j).
-j**2*(j - 1)*(j + 2)/5
Suppose 3 = -429*p + 432*p, 3*i - 7 = 2*p. Find m, given that -2/11*m**2 + 2/11*m**4 - 4/11*m + 4/11*m**i + 0 = 0.
-2, -1, 0, 1
Let a(y) be the first derivative of 6 + 0*y + 0*y**5 + 0*y**2 - 2/3*y**3 + 1/180*y**6 + 0*y**4. Let n(w) be the third derivative of a(w). Factor n(o).
2*o**2
Let h(z) be the third derivative of z**5/30 - 5*z**4/4 + 44*z**3/3 - 7*z**2 - 4*z. Determine v so that h(v) = 0.
4, 11
Let a = 141/4 + -1261/36. Factor 0*m**2 + 4/9*m**3 + 0 + 0*m + 2/9*m**4 - a*m**5.
-2*m**3*(m - 2)*(m + 1)/9
Let s(r) be the first derivative of -r**6/2 + 6*r**5/5 - 2*r**3 + 3*r**2/2 - 73. Factor s(m).
-3*m*(m - 1)**3*(m + 1)
Suppose -x = d + 2*d - 7, -8 = -2*x. Let q(z) be the first derivative of -4*z**2 - d + 4*z**4 + 0*z + 28/3*z**3. Factor q(b).
4*b*(b + 2)*(4*b - 1)
Let k(m) be the second derivative of m**5/390 + m**4/52 + 11*m**2/2 - 19*m. Let j(r) be the first derivative of k(r). Factor j(u).
2*u*(u + 3)/13
Let t(w) be the first derivative of -w**6/28 + 3*w**5/70 + 3*w**4/7 + 4*w**3/7 + 7*w**2 + 16. Let s(n) be the second derivative of t(n). Factor s(j).
-6*(j - 2)*(j + 1)*(5*j + 2)/7
Let k(f) be the second derivative of f**4/48 + f**3/8 + 266*f. Solve k(n) = 0 for n.
-3, 0
Let s = 380 + -378. Factor -6/7*d + 1 - 1/7*d**s.
-(d - 1)*(d + 7)/7
Let i(t) = t**3 + 10*t**2 + 11. Let d be i(-10). Suppose -d*w = -4*w. Find x such that -2*x + 6 - 3 - 3*x**2 - 2 + w*x = 0.
-1, 1/3
Let n(d) be the third derivative of d**5/450 + d**4/90 - 57*d**2. Factor n(q).
2*q*(q + 2)/15
Let q(l) be the first derivative of -l**4/18 + 2*l**3/27 + 10*l**2/9 + 16*l/9 + 67. What is y in q(y) = 0?
-2, -1, 4
Let s = 44 + 284. Factor -12*q - 4*q**3 - s*q**2 + 340*q**2 + 4*q.
-4*q*(q - 2)*(q - 1)
Let j = 20219/4 + -5054. Suppose -3/2*o**2 - 9/4*o**3 + 0*o + j*o**5 + 0 + 0*o**4 = 0. What is o?
-1, 0, 2
Let 6/13*j + 0 - 8/13*j**2 - 14/13*j**3 = 0. What is j?
-1, 0, 3/7
Let s(q) be the first derivative of -q**3/3 + 15*q**2 - 29*q - 354. Factor s(a).
-(a - 29)*(a - 1)
Let m(j) be the third derivative of j**6/300 + j**5/10 - j**4/60 - j**3 + 34*j**2 - 5*j. Let m(z) = 0. Calculate z.
-15, -1, 1
Factor 3*n**2 - 2*n**2 + 0*n**2 + 3*n**2 - 72*n + 0*n**2.
4*n*(n - 18)
Let f = -164 + 232. Let k = 137/2 - f. Solve 1/2 + k*v**3 - 3/4*v**2 - 3/4*v = 0.
-1, 1/2, 2
Let y(b) be the second derivative of -1/2*b**2 + 0*b**3 - 1/60*b**5 + 0 + 1/24*b**4 + b. Let k(f) be the first derivative of y(f). Factor k(a).
-a*(a - 1)
Let n(t) = -t**3 - 66*t**2 + 55*t - 799. Let s be n(-67). Factor 1/2*p**s - 11/2*p**3 + 0*p**4 - 4*p + 0 - 9*p**2.
p*(p - 4)*(p + 1)**2*(p + 2)/2
Let g = 71 + -41. Determine y so that -g*y**3 - 18*y**4 - y**5 + 0*y**5 + 0*y**4 + 50*y**2 - y**5 = 0.
