. Let y = k + -153/2. Find z, given that 1/2 + 9/4*z - 21/4*z**3 - y*z**4 + z**2 = 0.
-1, -1/2, -1/3, 2/3
Let -2*k + 80/3 - 2/3*k**2 = 0. What is k?
-8, 5
Let w(b) be the third derivative of 0 + 0*b + 1/10*b**3 + 1/100*b**5 + 1/20*b**4 - 10*b**2. Factor w(h).
3*(h + 1)**2/5
Let u be (6 - 7)*1*-3. Suppose 0 = u*s - 5*s + 12. Factor -2*p**3 + 1 - 1 - 9*p**2 + 5*p**3 + s*p.
3*p*(p - 2)*(p - 1)
Suppose 0 = -27*k + 22*k + 55. Factor 3*c**5 + 13*c + 11*c + k*c - 6*c**3 - 32*c.
3*c*(c - 1)**2*(c + 1)**2
Let v(h) be the first derivative of 0*h**2 - 1/3*h**3 + 0*h - 42 - 1/3*h**6 + 1/2*h**4 + 1/5*h**5. Find j such that v(j) = 0.
-1, 0, 1/2, 1
Let g = 27 + -25. Let k be (52/27 - g)/(1/(-120)). Find l such that -4/9 - 20/3*l**4 + 100/9*l**3 + 14/9*l**5 + 10/3*l - k*l**2 = 0.
2/7, 1
Let n(q) = -3*q + 10. Let z be n(-7). Let p = -12 + z. Factor -p - 3*o**2 + 12 + 3*o + 13.
-3*(o - 2)*(o + 1)
Let r(v) = v**2 + 3*v + 4. Let p be r(-3). Suppose 2*m = -2*m + 24. Factor x + x**3 + 2 - 2*x**2 + p*x**3 - m*x**3.
-(x - 1)*(x + 1)*(x + 2)
Let a = -3368 - -3371. Suppose -12/7*h**4 + 51/7*h**a - 48/7*h**2 + 9/7*h + 0 = 0. Calculate h.
0, 1/4, 1, 3
Let x = -36 + 35. Let n = x + 3. Determine q, given that -3*q**2 + q**3 - 4*q**3 - 3 + n + 3*q + 4 = 0.
-1, 1
Let t(v) be the third derivative of 27*v**8/560 - 9*v**7/35 + 9*v**6/20 - 2*v**5/5 + 5*v**4/24 - v**3/15 + 101*v**2. Solve t(h) = 0.
1/3, 2
Suppose -5*x = -8*x - 84. Let o = 88/3 + x. Suppose 0 + o*n**2 + 0*n - 10/3*n**3 = 0. Calculate n.
0, 2/5
Suppose v + 11 = a, -v + 11 = a - 2. Suppose -4*p = -4*y + 3*y - a, 4*y = 3*p - 9. Factor -2/11*r**p + 2/11*r**2 + 2/11*r - 2/11.
-2*(r - 1)**2*(r + 1)/11
Let i(q) be the first derivative of q**6/15 - 2*q**4/5 - 4*q**3/15 + 3*q**2/5 + 4*q/5 + 59. Let i(k) = 0. Calculate k.
-1, 1, 2
Let i(q) be the third derivative of 0*q**4 + 7/180*q**6 - 1/630*q**7 + 0*q**3 - 3*q - 2*q**2 - 49/180*q**5 + 0. Find y, given that i(y) = 0.
0, 7
Let h(p) be the second derivative of -p**6/45 + p**5/20 + p**4/12 - 13*p**3/6 + 5*p. Let l(r) be the second derivative of h(r). Factor l(s).
-2*(s - 1)*(4*s + 1)
Let r(v) = -v**3 + 3*v**2 + 6*v - 14. Let y be r(2). What is n in 2*n - 68/3*n**3 - 6*n**5 - 8*n**y - 20*n**4 + 4/3 = 0?
-1, -2/3, 1/3
Suppose 3*x = 4*q + 4, -1 = 5*q - 2*x - 3. Factor -4 + 25*r + 7*r**3 + 5 - 20*r**q - 2*r**3 - 11.
5*(r - 2)*(r - 1)**2
Let a be 1/9 + 220/45. Let k(u) be the third derivative of -1/60*u**6 + 0*u**4 + 0*u + 0 + 0*u**3 - 1/30*u**5 + a*u**2. Let k(j) = 0. Calculate j.
-1, 0
Let u(b) be the second derivative of b**6/90 - b**5/15 - 5*b**4/36 + b - 7. Let u(c) = 0. What is c?
-1, 0, 5
Suppose -697 - 986 = -51*u - 153. Factor 0 + 35/2*c**3 - 10*c - u*c**2.
