1, 1
Let u(x) be the second derivative of 7*x**5/20 + x**4/3 - 3*x**2/2 - 20*x. Let m(h) = -20*h**3 - 12*h**2 + 8. Let i(t) = 3*m(t) + 8*u(t). Factor i(l).
-4*l**2*(l + 1)
Let a(c) = -16*c**2 - 9*c**2 + 11*c - 3*c. Let v(x) be the first derivative of -x**3 + x**2/2 - 9. Let j(d) = 6*a(d) - 51*v(d). What is q in j(q) = 0?
0, 1
Let w be (-9)/(11 - (20 - 6)). Determine q, given that 3/5*q - 3/5*q**3 + 0 - 3*q**2 + w*q**4 = 0.
-1, 0, 1/5, 1
Let q(r) be the first derivative of -2*r**3/21 - 16*r**2/7 - 30*r/7 - 298. Factor q(m).
-2*(m + 1)*(m + 15)/7
Let x(v) be the third derivative of 0*v - 11/12*v**5 - 12*v**2 + 0*v**3 - 2/3*v**6 - 1/6*v**7 + 0 - 5/12*v**4. Find a such that x(a) = 0.
-1, -2/7, 0
Suppose 4*b = -4*h, 10 = 4*b - h + 3*h. Factor -b*z - 2*z**2 + 3*z + 3*z - 5*z.
-2*z*(z + 2)
Let w(s) be the first derivative of s**5/2 + 15*s**4/8 - 15*s**3/2 - 135*s**2/4 - 433. Factor w(f).
5*f*(f - 3)*(f + 3)**2/2
Let o(m) be the first derivative of 2*m**5/55 + 3*m**4/22 - 2*m**3/33 - 3*m**2/11 - 176. Factor o(h).
2*h*(h - 1)*(h + 1)*(h + 3)/11
Let n be 24/15 - (160/(-25) - -6). Let r(t) be the first derivative of -1/33*t**6 + 1/22*t**4 + 0*t + 1 - 2/55*t**5 + 0*t**n + 2/33*t**3. Factor r(p).
-2*p**2*(p - 1)*(p + 1)**2/11
Suppose 2*c - s = 704, -5*c - 468 = 2*s - 2228. Let v = -703/2 + c. Factor -n + v*n**2 + 1/2.
(n - 1)**2/2
Let w(d) = 4*d**4 + 6*d**3 + 6*d**2 + 10*d + 6. Let s(v) = 9*v**4 + 13*v**3 + 12*v**2 + 21*v + 13. Let r(m) = -6*s(m) + 13*w(m). Factor r(b).
-2*b*(b - 2)*(b + 1)**2
Let n = 52 + -49. Let o(x) = -3*x**3 + 24*x**2 - 39*x + 21. Let r(s) = -1. Let l(c) = n*r(c) + o(c). Factor l(f).
-3*(f - 6)*(f - 1)**2
Suppose g - 2*u = -10, -3*u = -4*g - 4*u + 14. Let -40/19 + 32/19*j - 2/19*j**g - 2/19*j**3 = 0. What is j?
-5, 2
Let h(v) = -v**4 + 3*v**3 - 6*v**2 + 6*v - 6. Let y(d) = -d**4 + 4*d**3 - 7*d**2 + 7*d - 7. Let j(i) = 7*h(i) - 6*y(i). Let j(t) = 0. What is t?
-3, 0
Let v(z) be the second derivative of -z**8/616 - z**7/385 - 9*z**2 - 28*z. Let p(n) be the first derivative of v(n). Factor p(r).
-6*r**4*(r + 1)/11
Let c(x) be the first derivative of 3 - x**4 - 3 + 1. Factor c(q).
-4*q**3
Let f(m) be the first derivative of 0*m**5 + 0*m**3 + 3/8*m**2 - 9 + 0*m - 3/8*m**4 + 1/8*m**6. Factor f(o).
3*o*(o - 1)**2*(o + 1)**2/4
Let a = -13529/175 + 1992/25. Let o = -9/5 + a. Let -o*x + 4/7 + 4/7*x**3 - 4/7*x**2 = 0. Calculate x.
-1, 1
Find f such that 13/7 - 25/7*f + 1/7*f**3 + 11/7*f**2 = 0.
-13, 1
Let w(d) be the third derivative of -d**6/480 - 11*d**5/240 + d**4/8 + 6*d**2 - 1. Factor w(c).
-c*(c - 1)*(c + 12)/4
Let f(n) be the third derivative of n**7/126 + 5*n**6/36 + 11*n**5/12 + 25*n**4/9 + 40*n**3/9 - 76*n**2. Let f(j) = 0. Calculate j.
-4, -1
Let w(q) be the first derivative of -q**3 - 15*q**2/2 + 7*q - 4. Let t(s) = s**2 + 7*s - 3. Let y(v) = 7*t(v) + 3*w(v). Find f, given that y(f) = 0.
