Calculate r.
0, 1, 3
Let r(w) be the second derivative of -w**5/50 + 9*w**4/2 - 405*w**3 + 18225*w**2 + 176*w. Factor r(l).
-2*(l - 45)**3/5
Let q = 64 + -34. Factor -q*d + 1392*d**3 + 14*d**2 + 13 - 1394*d**3 + 5.
-2*(d - 3)**2*(d - 1)
Suppose 68*d - 686 = 62. Let l(n) be the first derivative of -8/25*n**5 + 1/5*n**6 + 1/10*n**4 + 0*n**2 + 0*n**3 + d + 0*n. Find v, given that l(v) = 0.
0, 1/3, 1
Let c(h) be the second derivative of -3*h**5/100 - 13*h**4/20 - 23*h**3/10 - 33*h**2/10 - 16*h. Suppose c(l) = 0. Calculate l.
-11, -1
Let w be -3 - (-6 + 0)/1. Let z(x) be the first derivative of -2*x - 1/16*x**4 - 3/2*x**2 + 1 - 1/2*x**w. Suppose z(o) = 0. What is o?
-2
Let m(y) = -y**3 + 9*y**2 + y - 106. Let s(v) = v + 2. Let t(f) = m(f) - s(f). What is i in t(i) = 0?
-3, 6
Let f(o) be the first derivative of o**6/8 + 17*o**5/20 - 9*o**4/16 - 17*o**3/12 + 3*o**2/4 - 272. Find j, given that f(j) = 0.
-6, -1, 0, 1/3, 1
Determine y so that -1/3*y**2 - 22 + 25/3*y = 0.
3, 22
Suppose 8 = 2*b + 5*y, 5*y - 2*y + 12 = 3*b. Suppose -4*m + 4 = 4*q - 4, -b*q = -5*m + 10. Factor -3*c**3 + m*c**3 - 2*c**3 + 3*c**4.
3*c**3*(c - 1)
Let s(i) be the second derivative of -i**6/45 + 3*i**5/10 - 7*i**4/6 + 19*i**3/9 - 2*i**2 + 67*i. Factor s(t).
-2*(t - 6)*(t - 1)**3/3
Suppose -3*q**3 + q**2 - 54*q**2 - 11*q**2 + 20*q + 39*q**3 + 8 = 0. What is q?
-2/9, 1
Let z = 32 - 55. Let a be 2/8 - z/4. Find u, given that -2*u**3 + 4*u**2 + 2*u + 13*u**3 - a*u**3 - u + 2*u**4 = 0.
-1, -1/2, 0
Let k(p) be the first derivative of -p**5/10 + 33*p**4/8 - 121*p**3/2 + 1331*p**2/4 + 25. Suppose k(m) = 0. Calculate m.
0, 11
Let j(h) be the second derivative of h**4/66 + h**3/33 - 2*h**2/11 - 39*h - 1. Suppose j(c) = 0. Calculate c.
-2, 1
Let g(h) be the second derivative of -8*h**6/25 - 41*h**5/50 - 2*h**4/15 + 19*h**3/15 + 6*h**2/5 + 87*h + 2. Let g(l) = 0. Calculate l.
-1, -3/8, 2/3
Let p(k) be the first derivative of -4*k**3/21 + 42*k**2 + 592*k/7 - 826. Find d such that p(d) = 0.
-1, 148
Let j(n) be the third derivative of 20*n**2 + 0*n**3 + 0 - 1/30*n**5 + 1/3*n**4 + 0*n. Factor j(u).
-2*u*(u - 4)
Let d be (((-595)/(-14))/(-17))/(2/(-377)). Let p = d - 466. Factor p*s**5 + 45/4*s + 45/2*s**4 + 3/2 + 75/2*s**3 + 30*s**2.
3*(s + 1)**4*(7*s + 2)/4
Let c(k) be the first derivative of -125*k**4/4 + 125*k**3/3 + 10*k**2 - 20*k + 59. Find y such that c(y) = 0.
-2/5, 2/5, 1
Let w(r) be the first derivative of 1/21*r**3 - 3 + 1/35*r**5 + 0*r - 1/14*r**4 + 0*r**2. Suppose w(o) = 0. Calculate o.
0, 1
Let v be (12/(-10))/(35/(-175)). Let a(b) be the third derivative of 0 + 0*b - 1/5*b**5 - v*b**2 + b**3 + 1/8*b**4 - 3/40*b**6. Find t, given that a(t) = 0.
-1, 2/3
Let v(x) be the third derivative of x**5/60 - x**4/3 - 11*x**3/2 - 372*x**2. Factor v(d).
