
-2*(m - 1)*(m + 4)
Let f = -153/2 - -223. Let s = f - 146. Factor -s*x + 1/2*x**2 - 1.
(x - 2)*(x + 1)/2
Let s(y) = y**4 + y**2 + y + 1. Let l(q) = -5*q**5 + 59*q**4 - 150*q**3 + 139*q**2 - 46*q - 1. Let c(u) = l(u) + s(u). Factor c(b).
-5*b*(b - 9)*(b - 1)**3
Let u(p) be the third derivative of 5*p**8/336 + p**7/70 - p**6/60 - 8*p**2 - 3. Factor u(o).
o**3*(o + 1)*(5*o - 2)
Let r be -2*3 + (6 - 0). Let f(u) be the first derivative of 0*u**2 - 4 - 1/21*u**6 - 4/35*u**5 + 0*u**3 + r*u - 1/14*u**4. Find b, given that f(b) = 0.
-1, 0
Solve 16*g**2 - 157*g**2 - 4*g**4 + 52*g**3 - 63*g**2 + 252*g = 0.
0, 3, 7
Let w be (-88)/231*(105/18)/(-5). Let j(y) be the first derivative of -2/27*y**3 + 6 + 2/9*y - 2/9*y**4 + w*y**2. Solve j(u) = 0 for u.
-1, -1/4, 1
Factor -10/9 + 8/9*p**2 - 16/3*p**3 + 28/9*p.
-2*(2*p - 1)**2*(6*p + 5)/9
Let y(w) = -2*w - 5. Let h be y(5). Let a = h - -17. Suppose 4*z**2 + z + a*z - z**2 = 0. What is z?
-1, 0
Factor -41 + 123 - l**2 - 42 - 69*l - 40.
-l*(l + 69)
Let g = -15221/45 - -1353/4. Let s(c) be the third derivative of 0*c**4 + g*c**5 - 3*c**2 + 0*c + 0*c**3 + 0. Find w such that s(w) = 0.
0
Let c be 547/8205*(-5)/(-3). What is m in 2/3*m + 5/9*m**2 - c*m**3 + 0 = 0?
-1, 0, 6
Determine x so that -30/7 + 12/7*x**3 + 99/7*x + 81/7*x**2 = 0.
-5, -2, 1/4
Let s(w) be the second derivative of -1/63*w**7 - 1/45*w**6 - 1/9*w**3 - 1/3*w**2 + 0 + 1/15*w**5 + 5*w + 1/9*w**4. Find t such that s(t) = 0.
-1, 1
Let r(g) be the second derivative of -g**6/18 - 11*g**5/12 - 5*g**4/2 - 3*g - 7. Factor r(k).
-5*k**2*(k + 2)*(k + 9)/3
Let b(y) be the first derivative of 2*y**5/55 - 17*y**4/22 + 28*y**3/11 - 160. Let b(h) = 0. What is h?
0, 3, 14
Let x(r) = -56*r**2 - 330*r + 101. Let f(w) = -63*w**2 - 330*w + 102. Let q(u) = 5*f(u) - 6*x(u). Factor q(p).
3*(p + 16)*(7*p - 2)
Let n(o) be the third derivative of -o**7/735 + o**6/84 - o**5/30 + o**4/28 + o**2 + 68*o. Factor n(d).
-2*d*(d - 3)*(d - 1)**2/7
Let 2/7*d**2 + 16928/7 + 368/7*d = 0. What is d?
-92
Let g(d) be the third derivative of -1/24*d**4 + 0*d - 21*d**2 + 0 + 1/180*d**5 + 0*d**3. Find c, given that g(c) = 0.
0, 3
Let i be 2/(1 + 26/(-24)). Let b be i/(-20)*(45/(-12))/(-3). Factor 0*l + 3/2 - b*l**2.
-3*(l - 1)*(l + 1)/2
Suppose -2*x - 42 = 4*v, -4*x = v - 0*x + 21. Let s = -2 - v. Factor -11*b**3 - 4 - s*b**3 - 40*b**2 + 0*b**3 - 26*b.
-2*(b + 1)**2*(9*b + 2)
Suppose -3*a + 0*i = -5*i - 27, -2 = -a + 4*i. Suppose 2*p = -2*p + f + 4, 3*p + a = 5*f. Factor -3/2 - 9/2*v**3 - 3/2*v + 15/2*v**p.
-3*(v - 1)**2*(3*v + 1)/2
Suppose 3*n - 2*n - 2 = 0. Factor 2*x**3 + 6*x**n + 3*x**3 + x**3 - 3*x**3.
3*x**2*(x + 2)
Let o(u) = u**4 + u**3 + u. Let l(g) = -3*g**4 - 13*g**3 - 5*g**2 + 17*g + 10. Let r(m) = l(m) - 2*o(m). Factor r(c).
