Suppose -23 = 4*t - 3. Let n = t - -29. Factor -5*m**4 + 9*m**4 + 36*m**2 + n*m**3 + 16 + 48*m + 16*m**2.
4*(m + 1)**2*(m + 2)**2
Let l be 24/(-20)*(-25)/15. Let p(u) be the first derivative of 0*u**l + 2/9*u**3 - 4 - 2/3*u. Factor p(w).
2*(w - 1)*(w + 1)/3
What is d in -43*d**3 + 9*d + 96*d**3 - 52*d**3 + 3*d - 13*d**2 = 0?
0, 1, 12
Let a be 9/2*(-272)/(-51). What is z in -69 + a*z - 2*z**2 + 0*z - 3 = 0?
6
Let a(g) = g**3 - 4*g**2 + 3*g + 1. Let y be a(3). Suppose 0 = 15*z - 14*z - y. Solve 6*u**2 + z + 2*u**3 - 5*u**3 + 5*u**3 + 1 + 6*u = 0 for u.
-1
Let l(u) = u**3 - u**2 - u - 1. Let x(b) = -21*b**3 - 45*b**2 - 19*b + 19. Let y(i) = -14*l(i) - 2*x(i). Factor y(p).
4*(p + 1)*(p + 3)*(7*p - 2)
Let o(z) be the third derivative of z**8/16 - 6*z**7/35 - z**6/10 + 770*z**2. Factor o(r).
3*r**3*(r - 2)*(7*r + 2)
Let t(y) = -21*y + 25*y + 10 + 14. Let x be t(-5). Factor -3/4*s**3 + 0*s - 1/2*s**2 + 0 - 1/4*s**x.
-s**2*(s + 1)*(s + 2)/4
Let o be (-11)/(-3) - (-2)/3*-1. What is d in 433*d**o - 482*d**3 + 123*d**2 + 4 - 46*d**2 - 18*d - 14*d = 0?
2/7, 1
Suppose 29 = -x + 33. Find v such that -x*v + 8*v - 9*v - v**2 + 10 - 4*v = 0.
-10, 1
Let j(b) be the third derivative of -b**8/112 - 8*b**7/105 - b**6/5 - b**5/10 + 11*b**4/24 + b**3 + 25*b**2. Solve j(a) = 0 for a.
-3, -1, 2/3
Suppose 19*o = 34 + 42. Let q(k) be the third derivative of -k**2 + 0*k**3 + 0*k + 0 - 1/60*k**5 - 1/24*k**o. Solve q(l) = 0.
-1, 0
Factor 671*c**2 - 6*c**3 - 680*c**2 - c**4 + 0*c**4.
-c**2*(c + 3)**2
Suppose 5*h - 21 = 2*k, 2*h + 2 = 12. Factor -2 - 16/3*w + 2/3*w**4 + 0*w**3 - 4*w**k.
2*(w - 3)*(w + 1)**3/3
Let n(y) be the second derivative of -12/5*y**2 - 9/70*y**7 + 13*y + 14/5*y**3 - 11/10*y**4 + 0 - 57/100*y**5 + 3/5*y**6. What is a in n(a) = 0?
-1, 2/3, 1, 2
Determine a, given that 0 + 1/2*a**2 - 22*a = 0.
0, 44
Let y(p) = 3*p + 47. Let x be y(-15). Let t(d) be the first derivative of 10 + d**4 - x*d**3 - d - 1/5*d**5 + 2*d**2. Solve t(n) = 0 for n.
1
Let s(f) be the first derivative of -4805*f**3/3 - 930*f**2 - 180*f + 158. Determine q so that s(q) = 0.
-6/31
Suppose 76*w - 75*w - f - 3 = 0, -5*w + 3*f + 15 = 0. Let r(i) be the first derivative of 2/7*i - 6 - 1/21*i**w + 1/14*i**2. Factor r(d).
-(d - 2)*(d + 1)/7
Suppose 3*d + 8*d - 22 = 0. Let f(a) be the third derivative of 5/24*a**4 + 0*a + 0 - 1/12*a**5 + 0*a**3 - 10*a**d. Factor f(z).
-5*z*(z - 1)
Let u(j) be the third derivative of 0 - 3/8*j**4 + 0*j - 5*j**2 - 1/40*j**6 + 3/20*j**5 + 1/2*j**3. Find w such that u(w) = 0.
1
Let g(x) be the third derivative of -10*x**2 - 5/3*x**3 - 1/42*x**4 + 0 + 1/630*x**6 + 0*x**5 + 0*x. Let k(l) be the first derivative of g(l). Factor k(m).
4*(m - 1)*(m + 1)/7
Factor -7688/3 - 50/3*o**2 - 1240/3*o.
