*j**3 - 10*j + 157*j**2 + 184*j**2 = 0 for j.
-1/4, 0, 5
Let j(i) be the third derivative of -i**6/420 - i**5/105 + i**4/84 + 2*i**3/21 - 3*i**2 - 7*i. Factor j(h).
-2*(h - 1)*(h + 1)*(h + 2)/7
Let r = -56726/7 + 8104. Factor -8/7*g + 0*g**2 + 0 + 6/7*g**3 + r*g**4.
2*g*(g - 1)*(g + 2)**2/7
Let z(q) = 11*q**4 - 30*q**3 - 108*q**2 - 161*q + 9. Let i(v) = -5*v**4 + 15*v**3 + 56*v**2 + 80*v - 4. Let y(p) = 18*i(p) + 8*z(p). Factor y(o).
-2*o*(o - 19)*(o + 2)**2
Let i(v) be the second derivative of 0 - 2/3*v**3 - 1/12*v**4 + 5/2*v**2 + 28*v. Solve i(m) = 0.
-5, 1
Suppose -s + 581*l - 6 = 585*l, 14 = 3*s - 4*l. Let 18/11*x**4 + 26/11*x**3 - s*x**5 + 0 - 18/11*x**2 - 4/11*x = 0. Calculate x.
-1, -2/11, 0, 1
Let w be (308/980 - (-3)/(-5))/(17/(-7)). Determine n so that w*n**3 + 2/17*n - 4/17*n**2 + 0 = 0.
0, 1
Determine o, given that 111/2*o**2 - 105/2*o**3 + 105/2*o - 54 - 3/2*o**4 = 0.
-36, -1, 1
Let p = 5653 + -5653. Factor -2/15*b**3 + p*b + 0 - 4/15*b**2.
-2*b**2*(b + 2)/15
Let i(y) = 13*y**2 - 47*y + 22. Let o(j) = 28*j**2 - 94*j + 45. Let n(a) = -9*i(a) + 4*o(a). Determine r so that n(r) = 0.
2/5, 9
Suppose 5*y + 4*y - 3*y = -10*y. Determine z, given that 4/5*z**4 + 0 - 2/5*z**5 + 0*z**2 + y*z - 2/5*z**3 = 0.
0, 1
Factor -8/9*q**2 + 0 + 26/9*q.
-2*q*(4*q - 13)/9
Let f = -27 - -35. Suppose 32*g = k + 27*g + 23, -4*k - 2*g + 18 = 0. Factor -f - 1/2*t**k - 4*t.
-(t + 4)**2/2
Let v(d) be the third derivative of d**6/30 - 9*d**5/5 - 222*d**2. Factor v(w).
4*w**2*(w - 27)
Let n(j) be the first derivative of j**4/48 + j**3/12 + j**2/8 - 8*j - 2. Let r(w) be the first derivative of n(w). Solve r(l) = 0.
-1
Let v = -4 - -4. Suppose v*y + 2*y = 24. Factor -2*i**2 + 12 - y - i**3.
-i**2*(i + 2)
Let v(q) be the second derivative of q**6/60 + q**5/10 + q**4/8 + 1012*q. Suppose v(w) = 0. What is w?
-3, -1, 0
Let y = -8 - -12. Suppose y*v + w + 0*w - 18 = 0, -2*v = 3*w - 4. Factor -v*p**4 + 2*p**2 - 2*p**4 + 9*p**4 - 4*p**2.
2*p**2*(p - 1)*(p + 1)
Factor -8*z**2 + 1/4*z**3 - 17/2 - 67/4*z.
(z - 34)*(z + 1)**2/4
Let i be 3 + 54/6 + -7 + 1. Let n(w) be the third derivative of -1/5*w**5 + 0*w + 1/40*w**i - w**3 + 5*w**2 + 5/8*w**4 + 0. Find h such that n(h) = 0.
1, 2
Let z(k) be the first derivative of 7*k**4/24 + 5*k**3/12 - k**2/2 - 11*k + 8. Let c(i) be the first derivative of z(i). Factor c(f).
(f + 1)*(7*f - 2)/2
Let n(s) = -s**3 + 5*s**2 + 7*s - 4. Let d be n(6). Factor -16 + 3*c**d + 20*c + 66 - c**2.
2*(c + 5)**2
Let t(r) be the second derivative of r**4/3 + 28*r**3/3 + 96*r**2 - 293*r. Factor t(c).
4*(c + 6)*(c + 8)
Let o(c) be the first derivative of 9*c**4/4 - 55*c**3/9 + 29*c**2/6 - c/3 - 140. Let o(v) = 0. Calculate v.
1/27, 1
Let f(j) be the second derivative of -1/10*j**3 + 1/60*j**4 - 5*j + 0 + 1/5*j**2. Factor f(q).
