55
Suppose 20*h = 59*h. Suppose h*z - 1/3 + 1/3*z**2 = 0. Calculate z.
-1, 1
Let u(f) be the third derivative of f**6/60 - f**5/30 - f**4/12 + f**3/3 - 36*f**2. Find d such that u(d) = 0.
-1, 1
Let q(h) be the first derivative of -3/4*h**4 + 13 - 225/2*h**2 + 15*h**3 + 375*h. Factor q(d).
-3*(d - 5)**3
Let p = 79 + -49. Suppose n = -n + p. Factor -n*m**4 + 13*m**3 + m**3 + 5*m**3 + 3*m - 7*m.
-m*(m - 1)*(3*m - 2)*(5*m + 2)
Let f(i) be the second derivative of i**7/84 - i**6/60 - 3*i**5/20 + i**4/6 + 2*i**3/3 - i + 262. Factor f(v).
v*(v - 2)**2*(v + 1)*(v + 2)/2
Let h = -548 + 548. Suppose -y = -3*y + 3*y. Factor y + 1/4*v**2 + h*v.
v**2/4
Suppose 0*b = 2*q + 4*b + 8, 2*q = -5*b - 11. Let s(l) be the first derivative of 5 + 0*l - 1/6*l**q + 0*l**3 + 1/12*l**4. Factor s(k).
k*(k - 1)*(k + 1)/3
Let m(t) be the third derivative of -1/120*t**5 + 0*t + 0 + 1/24*t**4 - 7*t**2 + 0*t**3. Solve m(b) = 0 for b.
0, 2
Factor -45/4 - 11*r + 1/4*r**2.
(r - 45)*(r + 1)/4
Determine o, given that -6 - 10*o**2 - 18*o + 50/9*o**3 = 0.
-3/5, 3
Let m(g) be the first derivative of -3*g**5/10 + 9*g**3 - 243*g/2 - 705. Factor m(j).
-3*(j - 3)**2*(j + 3)**2/2
Factor 57*y - 32 + 9734*y**2 - 9731*y**2 + 134.
3*(y + 2)*(y + 17)
Let m(v) be the second derivative of 1/357*v**7 + 3/170*v**5 - 1/102*v**4 - 2*v + 0*v**3 + 0*v**2 - 1/85*v**6 + 0. Find j such that m(j) = 0.
0, 1
Factor -6*p**2 - 2*p + 3*p**3 - 10*p**3 + 6*p**3 + p**2 - 2*p.
-p*(p + 1)*(p + 4)
Let r(c) be the third derivative of 0*c**5 + 0*c**3 - 1/420*c**7 - 1/120*c**6 + 0*c**4 + 0 + 0*c - 19*c**2. Suppose r(l) = 0. What is l?
-2, 0
Let n be (0 - -1)*2/(-8)*(-549 + 548). Factor 1/2*m**3 + n*m**2 + 0*m + 1/4*m**4 + 0.
m**2*(m + 1)**2/4
Let s = -564 - -154535/274. Let q = 545/822 - s. Factor -q + 2/9*d**2 - 4/9*d.
2*(d - 3)*(d + 1)/9
Let n be -3*(20 - 19)/(2/(-2)). Let z(d) be the first derivative of 0*d**n - 1/15*d**6 - 4/25*d**5 + 0*d**2 + 5 + 0*d - 1/10*d**4. Factor z(b).
-2*b**3*(b + 1)**2/5
Let t(i) = 17*i**2 + 86*i + 9. Let j(l) = 4*l**2 + 22*l + 2. Let v(c) = -18*j(c) + 4*t(c). Factor v(o).
-4*o*(o + 13)
Let x(l) be the third derivative of -l**8/20160 - l**7/2520 + l**6/240 + 3*l**5/20 + 33*l**2. Let g(q) be the third derivative of x(q). What is i in g(i) = 0?
-3, 1
Let d = -47 - -50. Suppose 0 = 3*h - b + 3, d*b = h - 2 + 11. Factor -1/3*t**2 + 0*t - t**3 - 2/3*t**4 + h.
-t**2*(t + 1)*(2*t + 1)/3
Let u(k) = 25*k**4 - 88*k**3 + 209*k**2 + 49*k - 222. Let g(q) = 3*q**4 - 11*q**3 + 26*q**2 + 6*q - 28. Let h(f) = -51*g(f) + 6*u(f). Factor h(p).
-3*(p - 8)*(p - 2)**2*(p + 1)
Let w(q) be the second derivative of -1/21*q**3 - 3/14*q**2 - 18*q + 0 + 1/84*q**4. Let w(l) = 0. What is l?
