m - 1)*(4*m + 1)/2
Let o(b) be the third derivative of -b**6/120 - 7*b**5/20 + 15*b**4/8 - 23*b**3/6 + 11*b**2 - 26. Factor o(a).
-(a - 1)**2*(a + 23)
Let j(y) be the first derivative of 3*y**2 - 1/30*y**5 + 8 + 0*y**3 + 0*y - 1/4*y**4. Let g(h) be the second derivative of j(h). Factor g(p).
-2*p*(p + 3)
Let b(g) = -5*g**2 + 25. Let o = -22 - 3. Let k(j) = -j**2 + 4. Let m(u) = o*k(u) + 4*b(u). Factor m(r).
5*r**2
Let a = -202 - -162. Let s be ((-2)/a)/(6 - (-968)/(-165)). Factor 0 - 15/8*f**2 + s*f.
-3*f*(5*f - 1)/8
Let v be -1 + 4749*(-2)/(-4290). Let l = v - 2/143. Factor -l*j**2 + 2/15 + 2/5*j + 2/3*j**3.
2*(j - 1)**2*(5*j + 1)/15
Factor 2*h + 0 + 2/3*h**4 - 2*h**3 - 2/3*h**2.
2*h*(h - 3)*(h - 1)*(h + 1)/3
Let k(m) be the second derivative of m**5/60 + 5*m**4/12 + 19*m**3/9 + 4*m**2 - m - 66. Let k(h) = 0. What is h?
-12, -2, -1
Let x(l) be the first derivative of -4*l**3/21 + 10*l**2/7 - 16*l/7 + 172. Let x(w) = 0. What is w?
1, 4
Let h = 615 + -3068/5. Factor 9/5*i**2 + i**3 + 2/5 + h*i + 1/5*i**4.
(i + 1)**3*(i + 2)/5
Suppose -14/5*s + 9/5*s**4 + 13/5*s**3 + 1/5*s**5 - 9/5*s**2 + 0 = 0. Calculate s.
-7, -2, -1, 0, 1
Let k be (-7 - -12)*8/(-10). Let c be k/14 - (-69)/21. Factor c*h**2 - h**3 + 8 - 5*h + 2*h - 7.
-(h - 1)**3
Let z(k) be the second derivative of -3*k**6/40 - 3*k**5/8 + 23*k**4/48 - k**3/6 - 2*k + 47. Factor z(h).
-h*(h + 4)*(3*h - 1)**2/4
Let r(k) be the second derivative of 0*k**4 + 16*k + 0*k**2 + 0*k**3 + 1/180*k**5 + 0. Suppose r(s) = 0. Calculate s.
0
Let v(b) be the third derivative of -b**8/336 + b**7/210 + b**6/60 - b**5/30 - b**4/24 + b**3/6 - 91*b**2. Let v(l) = 0. Calculate l.
-1, 1
Solve -21*a**2 + 44996 + 2*a - 44996 = 0.
0, 2/21
Factor -90*f**3 - 720*f - 109*f**2 - 320 + 2*f**4 - 7*f**4 - 376*f**2.
-5*(f + 1)**2*(f + 8)**2
Find y such that 8/3 + 8/3*y - 2*y**2 - 8/3*y**3 - 2/3*y**4 = 0.
-2, -1, 1
Suppose 7 = 2*w + 3*j - 15, w = -3*j + 14. Factor 0*i**5 + 96*i**2 - 4*i**5 - w*i**4 - 36*i + 8*i**3 - 96*i**3 + 40*i**4.
-4*i*(i - 3)**2*(i - 1)**2
Let c be -6*1/(-10)*(-20239)/(-111). Let s = c - 109. Factor -s - 6/5*i**2 - 6/5*i - 2/5*i**3.
-2*(i + 1)**3/5
Let a(f) = -f + 1. Let w(h) = 4*h - 6. Let o(d) = -3*a(d) - w(d). Let p be o(-7). Find y such that -p + 10 - 2*y**4 + 2*y**2 = 0.
-1, 0, 1
Let b(d) be the second derivative of -d**9/13608 - d**8/2520 - d**7/1890 + 4*d**3/3 - 15*d. Let l(k) be the second derivative of b(k). Factor l(m).
-2*m**3*(m + 1)*(m + 2)/9
Let k(m) be the second derivative of -m**4/84 - 4*m**3/21 - m**2/2 - 888*m. Solve k(n) = 0.
-7, -1
Let z(y) be the first derivative of -2*y**5/5 - y**4 + 10*y**3/3 + 6*y**2 + 27. Factor z(r).
-2*r*(r - 2)*(r + 1)*(r + 3)
Let h(n) be the first derivative of n**6/21 + 8*n**5/35 - 3*n**4/7 - 8*n**3/21 + 5*n**2/7 + 126. Determine x so that h(x) = 0.