0, 2
Let b(u) be the third derivative of 0 - 1/15*u**5 + 5/6*u**4 + 0*u - 8/3*u**3 + 24*u**2. Factor b(k).
-4*(k - 4)*(k - 1)
Let m be (-9)/15*(-5 + 0). Suppose -4*l = -m*h - 13, 6*h = 5*l + 2*h - 16. Factor -15*z**3 - z - 2 + 27*z**2 - 20*z + 3*z**l + 8.
3*(z - 2)*(z - 1)**3
Let i(l) be the first derivative of -l**8/4200 - l**7/525 - l**6/150 - l**5/75 - l**4/60 - 13*l**3/3 - 3. Let p(z) be the third derivative of i(z). Factor p(f).
-2*(f + 1)**4/5
Let c(v) be the second derivative of 19*v**6/4 + 233*v**5/20 + 73*v**4/24 - 28*v**3/3 - v**2 - 31*v + 8. Solve c(m) = 0 for m.
-1, -2/57, 2/5
Suppose s + 3*u = 5, 2*s - 8 - 2 = -2*u. Factor 9*h**2 + 7*h**3 - 15*h**4 - 10*h**2 - 10*h**s + 19*h**5.
h**2*(h - 1)*(3*h - 1)**2
Let q be 4 + 21 + (-6734)/296. Determine j so that -3/8*j**2 - q - 15/8*j = 0.
-3, -2
Let m(r) = -r**3 - r**2 + r + 3. Let a be m(0). Factor 5*c**a + 7*c**2 - 6*c - 2*c**2 - 4*c.
5*c*(c - 1)*(c + 2)
Let c(r) be the first derivative of r**7/2940 + r**6/1260 - r**5/420 - r**4/84 - 16*r**3/3 - 11. Let s(v) be the third derivative of c(v). Factor s(o).
2*(o - 1)*(o + 1)**2/7
Let y(z) be the third derivative of 3*z**8/448 - z**7/72 - z**6/72 + 5*z**4/6 + 8*z**2. Let v(b) be the second derivative of y(b). Let v(a) = 0. What is a?
-2/9, 0, 1
Let m(x) = x**5 - x**4 + x**3 + 3*x**2 - x. Let p(n) = -n**4 - n**3 - n**2. Let v(y) = 2*m(y) + 2*p(y). Factor v(l).
2*l*(l - 1)**3*(l + 1)
Let c(u) = 19*u**3 + u**2 + 2*u + 14. Let m(j) = 22*j**3 + 2*j**2 + 2*j + 15. Let g(k) = 7*c(k) - 6*m(k). Factor g(q).
(q - 4)*(q - 2)*(q + 1)
Let q(j) be the first derivative of -10*j - 5/3*j**3 + 16 + 15/2*j**2. Solve q(m) = 0.
1, 2
Let 3*d**3 - 18*d**5 + 2/3 + 27*d**4 + 5/3*d - 43/3*d**2 = 0. What is d?
-2/3, -1/6, 1/3, 1
Let -200/3*t**2 + 5*t**3 - 50 - 365/3*t = 0. What is t?
-1, -2/3, 15
Let f be 10 - 17/(884/507). Suppose -f*y + 1/4 + 1/4*y**3 - 1/4*y**2 = 0. What is y?
-1, 1
Let w be 14 + 99/(-16 - -7). Suppose -4*l**w + 8/9 - 2*l**4 - 10/9*l**2 + 16/9*l = 0. What is l?
-1, -2/3, 2/3
Let a = -1106/165 - -106/15. Factor 2/11*n**3 - a*n**4 + 0*n + 2/11*n**2 + 0.
-2*n**2*(n - 1)*(2*n + 1)/11
Suppose -39*s + 44*s = 290. Let o be 5 + -4 - (-2)/36*s. What is v in 16/9 + 14/9*v**4 - 4/3*v**2 + 56/9*v - o*v**3 = 0?
-1, -2/7, 2
Suppose 4*x - 189 - 255 = 0. Suppose -x*p + 21 = -104*p. Determine z, given that -60/7*z + 36/7 + 4*z**2 - 4/7*z**p = 0.
1, 3
Let s(x) be the second derivative of 1/20*x**5 + 0*x**3 + 0*x**2 + 3*x + 1/12*x**4 + 0. Factor s(p).
p**2*(p + 1)
Let i(u) be the first derivative of 1029/5*u - 7 + 441/10*u**2 + 21/5*u**3 + 3/20*u**4. Factor i(s).
3*(s + 7)**3/5
Suppose -p = -4*p - 3*u + 12, -4*u = 8. Suppose 4*y - p = 2*y. Solve -2 - w**4 + 8*w - 2*w - 5*w + 3*w**2 - w**y = 0.