-5*(c - 1)*(c + 1)**2*(c + 2)
Let t be 1*(-1 + 0) - -3. Let k = 52368 - 52368. What is s in k - 2/7*s**t + 2/7*s = 0?
0, 1
Find a such that -2/3 - 1875/2*a**2 + 50*a = 0.
2/75
Let j be 49/(-42) + 3 + -1. Let y = 677/6 - 667/6. Determine a, given that -5/6 - j*a**2 + y*a = 0.
1
Let l(r) be the first derivative of 2*r**5/35 - 3*r**4/14 + 4*r**3/21 - 67. Determine j, given that l(j) = 0.
0, 1, 2
Let v(m) be the third derivative of 1/420*m**6 + 0*m**5 + 0 - 2/21*m**3 - 1/28*m**4 - 26*m**2 + 0*m. Factor v(s).
2*(s - 2)*(s + 1)**2/7
Suppose -2*g + 17 = 4*u - 5*g, u - g - 4 = 0. Let z(s) be the first derivative of -1/7*s**2 - 1/21*s**3 - u + 3/7*s. Determine h so that z(h) = 0.
-3, 1
Suppose 0 = 3*b - 6 - 12. Solve 3*c**5 - 3*c - 5*c**3 - b*c**2 + 5*c**3 + 6*c**4 = 0.
-1, 0, 1
Let t(d) be the first derivative of -1/3*d**2 + 2/45*d**3 - 9 + 8/15*d. Factor t(l).
2*(l - 4)*(l - 1)/15
Let q = 15230 - 15228. Factor 9/7*f + 3/7*f**q + 0.
3*f*(f + 3)/7
Let w(g) be the first derivative of -g**6/2160 + g**5/180 - g**4/48 - 25*g**3/3 + 42. Let x(j) be the third derivative of w(j). Factor x(n).
-(n - 3)*(n - 1)/6
Let z = -5458/5 + 1092. Let k be (-2 - -3)*(-2)/(-5). Factor k*s**2 + 0 + z*s.
2*s*(s + 1)/5
Suppose 8 = 61*a - 57*a. Suppose -4*k**3 + 8*k - 11*k**2 + 3*k**a - 11*k - k = 0. What is k?
-1, 0
Let c(z) be the first derivative of -5 - 15/2*z**5 + 65/4*z**4 + 0*z - 125/36*z**6 - 86/9*z**3 + 2*z**2. Factor c(j).
-j*(j + 3)*(5*j - 2)**3/6
Let k be (-57)/18 - (-8)/48 - -3. Let 0 + k*i - 1/3*i**2 = 0. Calculate i.
0
Factor -39 + 129 - 46 - 3*p - 44 + 3*p**2.
3*p*(p - 1)
Let r = -3479/6 - -580. Let n(w) be the second derivative of 1/15*w**3 + w - r*w**4 + 0*w**2 + 0 + 3/25*w**6 + 3/50*w**5. Determine b so that n(b) = 0.
-1, 0, 1/3
Factor 8*t**2 + 21*t**3 - 4*t + 18*t**2 + 28*t + 8*t**2 + 20*t**2.
3*t*(t + 2)*(7*t + 4)
Let f(t) be the second derivative of 1/4*t**4 + 0 - 9*t + 1/4*t**3 + 0*t**2 + 3/40*t**5. Find m, given that f(m) = 0.
-1, 0
Let k(p) be the second derivative of -p**3 + 3/2*p**2 - 5*p + 3/10*p**5 + 0 + 0*p**4 - 1/10*p**6. Determine j so that k(j) = 0.
-1, 1
Let g(p) = p**3 - 12*p**2 + 6*p - 2. Let f(d) = d**2 + d - 1. Suppose -334*s - 1 = -335*s. Let k(o) = s*g(o) + 6*f(o). Factor k(w).
(w - 2)**3
Let z(l) be the second derivative of -l**2 + 40*l + 1/20*l**5 - 7/6*l**3 - 1/2*l**4 + 1/15*l**6 + 0. Factor z(m).
(m - 2)*(m + 1)**2*(2*m + 1)
Solve 5/4*u**4 - 5/4*u**2 - 5/4*u + 5/4*u**3 + 0 = 0 for u.
-1, 0, 1
Let b(i) = 686*i + 8235. Let c be b(-12). Suppose -10 + 5/2*u**5 + 25/2*u**2 - 25/2*u**c - 5/2*u**4 + 10*u = 0. Calculate u.
-2, -1, 1, 2
Let v = -92 + 94. Factor 5 - 41*m - m**v + 41*m - 1.
