(c + 1)/4
Let h(s) be the third derivative of -1/32*s**4 + 0*s - 1/840*s**7 - 8*s**2 + 0 + 0*s**3 + 1/48*s**5 - 1/480*s**6. Factor h(t).
-t*(t - 1)**2*(t + 3)/4
Find h, given that 1/3*h**3 + 3*h**2 + 2/3 - 3*h - h**4 = 0.
-2, 1/3, 1
Let m(h) = -h**3 - 4*h**2 + 5*h + 4. Let a be m(-5). Factor 0*u**2 + 5*u**a + 7*u**4 - 11*u**4 - u**2.
u**2*(u - 1)*(u + 1)
Let f(g) be the second derivative of g**7/2520 + g**6/120 + 3*g**5/40 + 5*g**4/12 + 3*g. Let h(b) be the third derivative of f(b). Factor h(c).
(c + 3)**2
Let o(w) = 5*w**2 + 17*w + 23. Let l(f) = -10*f**2 - 35*f - 45. Let m(y) = -3*l(y) - 5*o(y). Factor m(q).
5*(q + 2)**2
Let t(j) = -j**2 + j + 11. Let d be t(0). Suppose -d*h = -8*h - 9. Factor 1/2*r**4 - 2*r + 1/2 + 3*r**2 - 2*r**h.
(r - 1)**4/2
Let g(o) be the first derivative of 8/5*o - 2 + 2/15*o**3 - 4/5*o**2. Find m, given that g(m) = 0.
2
Let b be ((-8)/(-100))/(126/15). Let h(z) be the second derivative of 0*z**3 + 1/35*z**5 - 1/42*z**4 + z - b*z**6 + 0 + 0*z**2. What is u in h(u) = 0?
0, 1
Let u(l) = 49*l**5 + 30*l**4 - 19*l**3 - 7*l**2 - 7*l - 7. Let f(w) = -16*w**5 - 10*w**4 + 6*w**3 + 2*w**2 + 2*w + 2. Let z(v) = 7*f(v) + 2*u(v). Factor z(y).
-2*y**3*(y + 1)*(7*y - 2)
Solve 20*c**3 + 6*c**3 + 2*c**3 - 8*c**2 - 20*c**4 = 0 for c.
0, 2/5, 1
Let b(i) = i**4 + i**3 - i**2 - 1. Let t(y) = 2*y**4 + y**3 - 4*y**2 - 3. Let x(p) = -3*b(p) + t(p). Factor x(n).
-n**2*(n + 1)**2
Let i(l) be the second derivative of -l**6/195 + l**4/78 + 11*l. Factor i(h).
-2*h**2*(h - 1)*(h + 1)/13
Let l = -6 - -9. Let c be 14/(-8) - (1 - l). Factor 1/4*v - c*v**3 - 1/4*v**2 + 1/4.
-(v - 1)*(v + 1)**2/4
Let z be 3/1*(-2 + 3). Find v such that -v**3 - 2*v**4 - 4 + z*v**3 + 2*v**2 + 4*v**2 - 2*v = 0.
-1, 1, 2
Determine l so that 8/11 - 26/11*l**2 + 7/11*l**3 + 20/11*l = 0.
-2/7, 2
Let b(a) be the third derivative of a**6/240 - a**5/30 + a**4/16 + 27*a**2. Suppose b(k) = 0. Calculate k.
0, 1, 3
Let k = -2/19 + 29/95. Factor -1/5*n**2 + 0 + 1/5*n**3 - k*n + 1/5*n**4.
n*(n - 1)*(n + 1)**2/5
Let z(b) be the third derivative of -b**5/300 - b**4/12 - 5*b**3/6 - 15*b**2 + 2*b. Factor z(v).
-(v + 5)**2/5
Let l(x) = -x**3 + 9*x**2 + 11*x - 8. Let r be l(10). Let m be -2 + 2*33/30. Find p such that 1/5*p**r + m*p + 0 = 0.
-1, 0
Let g(k) be the first derivative of k**2 - 2/3*k - 4/9*k**3 - 10. Factor g(y).
-2*(y - 1)*(2*y - 1)/3
Let j(h) be the third derivative of 0*h + 1/20*h**5 - 1/8*h**4 - 6*h**2 + 0 + 0*h**3. Let j(i) = 0. What is i?
0, 1
Let f(y) be the second derivative of 1/20*y**5 + 3*y + 0*y**2 + 0 + 1/12*y**4 + 0*y**3. Factor f(m).
m**2*(m + 1)
Let a be 10/(-16)*324/(-135). Factor 0*g + 0 - a*g**3 - 3/4*g**2 - 3/4*g**4.
