d**6/15 + d**4/3 + d**3/3 + 8*d - 17. Let h(c) be the first derivative of k(c). Factor h(f).
-2*f*(f - 1)*(f + 1)**3
Factor -20/7*h**2 - 4/7*h**3 - 12/7 - 4*h.
-4*(h + 1)**2*(h + 3)/7
Let w(r) be the third derivative of -r**6/660 + r**5/330 + 17*r**4/132 + 5*r**3/11 - 240*r**2 - 2. Suppose w(b) = 0. What is b?
-3, -1, 5
Let d(f) be the first derivative of -31 - 1/3*f**2 - 10/9*f**3 + 1/6*f**4 + 10/3*f. Let d(q) = 0. What is q?
-1, 1, 5
Let -2*n**3 - 237*n - 16 - 70*n**2 + 76*n**2 + 249*n = 0. What is n?
-2, 1, 4
Let t(v) be the second derivative of -4/21*v**3 - 25*v + 0 - 8/7*v**2 - 3/70*v**5 + 5/21*v**4. Factor t(s).
-2*(s - 2)**2*(3*s + 2)/7
Let q(r) = -8*r**3 - 12*r**2 + 12*r - 3. Suppose 4*a - 4 = 16. Let d(m) = m**3 + m - 1. Let i(b) = a*q(b) - 5*d(b). Factor i(x).
-5*(x + 2)*(3*x - 1)**2
Let l(t) be the first derivative of t**5/20 + 11*t**4/16 + 2*t**3 + 196. Find b, given that l(b) = 0.
-8, -3, 0
Let g = -111 - -137. Solve 31*r**3 + 80*r**2 + g*r**3 - 320*r - 62*r**3 = 0 for r.
0, 8
Let k(t) be the third derivative of 13*t**8/40320 + t**7/672 + t**6/720 + t**5/5 + 12*t**2. Let q(v) be the third derivative of k(v). Factor q(m).
(m + 1)*(13*m + 2)/2
Factor -46/11*i**2 - 240/11*i + 288/11 - 2/11*i**3.
-2*(i - 1)*(i + 12)**2/11
Let v = -20 - -23. Let s be (-40)/(-6)*v/4. Factor s*n**3 - 16*n**2 - 4*n - n**5 + 2*n**4 + 6*n**5 - 20*n**3.
n*(n - 2)*(n + 1)**2*(5*n + 2)
Let j(v) be the second derivative of -v**4/3 - 100*v**3 - 11250*v**2 - 182*v. Factor j(p).
-4*(p + 75)**2
Let g(m) = -m**2 + 5*m. Let j be 3/(-6)*-2 - -4. Let a be g(j). Find l such that a*l - l**3 - 1/3*l**5 - 1/3*l**2 + 0 - l**4 = 0.
-1, 0
Let u(i) be the first derivative of -1443*i**4/20 + 964*i**3/5 - 291*i**2/2 + 6*i/5 - 767. Factor u(l).
-3*(l - 1)**2*(481*l - 2)/5
Suppose -328/5*v + 0 + 4/5*v**2 = 0. Calculate v.
0, 82
Suppose 0 = -u - 3*t - 4, -5*t = 4*u + 9 - 7. Determine h so that -6/7*h + 0*h**u + 4/7 + 2/7*h**3 = 0.
-2, 1
Let k(q) = -q**2 + 9*q - 18. Let t be k(4). Factor 8*o**4 - 2*o**4 + 2*o - 7*o**t + o**5 + 9*o**3 - 12*o**4 + o**4.
o*(o - 2)*(o - 1)**3
Let u be 10/35 + (-135)/56 + 56/8. Solve 105/8*t + 147/8 - u*t**2 + 3/8*t**3 = 0 for t.
-1, 7
Let y = 4/1965 + 1306/1965. Factor -5/3*w**3 - y*w**4 - 2/3*w**2 + 0 + 0*w.
-w**2*(w + 2)*(2*w + 1)/3
Let h(z) be the third derivative of -z**7/42 - 7*z**6/12 - 49*z**5/12 + 117*z**2 + 2. Factor h(m).
-5*m**2*(m + 7)**2
Let u(y) = -y**3 - 4*y**2 + 19*y + 45. Let b be u(-6). What is x in 3/2*x**b - 3/2*x + 1/2*x**4 - 1 + 1/2*x**2 = 0?
-2, -1, 1
Suppose 4*c + q - 16 = 0, 2*c = 4*q - 6*q + 2. Suppose -2*j - j + c*n = -16, -2*j + 4*n + 12 = 0. Factor 3/2*v**4 + 0 + 0*v - 5/4*v**3 + 1/4*v**j.
v**2*(2*v - 1)*(3*v - 1)/4
Let z(r) be the first derivative of -4*r**3 - 9/5*r**5 + 0*r**2 - 10 + 6*r**4 + 0*r. Factor z(y).
