - 200*z**2 + 695*z - 690. Let x(h) = 6*p(h) + 5*r(h). Factor x(n).
5*(n - 34)*(n - 2)**2
Let m(a) be the second derivative of 2/3*a**4 + 9*a + 3/5*a**5 - 2*a**3 + 0 - 4*a**2. Let m(u) = 0. What is u?
-1, -2/3, 1
Let z(w) = -5*w**2 + 41*w - 94. Let s(n) = n + 1. Let v(d) = 4*s(d) + z(d). Find g such that v(g) = 0.
3, 6
Let c = -7 + 3. Let f(b) = 9*b**4 - 10*b**3 + 9*b**2 + 4. Let o(l) = 8*l**4 - 10*l**3 + 8*l**2 + 3. Let u(v) = c*o(v) + 3*f(v). Factor u(a).
-5*a**2*(a - 1)**2
Let j = -14558/7 + 2080. Factor 2/7 - j*r**4 + 4/7*r**3 - 4/7*r + 0*r**2.
-2*(r - 1)**3*(r + 1)/7
Let t be (-280)/240 + 44/33. Find y such that 0*y**3 + 1/3*y**2 - 1/6*y**4 + 0*y - t = 0.
-1, 1
Let g be (2*9/(-6))/(-12 + 14 - 3). Find t such that 1/6*t**4 + 0 + 1/3*t**g + 2/3*t - 7/6*t**2 = 0.
-4, 0, 1
Let f(i) be the third derivative of -i**7/1260 - i**6/120 - i**5/40 + 15*i**2. Factor f(u).
-u**2*(u + 3)**2/6
Let r be 0 + 10*4/(-8). Let v be (-5 - (-4 + 0)) + r/(-4). Factor 1/2*h + v + 1/4*h**2.
(h + 1)**2/4
Suppose -25*m = -4*n - 23*m + 22, 0 = n + 3*m + 19. Let 1/2*a**n + 1/2*a - 3 = 0. What is a?
-3, 2
Let f(b) be the first derivative of -3*b**4/4 - 3*b**3 + 27*b**2/2 - 15*b + 299. Let f(m) = 0. What is m?
-5, 1
Suppose -4*v + 5*k = 5, -4*k - 3 = -5*v + 2. Suppose 0 = -4*t + 25 - v. Suppose 7*s**2 - t*s + 0*s + 3*s = 0. Calculate s.
0, 2/7
Suppose 4*z - 3*w - 32 = 0, 3*z = 4*z - w - 9. Factor -7*t**2 + 7*t**2 - 10*t**2 + 3*t - z + 12*t.
-5*(t - 1)*(2*t - 1)
Let s(k) = -3*k**2 - 14*k - 24. Let l(v) = 12*v**2 + 57*v + 96. Let g(r) = 4*l(r) + 15*s(r). Factor g(d).
3*(d + 2)*(d + 4)
Let o be (-8 + 2)*(-15)/45. Factor -45/8*k + 21/8*k**o + 27/8 - 3/8*k**3.
-3*(k - 3)**2*(k - 1)/8
Let i(b) be the second derivative of -b**7/1400 + b**5/200 - b**3/2 - 9*b. Let c(a) be the second derivative of i(a). Factor c(u).
-3*u*(u - 1)*(u + 1)/5
Let o(v) be the first derivative of -4/3*v**3 + 0*v - 16 - 2/5*v**2. Factor o(n).
-4*n*(5*n + 1)/5
Let b(w) be the first derivative of w**3/6 + 55*w**2/4 - 57*w + 605. Factor b(n).
(n - 2)*(n + 57)/2
Factor 9 - 6338*p**2 + 6364*p**2 + 1 + 32*p + 4*p**3.
2*(p + 1)*(p + 5)*(2*p + 1)
Factor -3/4*a**5 + 0 - 9*a**3 - 15/2*a**2 - 9/2*a**4 - 9/4*a.
