Factor -3/2 - 3/2*t**4 + 6*t + 6*t**3 - 9*t**2.
-3*(t - 1)**4/2
Let u = 1450 - 1448. Determine k, given that 0*k + 2/5 - 1/10*k**u = 0.
-2, 2
Suppose 4*d - 2*s = 60, -3*d - 3*s + 30 = -d. Suppose 6 - 4*h**3 + 0*h**3 + h**3 + 12*h**2 - d*h = 0. What is h?
1, 2
Let t(m) be the first derivative of 13 + 0*m**2 + 0*m + 0*m**3 + 2/15*m**5 + 1/6*m**4. What is u in t(u) = 0?
-1, 0
Let p(v) be the third derivative of -v**6/40 + 7*v**5/10 - 41*v**4/8 - 28*v**3 - 445*v**2. Find s, given that p(s) = 0.
-1, 7, 8
Suppose -v + 3244*c + 16 = 3242*c, -45 = -5*v + 5*c. Let 14/13*s**v + 0 + 0*s - 2/13*s**3 = 0. Calculate s.
0, 7
Let v = -1413/2 + 707. Let q(p) be the first derivative of -1/4*p**4 + 0*p**3 - 6 + v*p**2 + 0*p. Suppose q(y) = 0. Calculate y.
-1, 0, 1
Let s(a) be the second derivative of a**7/14 - 9*a**6/10 + 6*a**5/5 - 5*a - 6. Determine o, given that s(o) = 0.
0, 1, 8
Let k(j) = -3*j**4 + 66*j**3 - 493*j**2 + 1459*j - 1040. Let h(r) = r**4 - 22*r**3 + 164*r**2 - 486*r + 347. Let p(y) = -11*h(y) - 4*k(y). Factor p(m).
(m - 7)**3*(m - 1)
Let i be (-39)/12 + 3 - (-63)/28. Let q(s) = s + 1. Let h be q(1). Factor 2/3*p**3 + 2/3 + i*p + h*p**2.
2*(p + 1)**3/3
Let 3*t**5 - 13*t**3 + 26*t**4 - 8*t**3 - 9*t**3 - 8*t**4 - 150 - 156*t**2 + 315*t = 0. What is t?
-5, 1, 2
Let 31/5*f - 1/5*f**2 + 0 = 0. What is f?
0, 31
Let n = -60639/4 + 15160. Solve -1/4*h**2 + 1/4*h**3 - 1/4*h + n = 0.
-1, 1
Suppose t - 15 = 4. Let 8*p + 4*p**2 + 3*p**4 - 7*p**3 - t*p**3 + 45*p**5 - 20*p**3 = 0. Calculate p.
-1, -2/5, 0, 2/3
Suppose -81/7*q**4 + 3/7*q + 81/7*q**2 + 0 - 87/7*q**3 + 12*q**5 = 0. Calculate q.
-1, -1/28, 0, 1
Let q = 2612 + -2608. Let 4/3*f**2 + 8/9*f**3 + 2/9 + 2/9*f**q + 8/9*f = 0. Calculate f.
-1
Let p = 1235/66 - 138/11. Let y = p - 17/3. Find m such that 5/4*m**3 - 5/4*m - y + 1/2*m**2 = 0.
-1, -2/5, 1
Let r(h) be the third derivative of 0*h + 1/24*h**4 + 1/60*h**5 - 1/3*h**3 - 8*h**2 + 0. Let r(l) = 0. What is l?
-2, 1
Let q(f) be the first derivative of 0*f + 3*f**2 + 3*f**4 - 3/5*f**5 + 11 - 5*f**3. Factor q(l).
-3*l*(l - 2)*(l - 1)**2
Solve -152071*g**2 - 116*g + 102 + 152067*g**2 - 318 = 0.
-27, -2
Let m(i) = 66*i**2 - 857*i - 9. Let k be m(13). Factor -q**3 + 1/3*q**k + q**2 - 1/3*q + 0.
q*(q - 1)**3/3
Let k(a) = -9*a**2 + 4*a + 8. Let r(g) = -16*g**2 + 7*g + 14. Let s(f) = -7*k(f) + 4*r(f). Find y, given that s(y) = 0.
0
Let b(u) = u**3 - 3*u**2 - u. Let r(f) = f**2 + 8*f**2 - 10*f**2. Let m(w) = 4*b(w) - 12*r(w). Factor m(a).
4*a*(a - 1)*(a + 1)
Let p be 5/6 - (5/2 + -2). Let n(r) be the third derivative of 0 + 3*r**2 - 13/120*r**6 - 3/20*r**5 + 0*r - 1/42*r**7 + p*r**3 + 1/24*r**4. Factor n(v).