-3*y**2*(y - 2)*(3*y - 2)
Let r(d) be the second derivative of 1/6*d**4 + 0 - 11*d - d**2 + 0*d**3. Suppose r(k) = 0. Calculate k.
-1, 1
Factor -45/7*k**5 + 0*k**2 + 0*k + 0 + 0*k**3 - 6/7*k**4.
-3*k**4*(15*k + 2)/7
Suppose 5*f = 3*o + 10, 0 = -132*f + 137*f - 25. Let 4 - 34*r**3 - 9/4*r**o + 57/4*r**4 + 38*r**2 - 20*r = 0. Calculate r.
2/3, 1, 2
Let l(n) be the second derivative of -3*n**5/5 + 89*n**4/4 - 253*n**3 + 363*n**2/2 + 2*n + 7. Factor l(s).
-3*(s - 11)**2*(4*s - 1)
Suppose 10004*f**3 + 6*f**4 - 3*f**4 - 9989*f**3 - 18*f**2 = 0. Calculate f.
-6, 0, 1
Suppose 37*b + 3*m = 32*b - 18, -2*m - 12 = -17*b. Let 2*z + b - 20/9*z**2 + 2/9*z**3 = 0. What is z?
0, 1, 9
Let f be 9/(40 + 5) + 1/(-5). Let l = -47/28 - -24/7. Determine r so that -1/2*r**2 + f*r + 0 - l*r**4 - 9/4*r**3 = 0.
-1, -2/7, 0
Let j = 5159/18 - 2557/9. Suppose -j*q + 5/4*q**2 + 5/4 = 0. What is q?
1
Let l(o) = 4*o**2 + 11*o - 12. Let v(q) = 9*q**2 + 23*q - 25. Let j(a) = 7*l(a) - 3*v(a). Factor j(b).
(b - 1)*(b + 9)
Suppose -261*c = -250*c - 22. Let x(q) be the second derivative of -1/2*q**4 + 1/15*q**6 + 3*q + 1/10*q**5 + 0 - 1/3*q**3 + c*q**2. Factor x(g).
2*(g - 1)**2*(g + 1)*(g + 2)
Let g = 149 + -224. Let v be (-130)/g - 4/3. Factor -v - 6/5*a**2 - 6/5*a - 2/5*a**3.
-2*(a + 1)**3/5
Suppose 5*s - 37 = -4*c, 3*c - 69*s + 74*s - 34 = 0. Solve 2/3 - 2/3*i**2 - 2*i**c + 2*i = 0 for i.
-1, -1/3, 1
Let o = 113 + -117. Let z be (19/5 + o)/(-1). Factor -2/5 + 1/5*q**3 + 2/5*q**2 - z*q.
(q - 1)*(q + 1)*(q + 2)/5
Let q(v) be the third derivative of -v**6/240 - v**5/4 - 29*v**4/48 + 320*v**2. Factor q(x).
-x*(x + 1)*(x + 29)/2
Let c(w) be the second derivative of w**7/21 - 4*w**6/15 + w**5/10 + 7*w**4/3 - 20*w**3/3 + 8*w**2 + 387*w. Suppose c(t) = 0. What is t?
-2, 1, 2
Let n(x) be the first derivative of 21 - 24*x**3 - 2/5*x**5 + 16*x**2 + 128*x + 11/2*x**4. Suppose n(v) = 0. What is v?
-1, 4
Let b(d) be the first derivative of -d**7/168 + d**5/24 + 8*d**3 + 22. Let o(y) be the third derivative of b(y). Factor o(s).
-5*s*(s - 1)*(s + 1)
Let x(y) be the first derivative of -2/15*y**5 + 0*y + 0*y**3 - 3 - 1/3*y**6 + 0*y**4 + 0*y**2. Factor x(i).
-2*i**4*(3*i + 1)/3
Let s = -49 - -52. Suppose -17 - 3*r**3 + 12*r**2 + 1 + 7*r**s + 0 = 0. What is r?
-2, 1
Let s(y) be the first derivative of 5/9*y**3 - 16 + 0*y - 1/15*y**5 + 1/2*y**2 + 1/12*y**4. Factor s(m).
-m*(m - 3)*(m + 1)**2/3
Let d(i) = -2*i**3 - i**2 - i + 1. Let p(q) = -7*q**3 + 15*q**2 - 54*q - 67. Let g(x) = 12*d(x) - 4*p(x). Factor g(z).
4*(z - 14)*(z - 5)*(z + 1)
Let m = 4 - 1. Let u(i) be the first derivative of 6*i + 4*i**m + 2 - 5 + 0*i + i**4 + 6*i**2 - 2*i. Factor u(k).