(d - 11)*(d + 3)
Let l be (-8)/2*(5 - 205/40). Solve 1/4*p**3 + l - 3*p**2 + p**4 + 5/4*p = 0.
-2, -1/4, 1
Let u(q) be the first derivative of -3*q**5/10 + 15*q**4/8 - 4*q**3 + 3*q**2 + 268. Solve u(t) = 0.
0, 1, 2
Factor -5*a**2 - a**3 + 1/3*a**4 - 2 - 17/3*a.
(a - 6)*(a + 1)**3/3
Suppose 5*w = -5*t, 2*w - 4*w - 28 = -5*t. Solve -19*q**3 + 11*q**3 + 4 + 4*q**5 - 6*q**2 + t*q - 2*q**2 + 4*q**4 = 0 for q.
-1, 1
Let f be (-54)/81 - ((-156)/(-63) - 4). Factor 0 - 3/7*l**2 + f*l.
-3*l*(l - 2)/7
Suppose 0*n = 5*n - 15. Suppose -6 = -4*u + 766. Solve -n*v + 193 - u + 3*v**2 = 0.
0, 1
Let p(q) = -7*q**3 + 64*q**2 + 160*q - 8. Let f(m) = m**3 + 2*m**2 - m + 2. Let i(v) = -4*f(v) - p(v). Factor i(w).
3*w*(w - 26)*(w + 2)
Let t(i) be the second derivative of -i**8/50400 + i**7/9450 + i**6/1800 - 7*i**4/12 - 13*i. Let h(x) be the third derivative of t(x). Factor h(j).
-2*j*(j - 3)*(j + 1)/15
Factor 57*l**3 + 51*l**3 - 36*l**3 + 11*l**3 + 20 + 40*l + 42*l**3 - 275*l**2.
5*(l - 2)*(5*l - 2)*(5*l + 1)
Suppose -24 = -5*p - 3*p. Suppose -7 + 3 = -2*q. Factor 16*h**q - 4*h - 8/3 - 28/3*h**p.
-4*(h - 1)**2*(7*h + 2)/3
Let i be 3/(-10) + -4 + (-219)/(-30). Suppose -3/5*s**4 - 12/5 + 6/5*s**i - 12/5*s + 9/5*s**2 = 0. Calculate s.
-1, 2
Let n(c) be the third derivative of 5*c**8/2016 + c**7/45 + 43*c**6/720 + c**5/45 - c**4/12 + 287*c**2. Determine o, given that n(o) = 0.
-3, -2, -1, 0, 2/5
Suppose -6*u = -21*u + 420. Let q(x) = 8*x**2 - 2*x. Let l(a) be the third derivative of a**5/60 + a**2. Let w(m) = u*l(m) - 4*q(m). Solve w(y) = 0 for y.
0, 2
Suppose 423*n**2 + 472*n**2 - 46*n**3 - 720*n - 295*n**2 + 5*n**4 + 161*n**3 = 0. What is n?
-12, 0, 1
Let x = 288 - 857/3. Let k(r) be the first derivative of -4/3*r - 2/15*r**5 + x*r**2 + 5/6*r**4 + 1 - 2*r**3. Let k(i) = 0. What is i?
1, 2
Let n(p) be the second derivative of p**5/40 - 89*p**4/12 + 7921*p**3/12 + 6*p - 2. Determine d so that n(d) = 0.
0, 89
Let q be (1/(-2))/(1/(-70)). Determine l so that q*l**4 + 13796*l**2 - 13310 + 1145*l**3 - 1421*l**2 + 13024*l + 29931*l = 0.
-11, 2/7
Let b(s) be the second derivative of 1/6*s**4 - 1/20*s**5 + 29*s + 0 - 3*s**2 + 5/6*s**3. Factor b(p).
-(p - 3)*(p - 1)*(p + 2)
Let a(p) be the second derivative of -p**6/1080 - p**5/270 - 11*p**2/2 + p. Let k(c) be the first derivative of a(c). Let k(f) = 0. Calculate f.
-2, 0
Solve 6*g**2 - 7*g**2 - 20*g + g**2 + 9*g**2 = 0.
0, 20/9
Suppose -5*s + 19 + 76 = 0. Let g = -16 + s. Factor -3*t**3 + 8*t**2 + 7*t**3 + t**g - t**3.
4*t**2*(t + 2)
Let b(o) be the third derivative of 1/60*o**6 + 0*o**4 + 1/60*o**5 + 0*o + 1/210*o**7 + 0*o**3 + 0 + 19*o**2. What is t in b(t) = 0?
-1, 0
Let r(d) = -5*d**2 - 13*d. Let m(t) = -4*t**2 - 12*t + 1. Let a(x) = 6*m(x) - 5*r(x). Determine n so that a(n) = 0.