-(v + 1)**3*(5*v - 2)
Let m be ((-7060)/(-24) - 5)/((-6)/4). Let o = m + 193. Factor 2/9*f + o - 2/9*f**3 - 2/9*f**2.
-2*(f - 1)*(f + 1)**2/9
Let i(w) = 43*w - 115. Let y be i(5). Factor -y*c**4 - 80*c**2 + 0 + 35/2*c**5 - 40*c + 180*c**3.
5*c*(c - 2)**3*(7*c + 2)/2
Factor 415*z + 5*z**5 + 430*z**4 + 1250*z**2 - 1377*z**3 + 546*z**3 + 2091*z**3.
5*z*(z + 1)**3*(z + 83)
Let d(l) be the second derivative of -5*l**7/168 - 17*l**6/120 - 3*l**5/80 + 3*l**4/16 - l + 62. Determine m so that d(m) = 0.
-3, -1, 0, 3/5
Let t = 8707 + -8705. Factor 32/3*i**t + 0 + 4/3*i + 41/3*i**3 + 13/3*i**4.
i*(i + 1)*(i + 2)*(13*i + 2)/3
Let c(y) = y**3 - 4*y**2 - 4*y - 5. Let q be c(5). Let n be (q + 1)/2*10. Factor -12*o**2 + 12*o - 6*o**n + 19*o**3 + 18*o**4 - 52*o**3 + 19*o**5 + 14*o**5.
3*o*(o + 1)**2*(3*o - 2)**2
Let g(r) = -3*r**4 - 24*r**3 + 93*r**2 - 6*r - 126. Let o(b) = -6*b**4 - 48*b**3 + 187*b**2 - 13*b - 253. Let d(m) = 11*g(m) - 6*o(m). Factor d(s).
3*(s - 2)**2*(s + 1)*(s + 11)
Suppose -4*y = -4*c + 1 - 13, -5*c + 9 = -2*y. Suppose -2*r = 4*w - y*w, 2*r = -5*w. Suppose -2/5*o + r + 8/5*o**2 - 8/5*o**4 + 2/5*o**3 = 0. What is o?
-1, 0, 1/4, 1
Let -36 - 3/2*b**2 + 15*b = 0. Calculate b.
4, 6
Let f be (-4)/(-2) + (-8 + 10 - 2). Let x(h) be the first derivative of -3 - 6/7*h + 2/21*h**3 + 2/7*h**f. Determine v, given that x(v) = 0.
-3, 1
Let n(z) be the second derivative of -3*z**6/10 + 3*z**5/40 + 5*z**4 + 31*z**3/4 + 9*z**2/2 - 11*z. Determine j, given that n(j) = 0.
-2, -1/2, -1/3, 3
Let h(x) = -35*x**2 + 2505*x + 158745. Let p(l) = 16*l**2 - 1253*l - 79373. Let q(g) = 7*h(g) + 15*p(g). What is a in q(a) = 0?
-126
Suppose -47 + 84 = -b. Let g = b + 42. Factor -2*d**2 - 4*d**5 - 3*d**4 - 4 + 9*d**2 - d**3 + 5*d**g.
(d - 2)**2*(d - 1)*(d + 1)**2
Let i(u) be the second derivative of u**8/5040 - u**7/2520 + 4*u**3/3 + 13*u. Let x(h) be the second derivative of i(h). What is w in x(w) = 0?
0, 1
Let a(w) be the first derivative of -w**7/21 + 4*w**6/15 - 3*w**5/5 + 2*w**4/3 - w**3/3 + 3*w + 13. Let t(b) be the first derivative of a(b). Factor t(p).
-2*p*(p - 1)**4
Let w be (1/3 - 1)*(-25)/((-8250)/(-891)). Factor 27/5*h + w*h**2 + 0 + 3/5*h**4 - 3*h**3.
3*h*(h - 3)**2*(h + 1)/5
Let m be ((-4)/(-12)*-2)/(28/22398). Let b = -532 - m. Determine t so that -t + b*t**2 + 2/7 - 5/7*t**3 + 1/7*t**4 = 0.
1, 2
Let c(m) = 3*m**2 + 3*m. Let d(h) = 2*h**2 + 2*h. Suppose 17 = 5*v - w, 3*v + 2*w + 2*w = 1. Let a(i) = v*c(i) - 2*d(i). Let a(k) = 0. Calculate k.
-1, 0
Let t be ((-2)/1 + 2)/(-2). Let p(d) be the second derivative of -1/9*d**3 + t - 5*d - 1/18*d**4 + 0*d**2. Factor p(g).
-2*g*(g + 1)/3
Let w = 8 + -3. Let f(r) be the third derivative of 0*r**3 + 0*r + 0 - 1/735*r**7 - 1/210*r**6 + 2*r**2 + 1/210*r**w + 1/42*r**4. Factor f(o).