4*(k + 1)**3
Let z(y) be the second derivative of -y**5/100 - 2*y**4/15 - y**3/6 - 21*y**2/2 + 24*y. Let x(h) be the first derivative of z(h). Factor x(t).
-(t + 5)*(3*t + 1)/5
Let s be 2/(-3)*(-810)/12. Let n(c) = 5*c**3 + 4*c**2 - 11*c - 14. Let q(t) = -55*t**3 - 45*t**2 + 120*t + 155. Let d(h) = s*n(h) + 4*q(h). Factor d(f).
5*(f - 2)*(f + 1)**2
Let k = -1233 - -1238. Factor -4/7*j - 8/7 - 4/7*j**4 + 1/7*j**k + 10/7*j**2 + 1/7*j**3.
(j - 2)**3*(j + 1)**2/7
Let q(v) be the first derivative of -18/5*v - 6/5*v**2 - 2 + 16/15*v**3 + 3/5*v**4 + 2/25*v**5. Suppose q(u) = 0. Calculate u.
-3, -1, 1
Let a be 2278/6426 + 10/135. Factor 36/7*y**2 + 0 - 18/7*y**3 + a*y**4 - 24/7*y.
3*y*(y - 2)**3/7
Let s(m) be the third derivative of -m**6/60 - 7*m**5/6 - 24*m**4 + 108*m**3 - 50*m**2. Find j such that s(j) = 0.
-18, 1
Suppose 2*r**3 - 20 + 38*r - 12 - 22*r - 12*r**5 + 72*r**2 - 6*r**3 - 40*r**4 = 0. Calculate r.
-2, -1, 2/3, 1
Suppose -127*k + 126*k - 1 = 0. Let g(l) = -l**4 + 2*l**3 + 8*l**2 + 2*l - 7. Let i(a) = -a**3 - a**2 + 1. Let d(w) = k*g(w) - 4*i(w). Factor d(p).
(p - 1)**2*(p + 1)*(p + 3)
Factor 1/8*i**5 + 1/4*i**4 + 0*i**2 + 0 + 1/8*i**3 + 0*i.
i**3*(i + 1)**2/8
Let o be 830*(0 + -4)/(-36). Let h = -92 + o. Let -2/9 - 2/3*q**2 + 2/3*q + h*q**3 = 0. What is q?
1
Let m(u) = -12 - 8 + 28 - 21*u**2 - 11 - 21*u - 12*u**3. Let c(v) = v**3 - v**2 - 1. Let y(j) = -3*c(j) - m(j). Determine i so that y(i) = 0.
-1, -2/3
Let v(r) be the first derivative of 32/27*r**3 + 2/45*r**5 + 0*r**2 + 34 + 0*r + 4/9*r**4. Factor v(i).
2*i**2*(i + 4)**2/9
Let i(z) = z**3 + 5*z**2 - 12*z - 21. Let w be i(-6). Factor -195 + 174 - 51*a - w*a**2 + 3*a**3 + 12*a.
3*(a - 7)*(a + 1)**2
Let o = -6 - -6. Suppose 0 = c - o*c - 4. Factor b**3 + 3*b**4 + 0*b**4 - c*b**3.
3*b**3*(b - 1)
Let a(w) be the third derivative of -1/8*w**4 + 0*w - 11*w**2 - 1/80*w**5 + 0 - 3/8*w**3. Solve a(s) = 0.
-3, -1
Let z be (-1)/21*-2 + (-2576)/(-735). What is x in z*x**5 + 114/5*x**2 + 134/5*x**3 + 48/5*x + 8/5 + 78/5*x**4 = 0?
-1, -2/3
Let y(x) be the first derivative of 2*x**3/3 + x**2 - 2*x - 4. Let h be y(1). What is i in 16*i + 3 + h*i + 12*i**3 + 15*i**2 + 12*i**2 = 0?
-1, -1/4
Let l(z) be the third derivative of -z**6/30 + 7*z**5/5 - 12*z**4 - 288*z**3 - 70*z**2. Find o, given that l(o) = 0.
-3, 12
Let b = 333 - 331. Let j(w) be the first derivative of 1/9*w**3 - b + 1/3*w - 1/3*w**2. Suppose j(h) = 0. Calculate h.
1
Let a be (-2)/4 - 27/(-2). Let x = a + -11. What is j in -7*j**2 + 3*j**2 + 2*j**3 + 2*j**4 + 2 - 2*j - x*j**5 - 2*j**3 + 4*j**3 = 0?
-1, 1
Let j = -12 - -15. Let o be (-4)/(-2) - (0 + -1). Factor -6*g**5 + 5*g**5 - 3*g**4 - 5*g**3 + 0*g**5 + j*g**o.
-g**3*(g + 1)*(g + 2)
Suppose -3*t - 7*a + 28 = -3*a, 14 = -3*t + 2*a. Let 5/3*k - 5/3*k**4 - 5/3*k**3 +