16/5*w - 2/15*w**2.
-2*w*(w + 24)/15
Suppose 4*l - 6 = l. Suppose 21 = 3*k + 3*s, 0 = -l*k - 0*s - 5*s + 29. Factor -17 - v**k - 8*v + 11 - v**2.
-2*(v + 1)*(v + 3)
Let v(n) be the second derivative of n**5/20 + 37*n**4/2 + 2738*n**3 + 202612*n**2 - 2*n + 19. Factor v(z).
(z + 74)**3
Suppose 3*h + 5*p = 4*p + 13, -3*p = -4*h. Suppose -9 + 24 = 5*s. Let 2*k - h - k - s - 10*k - 3*k**2 = 0. Calculate k.
-2, -1
Let x be (-3)/4 + (-7 - 23481/(-108)). Let n = -209 + x. What is f in 10/3*f**4 + 4/3*f + 0 - 16/3*f**3 + n*f**2 = 0?
-2/5, 0, 1
Let b = -1/378 + 649/378. Let o = -4618/7 - -660. Factor -o*k**2 - b*k - 18/7.
-2*(k + 3)**2/7
Let r(c) be the first derivative of -2*c**3/3 - 125*c**2 - 747. Factor r(b).
-2*b*(b + 125)
Let p(o) be the third derivative of -8/3*o**3 - 6*o**2 + 0 + 0*o + 1/3*o**4 - 1/60*o**5. Let p(n) = 0. What is n?
4
Let d(a) be the first derivative of -2/15*a**5 + 0*a**3 - 3 - 1/6*a**4 - 3/2*a**2 - 1/30*a**6 + 0*a. Let z(c) be the second derivative of d(c). Factor z(n).
-4*n*(n + 1)**2
Find x such that -3896*x**3 - x**2 + 3894*x**3 + 3*x**2 = 0.
0, 1
Let x(t) be the third derivative of t**7/420 + t**6/120 - t**5/24 - t**4/8 + 2*t**2 - 14. Suppose x(q) = 0. Calculate q.
-3, -1, 0, 2
Factor -32*h**2 - 28*h**3 - 24*h**2 + 205*h + 23*h**3 - 144*h**2.
-5*h*(h - 1)*(h + 41)
Let k(p) = p**3 - 25*p**2 + 32*p - 16. Let f be k(24). Suppose -f = -5*o - 156. Let 2/3*a**5 + 0*a**2 + 2/3*a**3 + 0*a - 4/3*a**o + 0 = 0. Calculate a.
0, 1
Factor 16847*g**2 - 36*g + 2 - 8*g**3 - 16931*g**2 + 38.
-4*(g + 1)*(g + 10)*(2*g - 1)
Let r be 1054/(-8) + 2/(-8). Let l be 24/11 - (-24)/r. Find s such that l*s**2 - 4*s**2 + 5*s**3 + 4*s**2 - 7*s**2 = 0.
0, 1
Let c(b) be the first derivative of -b**6/180 + b**4/12 + 3*b**3 + 32. Let o(m) be the third derivative of c(m). Find n, given that o(n) = 0.
-1, 1
Solve 56/9*j + 16/9 - 14/9*j**3 + 4*j**2 - 10/9*j**4 = 0 for j.
-2, -1, -2/5, 2
Determine p, given that -2/5*p**5 - 32/5*p**2 + 8/5*p**3 + 6/5*p**4 + 32/5 + 0*p = 0.
-2, -1, 2
Factor 4 + 10/3*u + 2/3*u**2.
2*(u + 2)*(u + 3)/3
Let w be 11*(-7 - -4)*(-21)/378. Factor 1/3*k**2 + w*k - 11/6*k**3 - 1/3.
-(k - 1)*(k + 1)*(11*k - 2)/6
Let k be ((-749)/(-84) - 9)*1*-6. Let 1/4 + k*j + 1/4*j**2 = 0. Calculate j.
-1
Factor -37/3*h**2 - 4*h - 5*h**4 - 1/3*h**5 + 0 - 13*h**3.
-h*(h + 1)**3*(h + 12)/3
Let h(j) = -18*j + 48. Let o(y) = y**2 - 17*y + 48. Let k(m) = -3*h(m) + 2*o(m). Factor k(t).
2*(t - 2)*(t + 12)
Let t(y) be the second derivative of -y**7/21 - y**6/5 + 2*y**4/3 + 13*y + 15. Factor t(h).
-2*h**2*(h - 1)*(h + 2)**2
Factor 0 + 2/17*m**3 + 2/17*m**2 - 2/17*m**4 - 2/17*m.
-2*m*(m - 1)**2*(m + 1)/17
Let o be (((-22)/33)/(-2))/(4/15). Find m such that 15/2*m - 45/4 - o*m**2 = 0.
3
Let x(o) = o**2 - 2*o - 12. Let s(i) = -1. Let d(t) = 3*s(t) + x(t). Factor d(b).