-1, 3
Let o be -2 - (-4)/(-8)*-6. Let k be (2/4)/(o/24). Solve k*n**2 - 3*n**4 - 33*n + 33*n = 0 for n.
-2, 0, 2
Suppose 9 - 12 = -u. Factor -2 - 3*k**u - 48*k**3 + 3*k**3 - 18*k**4 - 16*k - 44*k**2.
-2*(k + 1)**2*(3*k + 1)**2
Suppose 3*w - d - 17 = 0, 3*d + 16 = 5*w - 3*w. Let k(b) be the second derivative of -9/8*b**2 - 1/16*b**4 + 0 + w*b + 1/2*b**3. Factor k(q).
-3*(q - 3)*(q - 1)/4
Let x(u) be the third derivative of 0*u - 1/3*u**4 + 0 + 11*u**2 - 1/15*u**5 + 1/30*u**6 + 0*u**3. Factor x(n).
4*n*(n - 2)*(n + 1)
Let m(k) = k**3 + 10*k**2 + 2*k + 22. Let c be m(-10). Let i = 3 - 1. Factor 4*j**4 - 8*j**2 + 0*j**i + 6*j**c + 2*j**3.
2*j**2*(j + 1)*(2*j - 1)
Let y(v) be the first derivative of v**5/5 + 5*v**4/3 + 16*v**3/3 + 8*v**2 - 3*v + 13. Let g(n) be the first derivative of y(n). Factor g(l).
4*(l + 1)*(l + 2)**2
Let b(x) be the first derivative of -x**4/14 + 2*x**3/21 - 170. Suppose b(z) = 0. What is z?
0, 1
Find q such that 252/23 + 186/23*q + 40/23*q**2 + 2/23*q**3 = 0.
-14, -3
Let q be ((-44)/28 - (-6 - -3)) + -1. Let k = 224 + -221. Factor q*y**2 + 0 - 1/7*y**k + 0*y.
-y**2*(y - 3)/7
Let v be 4/(-4) + (54*-1 - -1). Let j = -54 - v. Solve -1/4*x**4 + 0 + j*x - 1/2*x**3 - 1/4*x**2 = 0.
-1, 0
Let c be 33 - 0 - (-1)/(-1). Suppose 5*f - g - 40 = 4*g, -c = -3*f + 5*g. Factor -f*p - 4*p**3 + 2*p**3 - 4*p**2 + 4 + 6*p.
-2*(p - 1)*(p + 1)*(p + 2)
Let c be 2/12 + 566/396. Let t = 16/9 - c. Factor 0 + 4/11*f**2 - 2/11*f - t*f**3.
-2*f*(f - 1)**2/11
Let s(r) be the second derivative of -r**6/540 + 2*r**5/45 - 4*r**4/9 + 5*r**3/6 - 2*r. Let y(o) be the second derivative of s(o). Factor y(a).
-2*(a - 4)**2/3
Let k be 4/12 - 55/(-15). Factor 3*i**2 + 3*i**3 - 7 + i - 4*i + k.
3*(i - 1)*(i + 1)**2
Let n = -3/9650 - -38609/28950. Factor -14/3*d - 5/6*d**3 - n - 11/3*d**2.
-(d + 2)**2*(5*d + 2)/6
Let a be 2 - (16 - 4)/(-4). Suppose -2*u = -a - 1. What is s in 12 + u*s**2 + s - 53*s + 9*s**2 + 4*s**2 = 0?
1/4, 3
Find x such that 5*x**5 + 27*x**3 - 30*x**2 - 47*x**3 - 20*x**4 - 35*x**3 = 0.
-1, 0, 6
Let b(v) be the second derivative of -v**7/1260 - v**6/180 - v**5/90 - 19*v**3/6 - 17*v. Let r(h) be the second derivative of b(h). Factor r(x).
-2*x*(x + 1)*(x + 2)/3
Let s(y) be the first derivative of -y**4/18 + 94*y**3/9 - 2209*y**2/3 + 207646*y/9 + 250. Factor s(f).
-2*(f - 47)**3/9
Let n(k) be the third derivative of -k**5/270 - 11*k**4/27 - 484*k**3/27 - 83*k**2. Solve n(q) = 0.
-22
Let b(z) be the third derivative of -1/12*z**4 - 13*z**2 - 1/150*z**5 + 0 + 0*z + 0*z**3. Find w, given that b(w) = 0.
-5, 0
Let b = -3135/4 - -784. Determine x, given that b*x**2 - 1/2*x + 0 = 0.
0, 2
Suppose 8*h + 1/2*h**2 + 39/2 = 0. What is h?