-3*a*(a + 1)**3*(a + 3)/4
Let p(a) = -a**2 + 9*a + 15. Let k be p(7). Let 15*y**4 + 5*y**4 + k*y**3 - 2*y**2 + 5*y**5 + 12*y**2 - 4*y**3 = 0. Calculate y.
-2, -1, 0
Let t(o) be the first derivative of 3*o**4/4 - o**3 - 3*o**2 - 48. Find u such that t(u) = 0.
-1, 0, 2
Suppose -2*p + 15 - 9 = 0. Find h such that 3*h**4 - 11*h**3 + 6*h**p + 2*h**3 = 0.
0, 1
Suppose 0 = -2*b + 3*v + 16, 5*b - 3*v = -8 + 30. Suppose -3/2*o**b - 11/2*o - 3 = 0. What is o?
-3, -2/3
Let i(c) = 68*c**3 + 132*c**2 + 16*c - 8. Let w(g) = 0 - 45*g**3 - 7 + 1 + 11 - 88*g**2 - 11*g. Let h(y) = 5*i(y) + 8*w(y). Find x, given that h(x) = 0.
-2, -1/5, 0
Factor 0*n - 10/9*n**4 + 2/9*n**5 + 8/9*n**3 + 0*n**2 + 0.
2*n**3*(n - 4)*(n - 1)/9
Determine i so that 2/7 - 19/7*i + 9/7*i**2 = 0.
1/9, 2
Suppose 6*s = -0*s + 6. Let z be -24*s/13 - -2. Factor 2/13*j + z*j**2 + 0.
2*j*(j + 1)/13
Let x(o) be the third derivative of o**9/3780 - o**7/315 + o**5/30 - 3*o**4/8 + 10*o**2. Let j(u) be the second derivative of x(u). Solve j(t) = 0 for t.
-1, 1
Suppose -5*u = 3*w - 22, 5*w - 2*w = -3*u + 12. Suppose -3*j + u*y = -7*j + 23, y + 22 = 3*j. Suppose j*v - 9*v + 4*v - 2*v**3 = 0. What is v?
-1, 0, 1
Let u(t) be the third derivative of -4/75*t**5 + 0*t - 1/15*t**4 + 0 - 1/60*t**6 - 1/525*t**7 + 0*t**3 - 3*t**2. Factor u(a).
-2*a*(a + 1)*(a + 2)**2/5
Factor -2*i**3 + 206*i + 241*i + 40*i**2 - 110*i**2 - 375*i.
-2*i*(i - 1)*(i + 36)
What is u in 75/4*u - 35/2*u**2 + 5/4*u**5 - 20*u**3 + 0 + 35/2*u**4 = 0?
-15, -1, 0, 1
Let j be (-144)/54*6/(-8). Suppose -5 - 27 + 36*c**j - 32*c - 22*c - 82*c = 0. What is c?
-2/9, 4
Let g(d) = 124 + 11*d**2 + 9*d**2 + 90*d + 6*d**2. Let y be (2/2)/(120/(-16) - -8). Let j(q) = 5*q**2 + 18*q + 25. Let b(a) = y*g(a) - 11*j(a). Factor b(c).
-3*(c + 3)**2
Let f = -8 - -4. Let i = 7 + f. Determine c, given that 24 - 2*c**i - 3*c**3 - 36*c - 2*c**3 + 4*c**3 + 18*c**2 = 0.
2
Let u(g) be the first derivative of -g**3/9 - g**2/3 - g/3 - 79. Find c, given that u(c) = 0.
-1
Let s(o) = -4*o**3 + 3*o - 1. Let p(l) = 69*l**3 + 15*l**2 - 54*l + 18. Let b(k) = p(k) + 18*s(k). Factor b(f).
-3*f**2*(f - 5)
Let q = 360 + -257. Let z = -103 + q. Factor 3/4*g**3 + z*g - 1/4*g**5 + 0*g**4 + 0 - 1/2*g**2.
-g**2*(g - 1)**2*(g + 2)/4
Let d(j) be the third derivative of -j**7/315 + 19*j**6/90 - 457*j**5/90 + 152*j**4/3 - 256*j**3 + 2*j**2 - 39. Let d(i) = 0. What is i?