(q - 2)*(q - 1)/5
Suppose -12*t + 8 = -8*t. Suppose -3*a + 5*a + 2 = t*f, 5*f - 5 = -a. Determine y, given that -17*y + 2*y**3 + a*y**3 + 15*y = 0.
-1, 0, 1
Let s(n) = n**4 + n**3 - 2*n**2 + n. Let i(j) = -4*j**5 + 8*j**4 + 2*j**3 - 6*j**2 + 2*j. Let m(k) = i(k) - 2*s(k). Find a such that m(a) = 0.
-1/2, 0, 1
Let h be ((-3)/(-4))/(36/(-90)*20/(-32)). Factor -2/3*d**2 + 0*d + 0 - 1/3*d**h.
-d**2*(d + 2)/3
Let t(d) be the third derivative of -d**8/420 + d**6/90 - 7*d**3/3 - 16*d**2. Let c(w) be the first derivative of t(w). What is z in c(z) = 0?
-1, 0, 1
Solve -104/3*m - 32/3 + 28/3*m**2 = 0 for m.
-2/7, 4
Let f(u) be the first derivative of -4*u**5/5 + 13*u**4 + 4*u**3/3 - 26*u**2 + 84. Find c, given that f(c) = 0.
-1, 0, 1, 13
Factor 4*k**2 + 16*k**2 - 45*k - 99*k + 48 + 16*k.
4*(k - 6)*(5*k - 2)
Find r such that -93*r + 2883 + 3/4*r**2 = 0.
62
Let h(v) = v + 14. Let f be h(-12). Let q be (6/18 - -1)/f. Determine z so that 1/3*z**3 + 4/3 - 7/3*z + q*z**2 = 0.
-4, 1
Let u(c) be the third derivative of 0*c + 1/12*c**4 - 1/3*c**3 - 1/120*c**5 - 5*c**2 + 0. Factor u(h).
-(h - 2)**2/2
Let h(u) = -u**5 + 4*u**4 - u**3 + 4*u**2 + 2*u - 2. Let t(o) = -o**5 + 2*o**4 + o**3 + o**2 + o - 1. Let f(q) = 3*h(q) - 6*t(q). Find a, given that f(a) = 0.
-2, 0, 1
Let r(q) be the first derivative of -q**6/240 - 3*q**5/40 - 5*q**4/16 - 7*q**3/12 + 10*q**2 - 17. Let k(n) be the second derivative of r(n). Factor k(l).
-(l + 1)**2*(l + 7)/2
Suppose 18*c + 17*c = 43*c. Let x(t) be the second derivative of -2/15*t**6 + 0*t**2 + 1/3*t**4 + 5*t + 2/3*t**3 - 1/5*t**5 + c. Factor x(d).
-4*d*(d - 1)*(d + 1)**2
Let x be 9 + 4102/(-840) + (-52)/(-48) + -1. Factor x*r - 3/5*r**2 + 0.
-3*r*(r - 7)/5
Let t = 1081 + -19457/18. Let k(y) be the second derivative of 0 + 1/36*y**4 + 11*y - t*y**3 + 0*y**2. What is p in k(p) = 0?
0, 1
Let m(l) be the first derivative of -7*l**4/4 - 5*l**3/3 + l**2 - 34. Factor m(g).
-g*(g + 1)*(7*g - 2)
Let j(i) be the second derivative of -3*i**5/140 - 19*i**4/14 - 36*i**3/7 - 606*i. Factor j(q).
-3*q*(q + 2)*(q + 36)/7
Let p(j) = -j + 12. Let r be p(9). Suppose -r*n + 4*n = 3. Factor -4*w**n - 3*w**4 + 3*w**3 + 4*w**3 + 0*w**4.
-3*w**3*(w - 1)
Let x(l) = -18*l**2 + 26*l + 4. Let g(o) = -18*o**2 + 28*o + 4. Let k(h) = 6*g(h) - 7*x(h). Factor k(a).
2*(a - 1)*(9*a + 2)
Suppose -f + 6 = 14. Let c be (-23)/f + 9/72. Factor -2/7 + 2/7*v**2 + 2/7*v - 2/7*v**c.
-2*(v - 1)**2*(v + 1)/7
Let g = -63051/4 + 15763. Let 1/2*s - g*s**2 + 0 = 0. What is s?
0, 2
Let n(u) = 9*u**2 - 4*u - 1. Let b(a) = -2*a**2. Let t(v) = -6*b(v) - n(v). Determine x, given that t(x) = 0.
-1, -1/3
Suppose 5*u = -2*t + 411 + 3209, 2*u - 1448 = 3*t. Let x = -3587/5 + u. Suppose 6/5 - x*p**2 + 12/5*p**3 + 3*p = 0. What is p?
-1/4, 1, 2
What is v in -4 + 16*v**5 + v**3 + 753*v + 3*v**3 - 757*v + 20*v**2 - 32*v**4 = 0?