-2, -1, 1
Let w(b) be the third derivative of -b**6/150 + 4*b**5/25 - 3*b**4/10 - 44*b**3/15 - 111*b**2 + 3*b. Factor w(a).
-4*(a - 11)*(a - 2)*(a + 1)/5
Let b(i) = -14*i**3 + 34*i**2 - 38*i + 12. Let n(z) = -27*z**3 + 69*z**2 - 78*z + 24. Let d(j) = 9*b(j) - 5*n(j). Solve d(x) = 0.
1/3, 2
Let -38/3*z**3 - 2/3*z**4 - 22*z**2 + 38/3*z + 68/3 = 0. Calculate z.
-17, -2, -1, 1
Suppose 0 = 20*u - 16*u + 8. Let p be -14*(-6)/33 + u. Find j, given that 4/11*j - 2/11*j**4 - 2/11*j**5 + 10/11*j**2 + p*j**3 + 0 = 0.
-1, 0, 2
Let c(w) = 4*w**2 - 8*w + 3. Let k(u) = -11*u**2 + 23*u - 9. Let a(m) = 8*c(m) + 3*k(m). Let d(z) = -z + 1. Let q(r) = -a(r) - 3*d(r). Factor q(i).
i*(i - 2)
Let n be -2*1/(-70) - (46/(-7) - -6). Factor 0*v + n*v**2 - 3/5.
3*(v - 1)*(v + 1)/5
Let t(r) be the first derivative of -r**5/40 + 17*r**4/24 - 20*r**3/3 + 16*r**2 - 2*r + 7. Let y(z) be the first derivative of t(z). Factor y(h).
-(h - 8)**2*(h - 1)/2
Suppose -45*k + 39 = 39. Factor 21/2*o**2 + k + 9/2*o.
3*o*(7*o + 3)/2
Find x such that -2 - 19*x + 267*x + 3*x**2 + 76*x + 2 = 0.
-108, 0
Let y = -966 - -968. Factor 4*n**3 + 0 - 8/5*n**4 - 17/10*n**y + 1/5*n.
-n*(n - 2)*(4*n - 1)**2/10
Let k(o) be the third derivative of o**5/180 + 43*o**4/36 + 1849*o**3/18 - 131*o**2. Factor k(z).
(z + 43)**2/3
Let p(q) = -3*q**3 - 2. Let z(s) = -4*s**4 + 36*s**3 + 240*s**2 + 544*s + 392. Let h(n) = -4*p(n) - z(n). Determine w so that h(w) = 0.
-2, 12
Suppose a + 2 = -2*q - a, 2*a - 3 = 3*q. Let n be 111/12 - 6 - (q + 4). Factor -1/4*y + 3/4*y**2 + n*y**3 + 0 - 3/4*y**4.
-y*(y - 1)*(y + 1)*(3*y - 1)/4
Let w(o) = 15*o**3 + 19*o**2 + 19*o + 15. Let k(x) = -7*x**3 - 9*x**2 - 9*x - 7. Let i(p) = -p - 2. Let d be i(11). Let r(n) = d*k(n) - 6*w(n). Factor r(y).
(y + 1)**3
Suppose -2/5*b - 2/5*b**4 - 4/5 + 6/5*b**2 + 2/5*b**3 = 0. What is b?
-1, 1, 2
Let x(a) be the second derivative of -11/20*a**4 + 12/5*a**3 + 3/100*a**5 + 0 + 54/5*a**2 - 21*a. Find m such that x(m) = 0.
-1, 6
Let r(t) = -8*t**4 + 33*t**3 - 48*t**2. Let x(z) = 55*z**4 - 230*z**3 + 335*z**2. Let a(f) = -20*r(f) - 3*x(f). Factor a(m).
-5*m**2*(m - 3)**2
Suppose 3 = 44*v - 55*v + 25. Let a be -2 + ((-16)/(-7))/1. Suppose 2/7*l**3 + 0 + 0*l - a*l**v = 0. What is l?
0, 1
Let s(n) = -7*n**3 - 11*n**2 - 9*n + 25. Let f(z) = 6*z**3 + 11*z**2 + 7*z - 26. Let a(p) = -5*f(p) - 4*s(p). Factor a(w).
-(w + 2)*(w + 5)*(2*w - 3)
Let 2*l**4 - 388*l**3 - 1224*l + 648 + 222*l**2 + 456*l**3 + 284*l**2 = 0. What is l?
-18, 1
Let y(h) = -3*h**3 + 7*h**2 + 4*h. Let r be -3 + 2 - -7*1. Let i = r + -2. Let u(t) = -15*t**3 + 36*t**2 + 21*t. Let s(x) = i*u(x) - 21*y(x). Factor s(p).
3*p**2*(p 