5*c*(c - 2)*(7*c + 2)/2
Let m be -10 - -12 - (1 - 5). Suppose 0 = -7*x + m*x + 2. What is b in 1 + 4*b**x + 5 - 4 + 5*b + b**3 = 0?
-2, -1
Find g such that 32/5*g**2 - 26/5*g - 2/5*g**3 - 12 = 0.
-1, 2, 15
Let y(l) = -6*l - 1. Let w be y(1). Let s(r) = -r - 4. Let n be s(w). Suppose -2*q - 5*q**3 - 9*q**3 + 10*q**n + 6*q**2 = 0. Calculate q.
0, 1/2, 1
Let m be 8 + (2 - (1881/10)/19). Let 3/10*i - 1/5 + 0*i**4 + 1/5*i**2 + m*i**5 - 2/5*i**3 = 0. What is i?
-2, -1, 1
Factor -24/7*y**2 - 2/7*y**5 + 8/7*y**4 + 4/7*y**3 + 0 - 18/7*y.
-2*y*(y - 3)**2*(y + 1)**2/7
Let u be (12/(-70))/(100/(-1050)). Determine p, given that -2/5*p + 0 + u*p**2 = 0.
0, 2/9
Determine x, given that 2/7*x**4 + 18/7*x**3 - 18/7*x - 4 + 26/7*x**2 = 0.
-7, -2, -1, 1
Let l(b) be the first derivative of -b**5/12 - 5*b**4/6 - 35*b**2/2 + 4. Let q(i) be the second derivative of l(i). Find m, given that q(m) = 0.
-4, 0
Suppose -75*f + 756 = -12*f. Let a(c) be the third derivative of -f*c**2 + 0 - 1/60*c**6 - 1/105*c**7 + 0*c + 1/30*c**5 + 0*c**3 + 1/12*c**4. Factor a(y).
-2*y*(y - 1)*(y + 1)**2
Suppose -2/5*d**2 + 432/5*d - 23328/5 = 0. What is d?
108
Suppose -4*z = -7 - 1. Factor 3*s**z + 0*s**3 - s**3 - 14*s**5 + s**2 - 24*s**4 - 5*s**3.
-2*s**2*(s + 1)**2*(7*s - 2)
Let n(i) be the first derivative of -1/3*i**3 + 0*i + 7/8*i**4 - 8 - 1/4*i**2 - 2/5*i**5. Factor n(g).
-g*(g - 1)**2*(4*g + 1)/2
Let z(l) be the second derivative of l**7/8820 - l**6/630 + l**5/140 - 13*l**4/12 - 5*l. Let a(w) be the third derivative of z(w). Find r such that a(r) = 0.
1, 3
Suppose -2*l - 5*x = -111, -66 = -l + 5*x + 12. Let q = l + -63. Suppose q - 1/5*m**4 + 1/5*m**2 - 2/5*m**3 + 2/5*m = 0. What is m?
-2, -1, 0, 1
Let t = -83 + 251/3. Let d = -298/15 - -308/15. Let w + 1/3 - 1/3*w**5 - w**4 + t*w**2 - d*w**3 = 0. Calculate w.
-1, 1
Let z(g) = -88 + 17*g**2 - 8*g**2 - 4*g + 3*g**2. Let m(y) = -4*y**2 + y + 29. Let c(f) = 16*m(f) + 5*z(f). Find p such that c(p) = 0.
-3, 2
Suppose -14*s + 11*s = -12. Factor 0*w**4 + 2*w**4 + s*w**4 - 73*w**5 + 88*w**5.
3*w**4*(5*w + 2)
Let z = 423/1981 + -20/283. Factor -z*x**3 - 1/7 + 1/7*x**2 + 1/7*x.
-(x - 1)**2*(x + 1)/7
Suppose 3*x - 5*t = 9, 2*t = -2*x - 2*t + 6. Suppose 4*h - x*h = 0. Factor 0*q**2 + 0 + h*q**4 - 1/2*q**5 + q**3 - 1/2*q.
-q*(q - 1)**2*(q + 1)**2/2
Let n(l) = 2*l**3 + 184*l**2 + 4224*l + 7744. Let u(s) = 4*s**3 + 369*s**2 + 8448*s + 15488. Let b(c) = -18*n(c) + 8*u(c). Factor b(t).
-4*(t + 2)*(t + 44)**2
Factor 0 - 2/11*r**5 + 0*r**4 + 0*r - 4/11*r**2 + 6/11*r**3.
-2*r**2*(r - 1)**2*(r + 2)/11
Let y(t) be the second derivative of t**8/3360 + t**7/630 - t**6/90 - 2*t**5/15 - t**4/6 + 4*t. Let m(u) be the third derivative of y(u). Factor m(d).
2*(d - 2)*(d + 2)**2
Let w(b) be the third derivative of -1/90*b**5 + 1/12*b**4 + 0 - 3*b**2 + 0*b + 0*b**3. Factor w(c).