-5, 0, 1
Let t(a) = -5*a + 2*a**2 - a - 1 + a + 6*a. Let m(v) = -3*v**2 - v + 2. Let p(d) = 3*m(d) + 4*t(d). Let p(u) = 0. Calculate u.
-1, 2
Let h(y) be the first derivative of -250*y**3/9 - 20*y**2/3 - 8*y/15 + 1. Determine o, given that h(o) = 0.
-2/25
Let b(t) be the third derivative of t**5/30 + 5*t**4/6 + 7*t**3 - 2*t**2 + 70. Factor b(f).
2*(f + 3)*(f + 7)
Let b(x) be the first derivative of -3*x**5/100 + x**4/5 - 3*x**3/10 - 32*x - 32. Let w(i) be the first derivative of b(i). Determine v, given that w(v) = 0.
0, 1, 3
Let d(v) be the third derivative of -v**6/24 + 2*v**5/3 - 15*v**4/8 - 15*v**3 + 42*v**2 - 2. Factor d(g).
-5*(g - 6)*(g - 3)*(g + 1)
Let s be 1/(-4) + (-144)/(-64). Let k be 55/(-77) + s/2. Factor -2/7*c**5 - 4/7*c**2 - k*c + 2/7*c**4 + 2/7 + 4/7*c**3.
-2*(c - 1)**3*(c + 1)**2/7
Suppose -2*k + 7 = -21. Let a be (8/(-6))/((-10)/15). Factor -2*u**3 - 45*u - u**3 + k + 21*u**a + 13.
-3*(u - 3)**2*(u - 1)
Suppose -u = 2 - 1. Let x(l) = l**5 - l**3 - l**2 + l + 1. Let r(c) = 2*c - 2*c**2 - 4*c**3 + 4*c**5 + 3*c - 3*c + 2. Let a(m) = u*r(m) + 2*x(m). Factor a(z).
-2*z**3*(z - 1)*(z + 1)
Let a(c) be the first derivative of c**6/720 + c**5/60 + c**4/12 - c**3 + 15. Let b(q) be the third derivative of a(q). Factor b(g).
(g + 2)**2/2
Factor -41*t - 9 + 24 + 43 + 60*t**3 + 296*t**4 - 298*t**4 - 19*t - 56*t**2.
-2*(t - 29)*(t - 1)**2*(t + 1)
Factor 54/5 - 3/5*k**3 + 9/5*k - 12/5*k**2.
-3*(k - 2)*(k + 3)**2/5
Let n(i) = -i + 9. Suppose -2*f = 2 - 14. Let z be n(f). Let -2 - t**3 + 2*t - 3*t**3 - t**4 + 2*t + z*t**4 = 0. Calculate t.
-1, 1
Find f, given that 609/5*f - 3/5*f**3 - 12/5*f**2 - 2646/5 = 0.
-18, 7
Let d(m) = 2*m**2 - 198*m - 164. Let l(c) = -c**2 + 98*c + 83. Let k(b) = 4*d(b) + 9*l(b). Solve k(f) = 0 for f.
-1, 91
Let j(d) be the second derivative of -d**4/2 - 3*d**3/4 + 86*d + 1. Factor j(b).
-3*b*(4*b + 3)/2
Solve -14/3*d**2 - 8 + 88/3*d = 0 for d.
2/7, 6
Let d(u) be the second derivative of 2*u**6/15 + 13*u**5/5 + 16*u**4 + 136*u**3/3 + 64*u**2 + 85*u. Suppose d(j) = 0. What is j?
-8, -2, -1
Let u(i) be the second derivative of 5/4*i**4 + 0*i**5 + 0 + 5/3*i**3 - 5*i + 0*i**2 - 1/6*i**6. Factor u(h).
-5*h*(h - 2)*(h + 1)**2
Let i be (-3)/(-12)*-3*-16. Let s = 15 - i. Factor -5*c**2 - 5*c**s + 5*c - 2 - 1 + 8.
-5*(c - 1)*(c + 1)**2
Suppose 0 = -6*k + 4*k + 912. Solve -456 + 30*o - 5*o**2 + k = 0 for o.
0, 6
Let l be (-4)/144*-146 - 3. Let i = -5/6 + l. Factor -4/9*x**3 + 0*x**4 + 0*x**2 + i*x**5 + 0 + 2/9*x.
2*x*(x - 1)**2*(x + 1)**2/9
Let o(h) be the first derivative of -h**6/90 + 2*h**4/3 + 3*h**3 + 16. Let m(s) be the third derivative of o(s). What is q in m(q) = 0?