-13, -3
Let i(y) be the second derivative of -y**6/45 + 19*y**5/15 - 397*y**4/18 + 76*y**3 - 108*y**2 + 5*y + 46. Let i(l) = 0. Calculate l.
1, 18
Let t be (33/9 - 2)*(-52)/(-130). Find j, given that 0*j + 2/3*j**2 - t = 0.
-1, 1
Let b(o) be the first derivative of o**3/3 - 2*o**2 + 4*o + 14. Determine w, given that b(w) = 0.
2
Suppose 0 = 2*j - 15 + 9. Let t = j - -5. Factor -74/5*q**3 + 0 - 8/5*q + 12*q**4 + t*q**2 - 18/5*q**5.
-2*q*(q - 1)**2*(3*q - 2)**2/5
Let j = 5 + 5. Let b = j + -10. What is p in -6/11*p**2 - 2/11*p + b - 6/11*p**3 - 2/11*p**4 = 0?
-1, 0
Suppose 169 - 13*o + o**2 - 6*o - 7*o = 0. What is o?
13
Let i be 0/(((-1)/(-3))/((-9)/(-27))). Let h(o) be the second derivative of 2/21*o**3 - 3*o + 0 + i*o**2 - 1/35*o**5 + 1/42*o**4 - 1/105*o**6. Factor h(r).
-2*r*(r - 1)*(r + 1)*(r + 2)/7
Let j = 677 + -677. Let h(g) be the first derivative of 1/8*g**4 + 1/12*g**6 + j*g**3 + 0*g**2 + 1/5*g**5 + 2 + 0*g. Factor h(s).
s**3*(s + 1)**2/2
Determine h, given that -14*h + 0*h**2 - 59 + 64 - 18 - h**2 = 0.
-13, -1
Let x(i) be the second derivative of i**4/18 - 43*i**3/9 - 44*i**2/3 - 42*i. Factor x(m).
2*(m - 44)*(m + 1)/3
Factor -2/3*a**3 + 0 - 8/3*a**2 + 0*a.
-2*a**2*(a + 4)/3
Let k(h) be the first derivative of h**4 - 392*h**3/3 + 4992*h**2 - 18432*h - 472. Find d, given that k(d) = 0.
2, 48
Suppose -161*a + 54 = -143*a. Find g such that 0*g**4 - 3/4*g**a + 3/8*g**5 + 0*g**2 + 3/8*g + 0 = 0.
-1, 0, 1
Let s(x) be the first derivative of 5/3*x**3 + 6 - 5/2*x**2 - 10*x. What is y in s(y) = 0?
-1, 2
Let k = 4403/8 - 550. Let s(o) be the first derivative of -2 + 0*o + 1/12*o**3 - k*o**2. Factor s(v).
v*(v - 3)/4
Let h(s) be the third derivative of -s**6/320 + 7*s**5/160 + s**4/64 - 7*s**3/16 - 135*s**2. What is v in h(v) = 0?
-1, 1, 7
Let j = 54 + -51. Suppose -4*r - j = -5*r. Factor 0*p**2 + 3/2*p**r + 0 - 3/2*p.
3*p*(p - 1)*(p + 1)/2
Let l(d) be the first derivative of -2*d**7/105 - d**6/10 - d**5/5 - d**4/6 + 19*d**2 + 3. Let t(z) be the second derivative of l(z). Let t(x) = 0. What is x?
-1, 0
Let v(l) be the second derivative of -l**5/5 + 7*l**4/3 - 12*l. Determine i, given that v(i) = 0.
0, 7
Let s(p) = -13*p - 11. Let w be -7 + (1 - -1) + 0. Let l be s(w). Factor 72*h**2 + 8 - 40*h + 27/2*h**4 - l*h**3.
(h - 2)*(3*h - 2)**3/2
Let o(u) = u - 13. Let j be o(17). Let c(k) be the third derivative of 0 - 1/4*k**j + 2/3*k**3 + 1/30*k**5 - 6*k**2 + 0*k. Factor c(w).
2*(w - 2)*(w - 1)
Let w(p) be the first derivative of -p**3/3 + 4*p**2 + 20*p - 456. Let w(v) = 0. What is v?
-2, 10
Let z(u) be the first derivative of -u**6/24 + u**5/12 + 9*u**2/2 + 34. Let y(n) be the second derivative of z(n). Find m, given that y(m) = 0.
0, 1
Factor 13/4*h**2 + 3 - 1/4*h**3 - 1/4*h**4 + 25/4*h.
-(h - 4)*(h + 1)**2*(h + 3)/4
Suppose -9*m + 11 = -16. Factor -2*b**3 + 4*b**5 + 12*b**4 - 2*b**3 + 4*b**2 + 16*b**m.
4*b**2*(b + 1)*