
-1, 3
Let t(j) = j**3 - 18*j**2 + 27*j - 5. Let r be t(16). Let s = 85 + r. Factor 2/9*x + 0 + s*x**2 - 2/9*x**3.
-2*x*(x - 1)*(x + 1)/9
Let r = 8 + -6. Suppose -r*o = 2*o - 16. Suppose -4*i**3 + 3*i**3 - 5*i**3 - 3*i**o = 0. What is i?
-2, 0
Let a(h) be the second derivative of -1/28*h**4 - 6*h + 0*h**2 + 1/21*h**3 + 0 - 1/70*h**5 + 1/70*h**6. Factor a(g).
g*(g - 1)*(g + 1)*(3*g - 2)/7
Let g(c) be the first derivative of -c**7/140 + c**6/120 + c**5/120 + 15*c**2/2 - 20. Let h(z) be the second derivative of g(z). Let h(k) = 0. What is k?
-1/3, 0, 1
Let j(f) = 11*f**2 + 17*f + 13. Let i(b) = -3 - 3 + 16*b + 0 + 3. Let y be i(1). Let a(w) = 5*w**2 + 8*w + 6. Let p(r) = y*a(r) - 6*j(r). Factor p(d).
-d*(d - 2)
Suppose 42 = -2*z + 3*z. Let m = z - 14. Determine j, given that -36*j**4 - 95 + m*j**5 + 8*j**3 + 95 = 0.
0, 2/7, 1
Let n be -28 + 26 + (-1)/(2/(-10)). Let k(d) be the first derivative of 8/5*d + 2/15*d**3 + d**2 - n. Factor k(r).
2*(r + 1)*(r + 4)/5
Let y(r) = -r**4 + r**3 + r. Let a = -89 + 88. Let z(x) = -4*x**5 - 8*x**4 - 16*x**3 - 4*x**2 - 4*x. Let l(p) = a*z(p) - 4*y(p). Find s such that l(s) = 0.
-1, 0
Let h(s) be the third derivative of -1/150*s**5 + 0*s**3 - 1/300*s**6 + 0 + 0*s + 1/30*s**4 - 25*s**2. Factor h(g).
-2*g*(g - 1)*(g + 2)/5
Let j(w) be the first derivative of -w**4/26 - 22*w**3/39 - 24*w**2/13 - 107. What is b in j(b) = 0?
-8, -3, 0
Let c = -116 + 92. Let v be 24/(-18) - -19*(-2)/c. Factor -1/4*b**2 - 1/4*b**3 + 0*b + 1/4*b**5 + v*b**4 + 0.
b**2*(b - 1)*(b + 1)**2/4
Suppose -22 = -93894*f + 93883*f. Factor 0 + 4/3*j**f + 16/9*j**3 - 4/9*j.
4*j*(j + 1)*(4*j - 1)/9
Suppose -3*q + 4*f + 56 = 0, -q - 5*f + 22 = q. Let t be (q + -15)*1*3. Let 6/5*v**t + 1/5*v + 4/5*v**4 + 0 + 1/5*v**5 + 4/5*v**2 = 0. What is v?
-1, 0
Suppose 159*t - 154 = 137*t. Let y(p) be the first derivative of -1/12*p**3 - 1/8*p**2 + 1/2*p - t. Factor y(f).
-(f - 1)*(f + 2)/4
Let k(b) be the third derivative of 1/105*b**6 + 1/42*b**4 + 0*b + 1/735*b**7 + 0 - 12*b**2 + 1/42*b**5 + 0*b**3. What is v in k(v) = 0?
-2, -1, 0
Let k = -7/32 + 37/96. Let z(a) be the second derivative of 0 - a**2 + 0*a**3 + k*a**4 - a. Find m such that z(m) = 0.
-1, 1
Let l be (-2)/4*-2 - 1. Let a be (-2)/5*4705/(-7528). Factor a + 1/4*i**4 + 0*i + l*i**3 - 1/2*i**2.
(i - 1)**2*(i + 1)**2/4
Let s be (-10)/3*(-114)/76. Let b(v) be the third derivative of 0 + 2*v**2 - v**3 - 1/20*v**s + 0*v - 3/8*v**4. Solve b(w) = 0.
-2, -1
Factor 858*x - 1716*x + x**2 + 8 + 852*x.
(x - 4)*(x - 2)
Let t(m) be the third derivative of -m**6/300 - 59*m**5/50 - 3481*m**4/20 - 205379*m**3/15 + 17*m**2 - 2. Suppose t(x) = 0. What is x?
-59
Let d(p) be the third derivative of p**8/120 + 23*p**7/525 - 29*p**6/300 - 31*p**5/150 + 11*p**4/30 + 8*p**3/15 + 6*p**2 - 11*p. Solve d(s) = 0 for s.