-(m - 2)*(m + 2)
Let i(z) be the first derivative of z**6/1800 - z**4/120 + 2*z**3 + 11. Let x(r) be the third derivative of i(r). Find u, given that x(u) = 0.
-1, 1
Let y be (30/9)/(4/12). Solve -28*a**2 - y*a**3 - 6*a**4 + 43*a**2 + a**4 = 0 for a.
-3, 0, 1
Let v(k) be the first derivative of -k**5/5 + k**4/4 + 4*k**3/3 - 2*k**2 - 146. Factor v(f).
-f*(f - 2)*(f - 1)*(f + 2)
Let o(c) be the second derivative of -1/25*c**6 + 0*c**2 + 0*c**4 + 0 + 3/100*c**5 - 6*c + 0*c**3 + 1/70*c**7. Determine k so that o(k) = 0.
0, 1
Let x(w) be the first derivative of -w**4/16 - 2*w**3/3 - 3*w**2/2 - 103. Factor x(b).
-b*(b + 2)*(b + 6)/4
Find d, given that 57/8*d + 7/2 + 1/8*d**3 + 15/4*d**2 = 0.
-28, -1
Let u(t) be the third derivative of t**5/12 + 5*t**4/12 + 194*t**2 + 2. Factor u(k).
5*k*(k + 2)
Let u(v) be the third derivative of v**5/120 + v**4/8 - 4*v**3/3 - 22*v**2. Factor u(w).
(w - 2)*(w + 8)/2
Let r(v) be the second derivative of -3*v**5/100 - 7*v**4/20 - 3*v**3/2 - 27*v**2/10 + 2*v - 114. What is d in r(d) = 0?
-3, -1
Let c = 3991/526295 + 2/9569. Let w(m) be the third derivative of 5*m**2 - 1/11*m**4 + 0*m + 0*m**3 - 16/165*m**5 + 0 + c*m**7 - 1/44*m**6. Factor w(z).
2*z*(z - 3)*(3*z + 2)**2/11
Find g such that 2/7*g**4 + 6/7*g**3 + 2/7*g**2 - 6/7*g - 4/7 = 0.
-2, -1, 1
Let f(k) be the first derivative of 1 + 1/2*k**3 + 12*k**2 + 96*k. Determine v, given that f(v) = 0.
-8
Let x(m) be the third derivative of m**6/270 + 19*m**5/270 - 5*m**4/54 - 172*m**2. Factor x(f).
2*f*(f + 10)*(2*f - 1)/9
Let l(w) = 3*w**3 - 11*w**2 + 8*w. Let s = -9 + 11. Let h(z) = -z**3 - 9*z**2 + 5*z**2 + 5*z**s. Let f(y) = h(y) - l(y). Factor f(k).
-4*k*(k - 2)*(k - 1)
Factor 40/3*i**2 + 0 - 4/3*i**3 - 100/3*i.
-4*i*(i - 5)**2/3
Let z(j) be the third derivative of j**5/270 + j**4/6 + 32*j**2. Factor z(w).
2*w*(w + 18)/9
Find s, given that 12*s**2 - 23 - 28*s**3 + 5 + 18 = 0.
0, 3/7
Let r(z) be the second derivative of 2*z**7/21 - 7*z**6/30 - 7*z**5/10 - z**4/4 + 13*z - 3. Suppose r(h) = 0. What is h?
-1, -1/4, 0, 3
Let f(w) = -26*w**2 + 668*w - 690. Let c(p) = 8*p**2 - 222*p + 229. Let z(t) = -16*c(t) - 5*f(t). Find x such that z(x) = 0.
-107, 1
Solve 27*f**4 + 780*f - 67 - 234*f**3 + 835 + 468*f + 219*f**2 = 0 for f.
-1, 16/3
Let l(r) be the third derivative of -r**5/25 + 11*r**4/30 - 4*r**3/5 + 46*r**2. Solve l(z) = 0.
2/3, 3
Let b(o) be the first derivative of 5*o**3 + 49*o**2/2 + 60*o - 9. Let n(z) = 5*z**2 + 16*z + 20. Let p(f) = 4*b(f) - 11*n(f). Determine l so that p(l) = 0.
-2
Suppose -2*l + 38 - 6 = 0. Suppose 3*b - 4*k = k - l, 2*b - 1 = k. Factor -8/9*g**2 + 2/9*g**5 + 0 + 10/9*g**4 - 16/9*g + 4/3*g**b.
2*g*(g - 1)*(g + 2)**3/9
Factor 0 + 15/2*i**2 - 1/2*i**3 + 0*i.
-i**2*(i - 15)/2
Factor -40*f**3 + 5*f**4 + 210*f + 2 - 1 + 1 - 2 + 5*f**2.
5*f*(f - 7)*(f - 3)*(f + 2)
Let k(p) = p + 