-3*g**2*(g + 1)**2/4
Let r be 0/(0 + (-3)/9*3). Factor r - 3/4*q**4 - 9/4*q**2 + 9/4*q**3 + 3/4*q.
-3*q*(q - 1)**3/4
Let n(z) be the second derivative of 0 - 1/18*z**4 + 1/3*z**2 - 2*z + 0*z**3. Factor n(l).
-2*(l - 1)*(l + 1)/3
Let v be 12/(-54) + (-3122)/45. Let l = 70 + v. What is c in -2/5*c + 0 - l*c**2 = 0?
-1, 0
Factor 4/5 - 4*z**2 + 2/5*z.
-2*(2*z - 1)*(5*z + 2)/5
Let p(y) be the first derivative of y**4/28 + 4*y**3/21 - 20. Determine a, given that p(a) = 0.
-4, 0
Factor 0*z - 9/2*z**2 - 3/2*z**3 + 0.
-3*z**2*(z + 3)/2
Let i be (-141)/1170 + (-4)/(-26). Let s(k) be the third derivative of 0 + i*k**3 + 0*k + 2*k**2 - 1/60*k**4 + 1/300*k**5. Factor s(j).
(j - 1)**2/5
Factor 2 + 0*w**4 - 3*w**5 + 24*w**2 - 6*w**4 - 2 + 12*w**3.
-3*w**2*(w - 2)*(w + 2)**2
Let o(x) be the third derivative of x**9/52920 + x**8/11760 - x**6/1260 - x**5/420 - x**4/6 - 2*x**2. Let p(j) be the second derivative of o(j). Factor p(a).
2*(a - 1)*(a + 1)**3/7
Let m(n) be the first derivative of n**6/2 + 6*n**5/5 - 3*n**4/4 - 2*n**3 + 36. Let m(y) = 0. Calculate y.
-2, -1, 0, 1
Let z(s) be the first derivative of -5*s**6/6 - 2*s**5 - 5*s**4/4 - 2. Factor z(l).
-5*l**3*(l + 1)**2
Let n(d) be the first derivative of 0*d**3 - 2 - 1/12*d**4 + 0*d**2 - 3*d. Let u(b) be the first derivative of n(b). Factor u(j).
-j**2
Suppose 0 = -3*n - w + 2*w - 5, -4*w = n - 20. Let q(v) be the first derivative of 2/9*v**3 - 1 + n*v - 1/12*v**4 - 1/6*v**2. Determine o, given that q(o) = 0.
0, 1
Factor 0 + 1/3*l**4 + 0*l - 1/3*l**3 + 1/3*l**5 - 1/3*l**2.
l**2*(l - 1)*(l + 1)**2/3
Let f(n) be the second derivative of -n**9/15120 + n**8/3360 + n**4/12 + n. Let i(m) be the third derivative of f(m). Determine c so that i(c) = 0.
0, 2
Let v(p) be the first derivative of -1/7*p**2 + 1/7*p**4 - 3 + 0*p + 0*p**5 + 0*p**3 - 1/21*p**6. Find c, given that v(c) = 0.
-1, 0, 1
Let d(z) be the second derivative of z**6/120 - z**5/40 - z**4/4 - z**3/2 + 4*z. Let v(y) be the second derivative of d(y). Factor v(a).
3*(a - 2)*(a + 1)
Let i(x) be the second derivative of x**4/108 + x**3/18 + x**2/9 + 9*x. Suppose i(f) = 0. Calculate f.
-2, -1
Let 4*j**4 + 0*j + 0 + 4/5*j**3 + 0*j**2 + 16/5*j**5 = 0. Calculate j.
-1, -1/4, 0
Let m(i) = i**4 + 1. Let f(b) = -225*b**5 - 765*b**4 - 741*b**3 - 126*b**2 + 84*b + 39. Let x(k) = -f(k) + 15*m(k). Find q such that x(q) = 0.
-2, -1, -2/5, 1/3
Let x(t) = t**3 + 9*t**2 - 11*t - 10. Let w be x(-10). Factor -1/5*i**3 + 4/5*i**2 + w - 3/5*i.
-i*(i - 3)*(i - 1)/5
Let p(m) = m**3 + m - 1. Let z(n) = 8*n**3 + n**2 + 5*n - 5. Let g(j) = -5*p(j) + z(j). Factor g(v).
v**2*(3*v + 1)
Suppose 0 = 4*i - 5*i. Suppose 5*q + 5 = 0, -x = -i*x - 4*q - 4. Factor -6/7*b**3 + 0*b - 4/7*b**2 + x.
-2*b**2*(3*b + 2)/7
Let p(b) be the first derivative of 4*b**5 - 155*b**4/4 + 220*b**3/3 - 55*b**2/2 - 30*b - 33. Let p(d) = 0. What is d?