-2*o*(o - 1)*(o + 1)*(o + 2)/7
What is q in 6*q + 1/2*q**3 - 14 + 15/2*q**2 = 0?
-14, -2, 1
Let t(v) be the second derivative of 0 + 1/5*v**2 - 1/6*v**3 + 1/30*v**4 - 2*v. Factor t(r).
(r - 2)*(2*r - 1)/5
Let m(x) be the first derivative of -x**4/84 - x**3/6 - 5*x**2/7 + 51*x + 34. Let j(u) be the first derivative of m(u). Factor j(y).
-(y + 2)*(y + 5)/7
Let h = -6 + 9. Let f be 5 - (2 - (2 - h)). Let -3*w**2 + 0*w + 3*w**3 + 0*w**3 + f*w**4 - 3*w + w**4 = 0. Calculate w.
-1, 0, 1
Let u = 28 - 26. Let f(z) = 9*z**2 - 2. Let a(y) = 3*y**2 - 1. Let t(o) = u*f(o) - 7*a(o). Let t(m) = 0. Calculate m.
-1, 1
Let h(z) be the third derivative of -z**9/15120 + z**7/1260 + 7*z**5/12 + 38*z**2. Let o(q) be the third derivative of h(q). Factor o(a).
-4*a*(a - 1)*(a + 1)
Let l = 31007/39 + -795. Let c(r) be the first derivative of -4/13*r + 3/13*r**2 + 4 - l*r**3. Solve c(n) = 0.
1, 2
Suppose q - 14 = -q. Factor 2*s - s**5 + 0*s**4 - s**5 + q*s**2 - 3*s**2 - 4*s**4.
-2*s*(s - 1)*(s + 1)**3
Let y(b) = -2*b**2 + 16*b + 44. Let p be y(16). Let v = p + 212. Suppose -2/3*w**5 + 0*w - 2/3*w**4 + 0 + 0*w**3 + v*w**2 = 0. Calculate w.
-1, 0
Let f(l) be the first derivative of -2/3*l**3 - 16 + 4*l**2 - 8*l. Factor f(r).
-2*(r - 2)**2
Let y(f) = -61*f + 3724. Let q be y(61). Let -2*j**2 - 4/3*j + 8/3*j**q + 8/3*j**4 + 2/3 = 0. Calculate j.
-1, 1/2
Let o(y) be the first derivative of -y**6/4 + 3*y**5/10 + 3*y**4/4 - y**3 - 3*y**2/4 + 3*y/2 - 58. Factor o(u).
-3*(u - 1)**3*(u + 1)**2/2
Let i(a) = 24*a**2 + 3*a - 2. Let c(l) = -13*l**2 - 2*l. Let y(j) = -11*c(j) - 6*i(j). Factor y(h).
-(h - 6)*(h + 2)
Suppose -8*o - 25 = -3*o. Let y(c) = -c**2. Let n(z) = 3*z**2 + 2*z. Let i(m) = o*n(m) - 10*y(m). Factor i(u).
-5*u*(u + 2)
Suppose -13*k - 17 = -95. Let n(g) be the first derivative of -5 - 3/10*g**2 - 9/20*g**4 + 2/5*g**k + 3/5*g**5 - g**3 + 0*g. Determine h, given that n(h) = 0.
-1, -1/4, 0, 1
Let m(p) be the third derivative of -11/120*p**6 - 7/60*p**5 - 4*p**2 - 1/3*p**3 + 0*p + 0 + 11/24*p**4 + 3/70*p**7. Factor m(b).
(b - 1)**2*(b + 1)*(9*b - 2)
Let r(a) be the third derivative of 0 + 0*a + 3/245*a**7 + 0*a**3 + 11*a**2 + 1/98*a**8 + 0*a**4 - 3/140*a**5 - 11/280*a**6. Find i such that r(i) = 0.
-3/2, -1/4, 0, 1
Let g be (-2)/(((-8)/(-12))/(-1)). Suppose 7*k**5 + 2*k**g + 0*k**3 - 6*k**4 - 10*k**5 - 5*k**3 = 0. What is k?
-1, 0
Let r(n) = -14*n**3 + 134*n**2 + 344*n + 64. Let a(o) = -29*o**3 + 265*o**2 + 688*o + 128. Let d(p) = 6*a(p) - 11*r(p). Let d(v) = 0. What is v?
-2, -1/5, 8
Let j(s) be the third derivative of 0 + 0*s - 1/1008*s**8 + 2/63*s**7 - 625/72*s**4 + 25/9*s**5 - 5/12*s**6 + 6*s**2 + 0*s**3. Let j(q) = 0. Calculate q.
0, 5
Let q be -1 + 3/10*190/84. Let t = 5/28 - q. Solve 0*y + t*y**2 + 0 = 0 for y.
0
Let i(g) be the second derivative of g**7/120 - g**6/15 