3, 16
Let j = -65 + 72. Suppose 28 = 4*a - 4*m, 0*a - 3*a - 4*m = j. Factor 2/5*b - 9/5*b**2 + 7/5*b**a + 0.
b*(b - 1)*(7*b - 2)/5
Suppose -4*x + 2 = -30. Factor 3*i**5 + x*i + i**5 - 8*i**3 - 4*i.
4*i*(i - 1)**2*(i + 1)**2
Suppose -5*r + w + 7290 = -w, -4*r - w = -5845. Let v be 3/((-54)/(-4)) - r/(-720). Determine z, given that 0 - 9/4*z**3 - v*z**2 - 3/4*z**4 - 3/4*z = 0.
-1, 0
Let f = -79 + 71. Let s be f/(-6) - (-60)/(-54). Factor 0 - s*p - 2/9*p**2.
-2*p*(p + 1)/9
Let k(q) = 5*q**2 - 479*q - 496. Let i(b) = -85*b**2 + 8140*b + 8435. Let c(l) = -2*i(l) - 35*k(l). Let c(u) = 0. What is u?
-1, 98
Let f(z) = -5 + 5 - 1 + z. Let a be f(4). Factor 5*u - 3*u + 2*u - u**a - 3*u**3.
-4*u*(u - 1)*(u + 1)
What is h in 0 + 1/5*h**4 + 1/5*h**3 - 4/5*h - 4/5*h**2 = 0?
-2, -1, 0, 2
Let u = 5 - 3. Let a be (6/(-7))/(u/(-14)). Solve 3*o**5 - 6*o**2 + 2*o + a*o**4 + 0*o**5 - 5*o = 0 for o.
-1, 0, 1
Factor 2/3*w**2 - 1/3*w**5 + 0*w**3 + 1/3*w - 2/3*w**4 + 0.
-w*(w - 1)*(w + 1)**3/3
Let c(b) be the second derivative of -7*b**6/240 + 13*b**5/60 + b**4/6 + 9*b**2 + b. Let u(p) be the first derivative of c(p). Solve u(y) = 0.
-2/7, 0, 4
Let n be 7 - (44 - -4)/(30/4). Factor -3/5*u**3 - n*u**4 + 3/5*u**2 + 0 + 3/5*u.
-3*u*(u - 1)*(u + 1)**2/5
Let f = 4609 - 18435/4. Determine k, given that -5/4 - 3/2*k - f*k**2 = 0.
-5, -1
Let x(w) = -5*w**4 + w**3 + 13*w**2 + 5*w. Let s(l) = 4*l**4 - 12*l**2 - 4*l. Let u be -2 - (4 - 2 - -2). Let g(r) = u*x(r) - 7*s(r). Let g(i) = 0. What is i?
0, 1
Let y be (-2295)/(-2040) + 62/(-112). Factor -16/7*r + 4/7*r**3 + 16/7*r**2 + 0 - y*r**4.
-4*r*(r - 2)*(r - 1)*(r + 2)/7
Let s(l) be the third derivative of 4*l**4 - 3/5*l**5 - 32/3*l**3 + 1/30*l**6 + 0 - 3*l**2 + 0*l. Solve s(u) = 0 for u.
1, 4
Suppose n + 40 = 3*n. Let j = 22 - n. Factor 2*h**4 + 1/2 - 1/4*h - h**3 - 5/2*h**j + 5/4*h**5.
(h - 1)*(h + 1)**3*(5*h - 2)/4
Let m(g) be the second derivative of -g**7/105 + 4*g**6/15 + g**5/50 - 2*g**4/3 + 590*g. Suppose m(l) = 0. Calculate l.
-1, 0, 1, 20
Let q = 9005/3 + -2991. What is r in -25/6*r**3 - 2 - q*r - 95/6*r**2 = 0?
-3, -2/5
Suppose 8 = -2*y - 4*j, -6 = -3*y + 49*j - 46*j. Find l, given that y*l + 4/3 - 1/3*l**2 = 0.
-2,