-2*(5*o + 62)**2/3
Let d(o) = -3*o**5 - o**4 + 20*o**3 + 44*o**2 + 33*o + 9. Let a(v) = v**4 + v**3 + v**2. Let l(z) = 2*a(z) - d(z). Factor l(q).
3*(q - 3)*(q + 1)**4
Determine z, given that 2*z**5 + 1294/7*z**3 + 468/7*z - 270/7*z**4 + 0 - 1986/7*z**2 = 0.
0, 2/7, 3, 13
Let h(x) = -x**2 + 1. Suppose 5*m + b = -10, -m - 4*b + 2 = 23. Let r(v) = -v - 1. Let p(n) = m*r(n) + h(n). Factor p(s).
-(s - 2)*(s + 1)
Let j be -21 - -29 - (-822)/39. Solve 54/13 + 686/13*d**3 + j*d + 882/13*d**2 = 0.
-3/7
Let k(q) = -q**3 - 15*q**2 + 27*q - 116. Let m be k(-17). Let p(l) be the third derivative of 1/12*l**4 + 0 + 0*l + 0*l**3 + m*l**2 + 1/60*l**5. Solve p(d) = 0.
-2, 0
Suppose 5*j = q + 21, -5*j + 2*q = 5*q - 17. Let -18*d**j + 12*d - 2*d**4 - 9*d**3 + 109*d**2 + 12*d**5 - 13*d**4 - 61*d**2 = 0. What is d?
-1, -1/4, 0, 2
Let i(s) be the third derivative of -s**7/70 - s**6/40 + s**5/10 + 130*s**2. Find b such that i(b) = 0.
-2, 0, 1
Let z(l) be the first derivative of 1/2*l**5 + 5/6*l**3 + 5/4*l**4 + 23 + 0*l**2 + 0*l. Factor z(s).
5*s**2*(s + 1)**2/2
Let m be -1*(-35)/28*(-16)/(-10). Let d(r) be the first derivative of 0*r - 4/3*r**3 + 8 - m*r**2. Factor d(s).
-4*s*(s + 1)
Suppose 20 = 15*m - 20*m - 5*c, -16 = -m + 4*c. What is j in -2/5 + 2/5*j**2 + m*j = 0?
-1, 1
Let h(q) be the first derivative of q**6/90 - q**5/15 + q**4/6 - 4*q**3 - 24. Let z(f) be the third derivative of h(f). Determine d so that z(d) = 0.
1
Suppose -f = -10*f + 18. Factor 1 + 36*w + w**f + 0*w**2 - 32*w + 2.
(w + 1)*(w + 3)
Let v(z) be the first derivative of -z**3/3 - 10*z**2 - 162. Solve v(b) = 0.
-20, 0
Find h, given that -48 + 735/2*h**3 - 576*h**2 - 75/2*h**4 + 294*h = 0.
2/5, 1, 8
Let b be (-1336)/1002*18/(-32). Solve 0 - 1/2*f + 1/4*f**4 + 0*f**3 - b*f**2 = 0.
-1, 0, 2
Suppose -123 - 25 = -4*a. Let f = 39 - a. Factor 0*j**f + 2/3*j**3 + 1/3*j**4 - 2/3*j - 1/3.
(j - 1)*(j + 1)**3/3
Let l(i) be the third derivative of i**7/1050 - 7*i**6/600 + 2*i**5/75 + 2*i**4/15 + 49*i**2. Factor l(j).
j*(j - 4)**2*(j + 1)/5
Let s = -14 - -28. Factor 12*c**3 + c - 4*c - s*c**3 + 5*c**3.
3*c*(c - 1)*(c + 1)
Factor -15/2 - 3/2*g**2 - 9*g.
-3*(g + 1)*(g + 5)/2
Suppose -4 = -5*d - y, 3*d + y - 44 = -40. Factor -2*i**4 + d*i**2 - 12/5*i**3 + 2/5*i**5 + 0 + 0*i.
2*i**3*(i - 6)*(i + 1)/5
Suppose 4*s + 0 - 1/9*s**2 = 0. What is s?
0, 36
Let s(h) be the second derivative of 2*h**6/15 + 6*h**5 + 253*h**4/3 + 280*h**3 + 392*h**2 - 3*h + 30. Find z, given that s(z) = 0.
-14, -1
Let r(t) = 3*t**2 - 17*t - 90. Let z be r(9). Factor -1/3*g**5 + g**3 + z - 4/3*g + 4/3*g**2 - 2/3*g**4.
-g*(g - 1)**2*(g + 2)**2/3
Suppose 0 = -3*t + 100 - 55. Factor -3*v**2 + 37 + 12*v**2 - t*v - 43.