-2*c*(c - 3)/3
Suppose 6*u = -3*u + 14*u. Factor u*i - i**2 + 0 - 1/2*i**3 + 1/2*i**4.
i**2*(i - 2)*(i + 1)/2
Suppose 372*w - 421*w**2 + 24 + 48 + 156*w**4 + 495*w**3 + 1075*w**2 + 15*w**5 = 0. What is w?
-6, -2, -1, -2/5
Let c = -63440/21 - -3022. Suppose c*g - 8/21*g**2 + 2/7 = 0. What is g?
-1/4, 3
Let s(z) be the first derivative of -2*z**5/5 + 3*z**4 - 8*z**3 + 8*z**2 - 217. Determine w so that s(w) = 0.
0, 2
Factor -9*z**4 + 21*z**3 + z**5 - 6*z + 23*z**4 + 6*z - 36*z**2.
z**2*(z - 1)*(z + 3)*(z + 12)
Let h = 382 + -148. Let n = -228 + h. Factor 0*z + 3/2*z**3 + 0*z**2 + 0 + n*z**4.
3*z**3*(4*z + 1)/2
Let f(b) be the third derivative of -b**7/70 - b**6/4 - 4*b**5/5 + b**2 - 150. Factor f(w).
-3*w**2*(w + 2)*(w + 8)
Let j = 29 + -26. Find c, given that 51*c + 11 + 2*c**2 + 36*c**2 - j + c - 33*c**3 = 0.
-2/3, -2/11, 2
Solve 3438*v**3 + 52029*v + 50880*v - 74*v**4 + 3*v**5 + 5196*v**2 - 97*v**4 + 12066*v - 165375 - 34866*v**2 = 0.
5, 21
Let c = -36611 - -109840/3. Find h such that -8/9*h**4 + 1/9*h**5 + 8/9*h + 0 + c*h**3 - 22/9*h**2 = 0.
0, 1, 2, 4
Let n(m) be the first derivative of -2*m**3/7 + 4*m**2/7 + 2*m + 65. Determine b, given that n(b) = 0.
-1, 7/3
Let c(w) = -w**2 + 168*w + 6891. Let k(z) = -6*z**2 + 841*z + 34456. Let d(n) = 11*c(n) - 2*k(n). Factor d(f).
(f + 83)**2
Suppose -4*n = y - 3*n - 1, -5*y + n = 7. Let l be (y/1 - -4) + 0. Solve -12*a**4 + l*a**3 - 4*a**2 + 17*a**5 + 9*a**3 - 13*a**5 = 0.
0, 1
Factor 3/5*q + 0 + 18/5*q**2.
3*q*(6*q + 1)/5
Let s be (-14)/(-6) - -6*2/(-6). Let q(c) be the second derivative of 1/2*c**5 + 0 + 5*c + 1/2*c**4 - s*c**3 + 2/15*c**6 - c**2. Factor q(i).
2*(i + 1)**3*(2*i - 1)
Let s(d) be the first derivative of -d**6/288 + d**5/80 - d**4/96 + 17*d**3/3 - 31. Let m(v) be the third derivative of s(v). What is o in m(o) = 0?
1/5, 1
Factor 25/7*p**2 + 20/7 - 9/7*p**4 - 1/7*p**5 - 48/7*p + 13/7*p**3.
-(p - 1)**3*(p + 2)*(p + 10)/7
Let h(w) be the third derivative of w**6/120 - 19*w**5/20 + 361*w**4/8 - 6859*w**3/6 + 27*w**2. Factor h(g).
(g - 19)**3
Factor -44*a + 2*a**2 - 67*a - 76 - 2 + 279*a - 92*a.
2*(a - 1)*(a + 39)
Let s(y) be the first derivative of -1/3*y**3 - 81*y + 23 + 9*y**2. Factor s(t).
-(t - 9)**2
Let a(p) = 4*p**2 - 188*p - 520. Let j(s) = 2*s**2 - 125*s - 347. Let v(l) = -5*a(l) + 8*j(l). Let v(t) = 0. Calculate t.
-11, -4
Let d = 663 - 663. Let y(n) be the first derivative of 3*n**4 - 6 + 2/3*n**6 + 4/3*n**3 + d*n**2 + 12/5*n**5 + 0*n. Suppose y(g) = 0. What is g?
-1, 0
Let q = 58 - 3. Factor 2*o**2 - 2*o**2 + 2*o**2 + q*o - 41*o.
2*o*(o + 7)
Let 0 + 23/2*b + 1/2*b**3 + 12*b**2 = 0. Calculate b.
-23, -1, 0
Let y(d) = -5*d**3 + 23*d**2 - 18*d + 2. Suppose 8*z - 4 = 10*z. Let i(f) = 5*f**3 - 22*f*