-5, -1, 0, 1
Suppose 9/4*j**4 + 41*j + 111/4*j**3 + 113/2*j**2 + 10 = 0. What is j?
-10, -1, -2/3
Let q(i) = i**2 + 3*i - 8. Let b be ((-133)/(-42) + 2/6)*6. Let f(h) = -3*h**2 - 10*h + 25. Let y(m) = b*q(m) + 6*f(m). Suppose y(o) = 0. What is o?
-3, 2
Let j(s) be the first derivative of -5*s**3/9 - 65*s**2 + 800*s/3 - 343. Suppose j(l) = 0. Calculate l.
-80, 2
Let m = 984 + -980. Let i(h) be the second derivative of -h**2 + 5/6*h**3 + 1/5*h**5 + 0 + 11*h + 11/12*h**m. Factor i(y).
(y + 1)*(y + 2)*(4*y - 1)
Let k(j) = 9*j**2 - 19*j + 10. Let b(w) = 35*w**2 - 75*w + 40. Suppose -2*l = 5*i + 18, -3*i + 8*l - 17 = 3*l. Let o(q) = i*b(q) + 15*k(q). Factor o(v).
-5*(v - 2)*(v - 1)
Find i, given that -3*i + 5/4*i**3 - 1 - 3/4*i**2 = 0.
-1, -2/5, 2
Factor -105*n**2 - 40*n**3 - 80*n**3 - 213*n + 121*n**3 - 107.
(n - 107)*(n + 1)**2
Let o(g) = 10*g**3 - g**2 + 2*g - 1. Let z be o(1). Factor z + 2*q**4 - 10 + 10*q - 6*q**2 - 6*q.
2*q*(q - 1)**2*(q + 2)
Find d such that -4/5*d**3 + 8/5*d**2 + 4*d - 24/5 = 0.
-2, 1, 3
Let p(h) be the first derivative of -h**4 + 0*h**2 + 27 + 0*h + 2/5*h**5 + 2/3*h**3. What is a in p(a) = 0?
0, 1
Let c be (-3 - (-14)/6) + (-21)/9. Let l(g) = -2*g**4 + 3*g**3 + 2*g**2 - 6*g. Let r(d) = -d**4 + 3*d**3 + d**2 - 5*d. Let k(j) = c*r(j) + 2*l(j). Factor k(q).
-q*(q - 1)*(q + 1)*(q + 3)
Let z be 11/3 + 1/3. Let h = -2 + z. Let -m - 16*m**2 - m + 20*m**2 - h*m**3 = 0. Calculate m.
0, 1
Let i = -394 - -396. Let g(k) be the second derivative of k**i + 4*k - 1/2*k**3 + 0 - 1/6*k**4. Determine s so that g(s) = 0.
-2, 1/2
Let s(f) = 29*f**2 + 19*f + 51. Let n(z) = 10*z**2 + 6*z + 18. Let o(i) = 17*n(i) - 6*s(i). Solve o(u) = 0 for u.
-3, 0
Let l(v) be the third derivative of -1/27*v**4 + 0*v + 1/270*v**6 - 1/90*v**5 + 4/27*v**3 + 1/945*v**7 - 11*v**2 + 0. Factor l(j).
2*(j - 1)**2*(j + 2)**2/9
Let g(y) be the second derivative of -3*y**7/28 - 7*y**6/10 - 13*y**5/10 - 11*y**4/12 - y**3/4 - 7*y - 5. Solve g(v) = 0.
-3, -1, -1/3, 0
Let q(p) be the second derivative of -p**5/10 - p**4/3 + 4*p**3/3 + 8*p**2 + 4*p - 8. Factor q(a).
-2*(a - 2)*(a + 2)**2
Let p(s) be the second derivative of -5*s**8/28 + 37*s**7/105 - 3*s**5/10 + s**4/6 - 4*s**2 - 8*s. Let d(c) be the first derivative of p(c). Solve d(w) = 0.
-1/2, 0, 1/3, 2/5, 1
Let s = -3/353 - -383/3530. Determine n, given that 1/5 - 4/5*n**2 - s*n - 1/2*n**3 = 0.
-1, 2/5
Let y(l) = -l - 3. Let v be y(-8). Factor -4 - 6 + 27*o - 42*o + v*o**3.
5*(o - 2)*(o + 1)**2
Let d(f) be the first derivative of -5*f**3/12 + 15*f**2/2 + 80*f - 533. Suppose d(t) = 0. What is t?
-4, 16
Let f(i) be the second derivative of i**8/1260 - i**7/315 + i**5/45 - i**4/18 + i**3/2 + 4*i. Let h(j) be the second derivative of f(j). Factor h(p).