-4, -1, -2/7, 1
Let k(p) be the third derivative of p**7/490 + 11*p**6/420 - 4*p**5/105 + 4*p**2 + p. Find q such that k(q) = 0.
-8, 0, 2/3
Let x(g) be the first derivative of 59 + g - 13/6*g**3 + 11/4*g**2. Determine u, given that x(u) = 0.
-2/13, 1
Let m(z) = 35*z**4 - 189*z**3 + 42*z**2 - 4*z + 4. Let h(k) = -k**3 - 2*k**2 - k + 1. Let x(g) = -4*h(g) + m(g). Factor x(o).
5*o**2*(o - 5)*(7*o - 2)
Factor r**2 - 24*r**3 + 12*r**3 - r**2 + 2*r**4.
2*r**3*(r - 6)
Let m(j) be the first derivative of -2*j**3/39 + 102*j**2/13 - 5202*j/13 - 105. Factor m(s).
-2*(s - 51)**2/13
Factor 4/3*s**5 + 0 - 5/3*s - 11/3*s**2 + 7/3*s**4 - s**3.
s*(s + 1)**3*(4*s - 5)/3
Suppose 0 = 2*a - 0*f - 5*f - 36, 0 = 5*a - 4*f - 90. Suppose 6*i + 0 = a. Solve b**3 - i*b - b**2 - 3 + 3 - b**2 = 0 for b.
-1, 0, 3
Let b(s) be the third derivative of 0 + 1/120*s**5 + 1/12*s**3 + 0*s - 1/24*s**4 - 14*s**2. Let b(o) = 0. What is o?
1
Let b(y) be the first derivative of -y**3/3 - 2*y**2 - 4*y - 7. Let k be b(-2). What is d in 5*d**3 - 8*d + k*d**2 - d**3 + 0*d**3 - 4*d**2 = 0?
-1, 0, 2
Suppose -4*b + 6 + 2 = 0. Let i(v) = 3*v**4 - 3*v**3 - 3*v**2 + 5*v - 2. Let m(s) = s**4 - s**3 - s**2 + 1. Let u(p) = b*m(p) + i(p). Find l such that u(l) = 0.
-1, 0, 1
Let l = -13 - -15. Suppose 0 = -l*g - 0*g + 4. Let 0*p**3 - 3*p**3 + g*p**3 + 0*p**3 + 4 - 3*p**2 = 0. Calculate p.
-2, 1
Factor -v**2 - 14*v**2 - 2*v**3 + 11*v**2 + 104*v + v**2 - 17*v**2 - 112.
-2*(v - 2)**2*(v + 14)
Let m(g) = 16*g**2 - 15*g**2 - 3 + 3*g - 4*g. Let a be m(3). Determine y so that 3 + 2 - 5 + a*y**2 - 3*y = 0.
0, 1
Factor -15/2*y**2 - 30 - 185/2*y.
-5*(y + 12)*(3*y + 1)/2
Let d be 251/(-20) + (-5)/20. Let f = d + 13. Factor 1/5*i**2 + 0 - f*i.
i*(i - 1)/5
Let n be (-9)/((-2507)/598 - 8/26). Suppose -5/2*p**3 + 25/2*p + 5 - 5/2*p**4 + 15/2*p**n = 0. Calculate p.
-1, 2
Let w(i) be the second derivative of -1/60*i**5 + 0*i**2 - 10*i - 1/12*i**4 + 0 - 1/9*i**3. Factor w(d).
-d*(d + 1)*(d + 2)/3
Let y(t) be the first derivative of 1/2*t**2 + 3 + 0*t + 0*t**3 - 1/90*t**5 - 1/12*t**4. Let f(j) be the second derivative of y(j). Factor f(i).
-2*i*(i + 3)/3
Let r(o) be the second derivative of -o**5/10 + 5*o**4/6 + o**3/3 - 5*o**2 - 11*o - 4. Factor r(j).
-2*(j - 5)*(j - 1)*(j + 1)
Let a(x) be the third derivative of -x**6/1260 + x**5/420 - 2*x**3/3 - 10*x**2. Let u(m) be the first derivative of a(m). Factor u(k).
-2*k*(k - 1)/7
Suppose 3*k - 2*m - 11 = -m, 3*k = 4*m - 1. Let 4*j - 9*j**5 - 8*j**3 - 4*j**k + 23*j**5 - 6*j**5 = 0. What is j?
-1, 0, 1
Let p(f) be the first derivative of f**5/10 - 19*f**4/8 + 17*f**3/3 - 766. Factor p(h).
h**2*(h - 17)*(h - 2)/2
Let a(h) = -h**2 + 15*h - 26. Let y be a(2). What is x in -3/2*x**2 + y - 1/2*x = 0?