3*(v - 2)*(3*v + 1)
Let o(b) be the third derivative of b**5/60 + 17*b**4/24 + 8*b**3/3 + b**2 + 60*b. Determine k, given that o(k) = 0.
-16, -1
Let w(o) be the second derivative of 1/90*o**6 + 0*o**2 - 3*o + 1/4*o**4 + 2/9*o**3 + 1 + 1/10*o**5. Factor w(v).
v*(v + 1)**2*(v + 4)/3
Let w(m) be the first derivative of -m**3/18 - 4*m**2/3 + 17*m/6 - 130. Factor w(p).
-(p - 1)*(p + 17)/6
Let v(y) be the first derivative of 2*y**3/3 - 31*y**2/2 + 15*y - 158. Suppose v(l) = 0. Calculate l.
1/2, 15
Factor 0 + 4*o - 2/11*o**2.
-2*o*(o - 22)/11
Let b be ((-80)/(-4) + -19)/((-6)/(-4) + -1). Factor -3/4*n**b - 9/4 + 3*n.
-3*(n - 3)*(n - 1)/4
Suppose -4*i = l - 19 - 4, -5*i = 4*l - 70. Let d = -10 + l. Let 0*j**3 + 6/7*j**d + 0*j + 0 - 9/7*j**4 + 3/7*j**2 = 0. Calculate j.
-1/2, 0, 1
Let o(x) be the third derivative of -x**8/420 + 2*x**7/105 - x**6/30 + 19*x**3/6 + 7*x**2. Let w(h) be the first derivative of o(h). Factor w(a).
-4*a**2*(a - 3)*(a - 1)
Let y(v) be the second derivative of 6*v + 0 - 3/80*v**5 - 1/24*v**4 + 0*v**2 + 1/168*v**7 + 0*v**6 + 0*v**3. Factor y(h).
h**2*(h - 2)*(h + 1)**2/4
Let c(p) be the second derivative of -18*p + 0 - 1/5*p**4 - 2/5*p**3 - 2/5*p**2 - 1/25*p**5. Factor c(y).
-4*(y + 1)**3/5
Let d = 11/25 + -61/150. Let l(p) be the third derivative of -d*p**5 - 4/15*p**3 + p**2 + 0*p + 0 - 1/5*p**4. Find t, given that l(t) = 0.
-2, -2/5
Let n(l) be the third derivative of l**6/1080 + l**5/90 + l**4/24 - l**3/3 + 4*l**2. Let s(y) be the first derivative of n(y). Factor s(t).
(t + 1)*(t + 3)/3
Let b(t) = -t**3 + t**2 - 2*t + 3. Let u(q) = q**4 - q**3 + 18*q**2 - 8*q + 21. Let s(h) = 14*b(h) - 2*u(h). Let s(a) = 0. Calculate a.
-3, -2, -1, 0
Let d = -2/787 + 797/3935. Factor -d*h**2 + h - 6/5.
-(h - 3)*(h - 2)/5
Let y(p) be the third derivative of 4*p**5/45 + 13*p**4/3 + 169*p**3/2 + 159*p**2. Solve y(m) = 0.
-39/4
Let u(i) be the first derivative of i**3/9 + i**2/6 + 41. Find d, given that u(d) = 0.
-1, 0
Let n(l) be the second derivative of -l**4/54 + 154*l**3/27 - 5929*l**2/9 + 3*l + 54. Suppose n(d) = 0. What is d?
77
Suppose 2*a - 34 = -4*p, 3*a - 4*p = -3*p + 23. Suppose -15 = -2*y - a. Determine i, given that 0*i + 0 + 0*i**4 - i**2 - 1/2*i**5 + 3/2*i**y = 0.
-2, 0, 1
Let c(b) be the third derivative of b**6/480 + b**5/120 - b**4/96 - b**3/12 + 16*b**2 + b. Determine l so that c(l) = 0.
-2, -1, 1
Let p be (2 + -1)/(2/4). Let l be 2365/275 - (4 + 3). Factor 0 + l*z - 2/5*z**p.
-2*z*(z - 4)/5
Let 0*t**2 + 126*t**4 + 13*t**2 - 124*t**4 - 8*t - 10*t**3 + 3*t**2 = 0. Calculate t.
0, 1, 2
Let o(x) be the third derivative of -x**6/40 - x**5/5 + 11*x**4/8 - 3*x**3 + x**2 - 124. Suppose o(u) = 0. Calculate u.
-6, 1
Let g = -2210 + 2210. Let z(w) be the second derivative of g*w**2 + 5/2*w**4 + 0 - 15/8*w**5 - w**3 + 13*w. Factor z(k).
-3*k*(5*k - 2)**2/2
L