4*(p - 1)**3*(p + 1)/3
Let b = -21 + 36. Suppose -8*z = -b*z. Let 0*i + 3/5*i**2 + 3/5*i**4 + z + 6/5*i**3 = 0. Calculate i.
-1, 0
Let x = -377/11 + 3437/99. Factor 4/9*i**3 + 2/9 - 2/9*i**5 - 2/9*i - x*i**2 + 2/9*i**4.
-2*(i - 1)**3*(i + 1)**2/9
Let z(t) be the first derivative of -t**5/60 + t**4/3 + 9*t**2 - 20. Let o(p) be the second derivative of z(p). Determine m so that o(m) = 0.
0, 8
Let p be (-6)/27 - 5864/(-1197) - 4. Let l = -2/19 + p. Factor l*t + 2/7*t**4 - 4/7*t**3 - 2/7 + 0*t**2.
2*(t - 1)**3*(t + 1)/7
Solve 6136/9*t**2 + 134/9*t**4 + 512/9*t - 8192/9 - 2432/9*t**3 - 2/9*t**5 = 0.
-1, 2, 32
Let r(j) be the second derivative of j**7/168 - j**6/40 - j**5/16 + j**4/16 + j**3/6 + 12*j. Factor r(o).
o*(o - 4)*(o - 1)*(o + 1)**2/4
Let o(s) = -4*s**2 - 9*s + 1. Let a be o(-1). Let c(w) be the third derivative of 1/480*w**a + w**2 + 0*w**3 + 0 + 0*w**4 + 0*w + 0*w**5. Factor c(h).
h**3/4
Let i = 18 + -2. What is c in 4*c - 16*c**3 - 14*c**2 - 16*c**2 + 2*c**2 - i*c = 0?
-1, -3/4, 0
Let j = 5 + -16. Let v(p) = p + 19. Let a be v(j). Factor -10*f - 6 - a*f**2 + 7*f**3 - 9*f**3 + 2.
-2*(f + 1)**2*(f + 2)
Let w be (-66)/627 + (-2986)/(-570) - 5. Factor w*h**4 + 26/15*h**2 - 4/5*h**3 + 8/15 - 8/5*h.
2*(h - 2)**2*(h - 1)**2/15
Let x = -28 - -33. Find r such that -571*r**3 - 234*r**2 + 18*r + 114*r - 66*r**4 + 9*r**x - 24 + 754*r**3 = 0.
1/3, 1, 2
Let k(z) be the third derivative of 0*z + 11/60*z**5 + 0 + 1/40*z**6 + 1/4*z**4 - 1/336*z**8 - 29*z**2 + 0*z**3 - 1/70*z**7. Factor k(c).
-c*(c - 2)*(c + 1)**2*(c + 3)
Let o be 3 - (5 - 3)/(4/(-6)). Let u(w) be the first derivative of 0*w**2 + 0*w**3 + 0*w - 1/10*w**4 - 3 + 4/25*w**5 - 1/15*w**o. Factor u(d).
-2*d**3*(d - 1)**2/5
Let 3*i**2 + 0*i**2 + i**2 + 0*i**2 - 12*i = 0. Calculate i.
0, 3
Let b(a) = -31*a - 120. Let i be b(-6). Let y = i - 66. Factor -2/9*w**2 + 0 + y*w.
-2*w**2/9
Let d(u) be the first derivative of -1/6*u**3 + 1/10*u**5 + 1 + 1/8*u**4 + 0*u - 1/4*u**2. Solve d(c) = 0 for c.
-1, 0, 1
Suppose 5*v = -4*i + 43, 2*i - 26 = v + v. Suppose -12*p**3 - 3 - i*p - 4 - 1 + 16*p**3 = 0. Calculate p.
-1, 2
Let v(p) be the third derivative of p**6/90 - p**5/15 - 4*p**4/3 + 160*p**3/9 - p**2 + 4*p. Factor v(o).
4*(o - 4)**2*(o + 5)/3
Let h(o) be the first derivative of -5*o**3/6 - 15*o**2/2 + 40*o - 131. Factor h(p).
-5*(p - 2)*(p + 8)/2
Suppose 60*b - 62*b - 25 = -5*d, -20 = -4*d + 5*b. Let f(o) be the second derivative of 0 + 1/48*o**4 + 9/8*o**2 + 1/4*o**3 - d*o. Let f(v) = 0. Calculate v.
-3
Let t be ((-4 - 36/45) + 6)*5/3. Determine f, given that 2*f**t + 4/5*f + 3/5*f**3 - 8/5 = 0.
-2, 2/3
Let s(k) be the first derivative of k**6/12 - 7*k**5/10 + 15*k**4/8 - 13*k**3/6 + k**2 - 206. Fact