-1/3, 0
Let g(f) be the second derivative of -f**4/6 + 3*f**3 + 702*f. Factor g(d).
-2*d*(d - 9)
Let z = 13640 - 13635. Find v, given that 3/5 + 12/5*v**2 + 12/5*v - 6/5*v**z - 3*v**4 - 6/5*v**3 = 0.
-1, -1/2, 1
Let s(p) be the first derivative of 24 + 0*p - 1/10*p**2 - 1/15*p**3. Suppose s(l) = 0. Calculate l.
-1, 0
Let w(g) be the second derivative of -3/8*g**2 + 1/48*g**4 - 1/12*g**3 - 9*g + 0. Factor w(t).
(t - 3)*(t + 1)/4
Let n(o) be the first derivative of -4*o**5/5 + 5*o**4 + 44*o**3/3 - 66*o**2 + 72*o + 691. Determine q, given that n(q) = 0.
-3, 1, 6
Let x be 5 - 3 - 15/(-1). Let k be (0 - 0) + (19 - x). Determine w so that -4 - 3*w**2 + k*w + w**2 + 4*w**2 = 0.
-2, 1
Let a(l) = -16*l**3 - 12*l**2 - 10*l - 30. Suppose 3*m - v - 7 = 0, -3*m + 4 = -2*m - 2*v. Let x(b) = -b**3 + b - 1. Let s(y) = m*a(y) - 28*x(y). Factor s(p).
-4*(p + 2)**3
Suppose 0 = -90*k + 97*k - 21. Let t(i) be the first derivative of -2 + i**k - 3/2*i**2 + 0*i. Factor t(a).
3*a*(a - 1)
Let n(i) = -2*i**3 - 22*i**2 + 62*i - 38. Let s(u) = -15*u**3 - 155*u**2 + 435*u - 265. Let l = -110 - -113. Let f(d) = l*s(d) - 20*n(d). Factor f(z).
-5*(z - 1)**2*(z + 7)
Suppose 0 = -r + 3*g + 10, -44*r + 47*r - g = 14. Let p(i) be the first derivative of -1/8*i**6 + 0*i**3 + 0*i**2 + 0*i**5 + 3/16*i**r - 5 + 0*i. Factor p(f).
-3*f**3*(f - 1)*(f + 1)/4
Let d(o) be the first derivative of -o**4/30 - 2*o**3/9 - 2*o**2/5 + 57. Factor d(x).
-2*x*(x + 2)*(x + 3)/15
Let m(c) = -8*c + 4. Let j(n) = 7*n - 3. Let u(q) = -6*j(q) - 5*m(q). Let p be u(-2). Find x, given that 2*x**p - 14/5*x - 2/5*x**3 + 6/5 = 0.
1, 3
Let w(d) be the first derivative of -12 + 3/5*d**3 - 3/10*d**2 + 3/25*d**5 - 9/20*d**4 + 0*d. Find m such that w(m) = 0.
0, 1
Suppose -5*o = 4*m - 0*o - 1, 3*m - 3*o - 21 = 0. Factor 8*q**4 - 5*q + m*q**3 - 12*q**5 + 18*q - 13*q.
-4*q**3*(q - 1)*(3*q + 1)
Let g be 192/(-64)*(2/2 + 8). Let q(t) = t**2 + 26*t - 25. Let k be q(g). Suppose -4/3*x + 2/3*x**k + 2/3 = 0. What is x?
1
Let o(a) = 20*a**2 - 64*a + 44. Let v(n) = 4*n**2 - 13*n + 9. Let j(y) = 3*o(y) - 16*v(y). Let j(b) = 0. What is b?
1, 3
Let h(u) be the third derivative of 0*u + 1/60*u**6 + 0*u**3 - 1/30*u**5 - 1/12*u**4 + 1/105*u**7 + 0 - 21*u**2. Factor h(y).
2*y*(y - 1)*(y + 1)**2
Let c = -2568 - -2571. Factor 3/4*v**2 + c*v + 0.
3*v*(v + 4)/4
Let m be (-208)/1248*(0 - 18). Determine c, given that -6/5*c**2 + 2/5*c**m + 0*c + 8/5 = 0.
-1, 2
Let n(a) be the third derivative of a**6/240 - 3*a**5/40 - 5*a**4/24 - 2*a**2. Factor n(t).
t*(t - 10)*(t + 1)/2
Solve -28 + 87 + 17*n**2 - 39 + 40*n + 8*n**2 + 5*n**3 = 0.
-2, -1
Let l(q) be the third derivative of q**8/5040 - q**7/630 - q**6/60 + q**5/20 + 22*q**2. Let t(d) be the third de