(b - 5)*(b + 3)
Let u(b) be the first derivative of -4*b - 1/4*b**4 + 0*b**2 - 3/5*b**5 + 7/3*b**3 + 1/6*b**6 - 18. Factor u(t).
(t - 2)**2*(t - 1)*(t + 1)**2
Factor -12 - 4/3*j + 12*j**2 + 4/3*j**3.
4*(j - 1)*(j + 1)*(j + 9)/3
Let k(p) be the first derivative of 2*p**6/3 + 36*p**5/35 - 5*p**4/7 - 12*p**3/7 - 4*p**2/7 + 77. What is i in k(i) = 0?
-1, -2/7, 0, 1
Let l be 2*1 - (-1 + 0). Solve -15*x**2 + 4 + 3 - 11*x**l - 2 + x**3 = 0.
-1, 1/2
Let w(s) = 4 + s**2 + 2 - 5*s - 2. Let a(h) = -h**2 + 1. Let k(g) = -6*a(g) - w(g). Find z, given that k(z) = 0.
-2, 1
Let y(o) be the first derivative of -o**4/4 - 14*o**3/3 - 7*o**2 - 10*o + 2. Let i be y(-13). Factor -7*x - 12*x**i - 9*x**2 - 11*x**2 - x.
-4*x*(x + 1)*(3*x + 2)
Let y(k) = -266*k + 4527. Let z be y(17). Factor 0*d + 10/3*d**4 + 2/3*d**z + 14/3*d**3 + 0 + 2*d**2.
2*d**2*(d + 1)**2*(d + 3)/3
Solve 4*j - 34*j**4 + 29*j**3 - 24*j**2 + 34*j**4 - 9*j**4 = 0 for j.
0, 2/9, 1, 2
Let k = 91751/28 + -13105/4. Suppose -16/7 - k*t + 2/7*t**2 = 0. What is t?
-2, 4
Factor 3/7*w**4 + 0 + 216/7*w + 36/7*w**2 - 30/7*w**3.
3*w*(w - 6)**2*(w + 2)/7
Suppose 0 = u + 20. Let n = u + 25. Factor -n*l**2 + 6*l - 12 + 2*l + 2*l**2 + 4*l.
-3*(l - 2)**2
Let q(h) be the second derivative of -h**7/168 - h**6/36 + h**5/8 + 11*h**3/6 + 8*h. Let y(r) be the second derivative of q(r). Let y(b) = 0. Calculate b.
-3, 0, 1
Let -292*t**3 + 20*t**2 + 2*t**2 + 2*t + 290*t**3 - 22 = 0. Calculate t.
-1, 1, 11
Let m = 28 + -16. Let g(i) = -i + 12*i**3 + 4*i**2 + 15*i - m + 0*i**2 - 10*i**3. Let d(w) = w**3 + 3*w**2 + 9*w - 8. Let v(o) = -8*d(o) + 5*g(o). Factor v(z).
2*(z - 2)*(z - 1)*(z + 1)
Factor 32*t - 197 + 113 - 48*t**2 - 3*t**5 + 11*t**4 + 100 + 4*t**3.
-(t - 2)**3*(t + 2)*(3*t + 1)
Let o(h) = -2*h**4 - 6*h**3 + 5*h**2 + 6*h - 3. Let a(t) = 6*t**4 + 20*t**3 - 16*t**2 - 20*t + 10. Let z(w) = -6*a(w) - 20*o(w). Factor z(m).
4*m**2*(m - 1)*(m + 1)
Let k be 115/35 - (-2)/(-7). Let u be (12/30)/(k/30). Solve -u*b + 2 - 5 - 3*b**2 + 3*b**2 - b**2 = 0 for b.
-3, -1
Suppose 3 - 5/2*w + 1/2*w**2 = 0. Calculate w.
2, 3
Let q(t) be the third derivative of -t**6/180 + t**4/12 - 11*t**3/6 - 18*t**2. Let h(p) be the first derivative of q(p). Factor h(b).
-2*(b - 1)*(b + 1)
Factor 19*l**3 - 6*l**3 - 278*l**2 - 60 + 107*l**2 + 192*l + 14*l**3.
3*(l - 5)*(3*l - 2)**2
Factor 11/4*x**2 + 25/4 - 1/4*x**3 - 35/4*x.
-(x - 5)**2*(x - 1)/4
Suppose 2*t + 12 - 6 = 4*f, -t + f = 0. Determine p, given that 0 + 8/3*p**t + 2/3*p**5 + 0*p + 0*p**2 - 8/3*p**4 = 0.
0, 2
Find s, given that 222*s - 242*s + 46*s**2 - 42*s**2 = 0.
0, 5
Suppose 0 = 7*g - 19 + 5. Determine r so that -6 + r**g - 4 + 9 = 0.