1, 6
Let k(d) = d**2 - 9*d + 16. Let v be k(5). Let q be v*124/10*-5. Suppose q*p**5 + 4*p**3 - 250*p**5 - 2*p**3 = 0. What is p?
-1, 0, 1
Let s(f) be the second derivative of -5*f**4/12 - 5*f**3 + 35*f**2/2 - 41*f. What is q in s(q) = 0?
-7, 1
Find z, given that -2/11*z**4 - 4/11*z**2 + 10/11*z - 12/11*z**3 + 6/11 + 2/11*z**5 = 0.
-1, 1, 3
Let v(b) be the third derivative of -b**7/3780 - b**6/405 - b**5/135 - b**3/6 + 3*b**2. Let r(f) be the first derivative of v(f). Factor r(t).
-2*t*(t + 2)**2/9
Let m(y) be the third derivative of y**7/1470 - y**6/840 - y**5/105 + y**4/42 + 17*y**2. Factor m(v).
v*(v - 2)*(v - 1)*(v + 2)/7
Let y(v) = v**3 - 8*v**2 + 3*v - 12. Let a be y(8). Find x, given that -8*x - 9*x - 2*x**2 + 15*x + a = 0.
-3, 2
Let a = 1545/20672 - 9/323. Let q = a - -93/64. What is r in -6*r**5 + 0*r - 9/2*r**4 + 0*r**2 + q*r**3 + 0 = 0?
-1, 0, 1/4
Let d be -22*1*(-27)/(-12)*2. Let n be (-15 - -12)/(d/6). Suppose 16/11*g - 6/11*g**3 - 8/11 - n*g**2 = 0. What is g?
-2, 2/3, 1
Determine l so that 9/2*l - 6 + 3/2*l**2 = 0.
-4, 1
Let j = 20 + -18. Factor -28 - 18*o**4 - 12*o**3 - j*o**2 + 28.
-2*o**2*(3*o + 1)**2
Let m(n) be the second derivative of 5*n - 4/5*n**3 + 1/75*n**6 + 0 + 2/25*n**5 + 9/5*n**2 - 1/15*n**4. Factor m(h).
2*(h - 1)**2*(h + 3)**2/5
Let l(d) = -3*d + 0*d + 5*d + 3*d**3 - 3*d**4 + 6*d**4 + 2. Let k(o) = 16*o**4 + 16*o**3 + 11*o + 11. Let s(p) = 2*k(p) - 11*l(p). Factor s(h).
-h**3*(h + 1)
Let n(c) be the second derivative of c**7/105 - 4*c**6/25 + c**5/5 + 2*c**4/5 - 11*c**3/15 + 352*c. Determine k so that n(k) = 0.
-1, 0, 1, 11
Let o(j) be the first derivative of 2*j**3/9 - 11*j**2/3 - 8*j - 745. Find h such that o(h) = 0.
-1, 12
Let l(u) be the first derivative of -u**4/32 + 23*u**3/24 - 15*u**2/4 + 845. Factor l(p).
-p*(p - 20)*(p - 3)/8
Factor 3322 - 928*d + 50502 + 2*d**2 + 2*d**2.
4*(d - 116)**2
Let g be (-180)/25 - -8 - (-63)/15. Suppose 2/3*u**3 - 1/3 - 2/3*u**2 - u + u**4 + 1/3*u**g = 0. Calculate u.
-1, 1
Suppose -29*j = -34*j + 15. Suppose -2*x**2 + x**5 + 11*x**4 - 2*x**4 + 2*x**5 + 5*x**2 + 9*x**j = 0. Calculate x.
-1, 0
Factor 0 - 2/3*d**3 - 2/3*d**4 + 2/3*d + 2/3*d**2.
-2*d*(d - 1)*(d + 1)**2/3
Let a be -5 + ((-148)/(-30) - 6/(-36)). Let v(l) be the second derivative of -3/4*l**5 - 8*l + 0*l**2 - 2*l**3 + a*l**6 + 2*l**4 + 0. Factor v(z).
3*z*(z - 2)**2*(z - 1)
Let g(m) be the third derivative of 0 + 1/12*m**4 + 27*m**2 - 1/504*m**8 + 1/105*m**7 - 1/9*m**3 - 1/90*m**6 - 1/45*m**5 + 0*m. Factor g(k).
-2*(k - 1)**4*(k + 1)/3
Let i(w) be the third derivative of 0 + 6*w**2 + 1/120*w**5 + 0*w - 1/48*w**4 + 0*w**3. Factor i(h).
h*(h - 1)/2
Let d = 4 - 1. Suppose 4*n = -3*h + 4*h + 17, 0 = -5*h - 5*n + 40. Fac