-1/2, 1
Let v(j) be the second derivative of j**6/300 + j**5/50 + j**4/30 - 11*j**2/2 + j. Let a(z) be the first derivative of v(z). Factor a(x).
2*x*(x + 1)*(x + 2)/5
Let r(n) = -4*n**4 - 4*n**3 - 8*n**2 - 4*n + 4. Let s(p) = -5*p - 4*p**4 + 2*p**2 - 298*p**3 - 11*p**2 + 5 + 295*p**3. Let o(d) = 5*r(d) - 4*s(d). Factor o(y).
-4*y**2*(y + 1)**2
Let b be -1*2*(-4)/6*(-105)/(-28). Factor 88/7*x**3 - 16/7*x**2 + 50/7*x**b + 0 + 0*x - 20*x**4.
2*x**2*(x - 2)*(5*x - 2)**2/7
Suppose 20 = 3*t + 36*o - 41*o, 0 = 5*t + 2*o - 54. Suppose -35/2*w**3 - t + 25/2*w**4 - 5/2*w**2 - 5/2*w**5 + 20*w = 0. What is w?
-1, 1, 2
Let p be (-119)/(-21)*-2 + 12. Factor 0*h**2 - 2/3 + 4/3*h**3 - 4/3*h + p*h**4.
2*(h - 1)*(h + 1)**3/3
Let 79*g**2 + 1251*g**4 - 9*g**5 - 24*g + 5*g**2 - 102*g**3 - 1200*g**4 = 0. Calculate g.
0, 2/3, 1, 2
Let i be (48/21)/4*28/8. Factor 0 - 2/3*w**i + 7/3*w**3 + 0*w + 3*w**4.
w**2*(w + 1)*(9*w - 2)/3
Let r(t) be the first derivative of -5*t**7/84 - t**6/4 - 3*t**5/8 - 5*t**4/24 + 22*t + 12. Let q(m) be the first derivative of r(m). Factor q(n).
-5*n**2*(n + 1)**3/2
Let u(g) = g - 4. Let a be u(-4). Let i be 16/6*(-6)/a. Let 4*s**3 - 2*s**3 - i*s**4 - 6*s**3 - 5*s**3 + 9*s**5 + 2*s**2 = 0. What is s?
-1, 0, 2/9, 1
Let y(w) = 20*w - 16. Let h be y(2). Suppose -17*j + h = -11*j. Factor -4*x**3 + 4/3*x**j + 4*x + 4/3*x**2 - 8/3.
4*(x - 2)*(x - 1)**2*(x + 1)/3
Let s(k) = -k**3 + 7*k**2 + 14*k + 9. Let v be s(9). Let w(m) = 2*m**3 + 53*m**2 - 27*m + 3. Let a be w(v). Factor 10/3*h**a + 0 - 2*h**2 + 0*h.
2*h**2*(5*h - 3)/3
Let r = -236 + 236. Let w(g) be the first derivative of -1/4*g + r*g**2 + 1/6*g**3 + 0*g**4 + 2 - 1/20*g**5. Factor w(l).
-(l - 1)**2*(l + 1)**2/4
Solve 22*s**3 - 4*s - 3 - 9*s**3 - 3 - 9*s**3 + 3*s**2 - 2*s**4 + 5*s**2 = 0 for s.
-1, 1, 3
Suppose -18 = -2*u - 5*h, 3*h + 20 = 4*u + 5*h. Let k be (2 - -2)/(-8)*0/u. Factor 0*x + k*x**2 + 0 + 2/9*x**4 + 2/9*x**3.
2*x**3*(x + 1)/9
Let p(w) be the first derivative of -2*w**5/45 - w**4/18 + 4*w**3/9 - 103. Factor p(q).
-2*q**2*(q - 2)*(q + 3)/9
Let k(d) = -4*d**4 + 191*d**3 + 420*d**2 - 11*d + 11. Let o(x) = x**4 - 38*x**3 - 84*x**2 + 2*x - 2. Let r(c) = -2*k(c) - 11*o(c). Factor r(n).
-3*n**2*(n - 14)*(n + 2)
Find k such that -19/4*k**3 - 7/2*k**2 + 0*k - k**4 + 0 + 1/4*k**5 = 0.
-2, -1, 0, 7
Let r(w) = w**2 - 1. Suppose 0 = -4*v - 0*v + 2*z + 2, -3*v + 8 = 5*z. Let b(j) = -10*j**2 + 15*j + 15. Let q(c) = v*b(c) + 15*r(c). Factor q(g).
5*g*(g + 3)
Let k(p) = p**2 + p + 3*p + 9 + 2*p. Let n(b) = -10*b + 61. Let f be n(6). Let o(i) = i**2. Let u(y) = f*k(y) - 4*o(y). Factor u(h).
-3*(h - 3)*(h + 1)