-1, 1
Let w = -170 + 283. Let d = w + -113. Determine r so that 22/5*r**3 + d + 18/5*r**2 - 4/5*r = 0.
-1, 0, 2/11
Let g(d) be the second derivative of -d**4/12 - d**3/6 + d - 3. Factor g(a).
-a*(a + 1)
Let i(c) be the first derivative of c**3 + 33*c**2 - 69*c + 120. Find z such that i(z) = 0.
-23, 1
Factor -b**3 + 0*b**3 + 131*b - 263*b + 22*b**2 + 155*b.
-b*(b - 23)*(b + 1)
Let j(f) = -f**5 - 13*f**4 + 11*f**3 - 3. Suppose 0 = 4*p + 4, 2*y + 2*p = -2*p - 8. Let w(k) = -12*k**4 + 10*k**3 - 2. Let l(a) = y*j(a) + 3*w(a). Factor l(t).
2*t**3*(t - 4)*(t - 1)
Let x = 14 + -16. Let k be (-76)/(-80) + x*12/32. Factor k*y**4 + 2/5*y**3 + 0*y**2 - 2/5*y - 1/5.
(y - 1)*(y + 1)**3/5
What is w in -61/7*w + 12/7 - 4/7*w**3 + 53/7*w**2 = 0?
1/4, 1, 12
Let c(l) = l**2 - 8*l + 17. Let j be c(5). Factor 8*v**j + 2*v**3 - 3*v**3 + 6*v - 7*v**2 - 4*v.
-v*(v - 2)*(v + 1)
Suppose -4*z + 6 = -3*p - 23, -4*z + 14 = 2*p. Let a be -2 - (-26)/(-5)*z/(-9). Solve -40/9*l**2 - 40/9*l**4 + a*l**5 + 0 + 22/3*l**3 + 8/9*l = 0 for l.
0, 1/2, 2
Let l = -12 + 15. Suppose -3*k - 21 = -6*k - 4*r, 3*k - l = 2*r. What is w in -2*w - 6*w + 8*w - k*w**3 - 5*w**5 + 9*w**4 - w**2 = 0?
-1/5, 0, 1
Let l(o) be the third derivative of 5*o**8/336 - o**7/14 - 3*o**6/8 - 5*o**5/12 - 23*o**2. Factor l(v).
5*v**2*(v - 5)*(v + 1)**2
Solve -424/7*j**3 + 308*j - 76/7*j**4 - 196 - 4/7*j**5 - 40*j**2 = 0 for j.
-7, 1
Suppose 4 = 3*o + o. Suppose 7 = 2*p - o. Factor -2*q**2 - p*q - 2*q + q**2 + 4*q**2.
3*q*(q - 2)
Let y be 3 + 63/49 - 4. Let v(a) be the first derivative of -1 - y*a - 2/21*a**3 - 2/7*a**2. Let v(h) = 0. Calculate h.
-1
Let t(a) be the second derivative of 1/10*a**6 + 0*a**5 - 1/4*a**4 + 12*a + 0*a**3 + 0 + 0*a**2. Factor t(b).
3*b**2*(b - 1)*(b + 1)
Let q = -3 + 14. Let l be q/((-5)/(-5)) - 0. Factor 1 - 1 + 4 - 5*a**2 - 18*a + 28*a**3 + l*a**2.
2*(a + 1)*(2*a - 1)*(7*a - 2)
Factor 2/3*m**2 + 14/3 + 16/3*m.
2*(m + 1)*(m + 7)/3
Let z(w) be the third derivative of -w**7/420 - w**6/40 - w**5/10 - w**4/6 - 299*w**2. Find d such that z(d) = 0.
-2, 0
Let q(i) be the third derivative of i**7/630 - i**6/90 + i**5/30 + 5*i**4/12 + 9*i**2. Let p(u) be the second derivative of q(u). Factor p(x).
4*(x - 1)**2
Suppose -3*n = -2*k - 26, n + 2*k = 4*k + 2. Suppose -n = -v - 2*s, -3*v + 32 = 4*s + s. Factor -26/7*i**3 + 0 - 2/7*i**5 + 24/7*i**2 - 8/7*i + 12/7*i**v.
-2*i*(i - 2)**2*(i - 1)**2/7
Let -27*s**2 + 44*s - 24*s + 58 + 24*s**2 + 7*s + 58*s = 0. What is s?
-2/3, 29
Suppose 141*o - 320*o**2 + 329*o - 70*o + 16*o**4 + o**5 + 0*o**5 + 24*o**3 = 0. Calculate o.
-10, 0, 2
Let h = -5819 - -5819. What is v in 25/4*v**3 + h*v + 5*v**4 + 0 + 5/4*v**5 + 5/2*v**2 = 0?
-2, -1, 0
Let k(x) be the third derivative of x**6/200 - 9*x**5/20 - 71*x**4/20 - 48*x**3/5 - 87*x**2 + 2*x.