-1/4, 1, 6
Factor 10*x**3 - 2*x**4 + 8*x**2 - 6*x**2 + 8 - 27*x + 11*x - 2*x**5.
-2*(x - 1)**3*(x + 2)**2
Let f(a) be the second derivative of -a**4/3 - 52*a**3/3 - 338*a**2 - 16*a. Let f(b) = 0. Calculate b.
-13
Let v(y) be the third derivative of y**9/60480 + y**8/20160 + y**5/20 + y**2. Let i(s) be the third derivative of v(s). Factor i(f).
f**2*(f + 1)
Let x be -1 + 404/(-1476)*-5. Let c = x - 6/41. Factor -2/9*y**3 + 0 + 0*y + c*y**2.
-2*y**2*(y - 1)/9
Let k(t) = -5*t**4 - 20*t**3 - 14*t**2 + 20*t + 15. Let h(u) = -10*u**4 - 40*u**3 - 29*u**2 + 40*u + 30. Let q(p) = -4*h(p) + 9*k(p). Factor q(g).
-5*(g - 1)*(g + 1)**2*(g + 3)
Let f(x) = -155*x**2 - 335*x - 715. Let u(d) = 11*d**2 + 24*d + 51. Let k(m) = -6*f(m) - 85*u(m). Factor k(v).
-5*(v + 3)**2
Let b(v) be the second derivative of -1/30*v**5 + 1/12*v**4 - 1/2*v**2 - 1/60*v**6 + 0 - v + 1/3*v**3. Let d(n) be the first derivative of b(n). Factor d(c).
-2*(c - 1)*(c + 1)**2
Let z(o) be the third derivative of 0 + 3/40*o**5 - 6*o**2 + 0*o + 1/8*o**4 + 0*o**3 + 1/80*o**6. What is y in z(y) = 0?
-2, -1, 0
Let c = 9/13 - -7/65. Let 0 - c*j**3 + 0*j**2 + 0*j**4 + 2/5*j**5 + 2/5*j = 0. Calculate j.
-1, 0, 1
Let z(c) be the second derivative of 0*c**4 + 0 + 1/180*c**6 + 1/90*c**5 - 1/2*c**2 + 2*c + 0*c**3. Let b(r) be the first derivative of z(r). Factor b(o).
2*o**2*(o + 1)/3
Let s(h) be the first derivative of 3 + h + h**3 + 1/4*h**4 + 3/2*h**2. Suppose s(r) = 0. What is r?
-1
Let r(y) be the second derivative of -1/42*y**4 - 1/7*y**2 + y + 0 - 2/21*y**3. Determine d, given that r(d) = 0.
-1
Let z(u) be the second derivative of -u**4/18 + u**3/9 + 5*u. Solve z(i) = 0 for i.
0, 1
Let r(x) be the third derivative of x**6/6 - 2*x**5/15 + 9*x**2. Suppose r(y) = 0. Calculate y.
0, 2/5
Suppose 3*u = -u - 5*j + 13, 4*j = 20. Let g be (14/(-21))/(0 + u). Factor -2/9*s**2 + 0 - g*s.
-2*s*(s + 1)/9
Let x(o) be the second derivative of -11/15*o**6 - o**4 + o**2 + 1/3*o**3 - o - 7/5*o**5 - 1/7*o**7 + 0. What is r in x(r) = 0?
-1, 1/3
Let g(l) be the first derivative of -3*l**4/8 + 19*l**3/6 - 33*l**2/4 + 9*l/2 + 11. Let g(o) = 0. What is o?
1/3, 3
Suppose -3*n - 2*v + 840 = 0, -2*n + 7*v - 4*v = -560. Let o = n + -830/3. Determine q so that -22/9*q**4 + 4/9*q**3 + 0 + 0*q**2 + 0*q + o*q**5 = 0.
0, 1/3, 2/5
Suppose 6 = p + p. Factor 3*b**2 - 3 - 5*b + p*b + b**2 - 3*b**2.
(b - 3)*(b + 1)
Let -j - 1/2*j**4 + 1/2*j**2 + 0 + j**3 = 0. What is j?
-1, 0, 1, 2
Suppose 3*p + 12 = 3*k, 3*k - 6*k = -2*p - 11. Let n be 0 + (2 - (3 + -3)). Factor k*v**n + 4*v - 2*v**2 - 3*v.
v*(v + 1)
Let k(c) = c**3 + 7*c**2 - 9*c - 8. Let w be k(-8). Let f be 0 + 3 + 1 + w. What is q in 2*q**2 - q + 4*q - 3*q**2 - f*q = 0?
-1, 0
Let b = -1318/13 + 1