-2, 2
Determine j, given that 49/8 + 63/8*j + 1/8*j**3 + 15/8*j**2 = 0.
-7, -1
Let p(q) be the third derivative of -q**8/1512 - 2*q**7/315 + 4*q**6/135 - q**5/135 - 5*q**4/36 + 8*q**3/27 - 150*q**2. Let p(m) = 0. What is m?
-8, -1, 1
Factor -2*r**2 - 52*r - 486 + 214 + 222.
-2*(r + 1)*(r + 25)
Suppose 3 = -2*l + 5. Let j be (l - -2) + 0/4. Let -2*a + 5 - 2*a**j - 3 + 4*a**2 - 2 = 0. What is a?
0, 1
Let r(v) = -13*v - 3 - 4*v**2 + 7 + 3*v**2. Let m(b) = -12*b + 4. Let l be (45/36)/(6/8 - 1). Let w(z) = l*m(z) + 4*r(z). Let w(o) = 0. Calculate o.
1
Let a(t) be the second derivative of 0 + 1/2*t**2 + 6*t + 5/16*t**4 + 2/3*t**3 - 1/40*t**5 - 1/24*t**6. Determine n so that a(n) = 0.
-1, -2/5, 2
Let k = 26/15 + -212/105. Let a = k + 24/35. Factor 0 - a*s**2 - 4/5*s.
-2*s*(s + 2)/5
Let m(d) = d**3 + 11*d**2 + 3*d - 6. Let k be m(-4). Let p be 2/(-9) + k/18. Factor 5*h**5 - 46*h**3 - h**4 - 3*h**p + h + 43*h**3 + h**2.
h*(h - 1)**2*(h + 1)*(2*h + 1)
Let k be 3*340/45 - (-1190)/(-170). Factor 1/3 + 64/3*q**5 - 52/3*q**3 + k*q**2 - 16*q**4 - 4*q.
(q - 1)*(q + 1)*(4*q - 1)**3/3
Determine w so that 8*w**3 + 13*w - 10/3 - 4/3*w**4 - 49/3*w**2 = 0.
1/2, 1, 2, 5/2
Let h(k) = -2*k**2 + 7*k + 155. Let t be h(-7). Let p(w) be the first derivative of 2*w**2 + 0*w + t + 4/3*w**3. Let p(s) = 0. What is s?
-1, 0
Determine x so that 2*x**4 + 4 + 36 + 75*x**3 - 42*x**2 + 3*x + 13*x - 91*x**3 = 0.
-2, -1, 1, 10
Let m(y) be the third derivative of 7*y**5/30 - 25*y**4/6 + 7*y**3/3 - 722*y**2. Factor m(c).
2*(c - 7)*(7*c - 1)
Let x = 20685/8 + -2590. Let t = -33/8 - x. Factor -t*g**2 + g - 3/4.
-(g - 3)*(g - 1)/4
Let c(u) = -2*u - 10. Let f be c(-6). Let w(i) be the third derivative of 0*i - 1/40*i**6 - 1/4*i**4 + 3/20*i**5 + 0*i**3 + 0 + 3*i**f. Factor w(v).
-3*v*(v - 2)*(v - 1)
Let c(z) be the second derivative of 3*z**5/40 - 11*z**4/16 - 21*z**3/8 - 832*z. Find w, given that c(w) = 0.
-3/2, 0, 7
Let r(i) be the third derivative of -8*i**5/75 - 11*i**4/20 - 2*i**3/15 - 187*i**2 - 1. Find m, given that r(m) = 0.
-2, -1/16
Suppose -105*q = 55*q - 320. Factor -8/3 + 16/5*a + 2/15*a**3 - 6/5*a**q.
2*(a - 5)*(a - 2)**2/15
Let -22*f**3 + 22*f - 1/2 + 1/2*f**2 = 0. What is f?
-1, 1/44, 1
Let v(o) = -114*o - 226. Let p be v(-2). Factor -4/7 + 10/7*f - 6/7*f**p.
-2*(f - 1)*(3*f - 2)/7
Let g = -530 - -534. Let y(z) be the third derivative of 0*z + 0 - g*z**2 + 1/3*z**3 + 1/8*z**4 + 1/60*z**5. Factor y(r).
(r + 1)*(r + 2)
Let q(m) be the third derivative of 35*m**6/144 - 17*m**5/48 + m**4/8 + m**3/18 - m**2 - 35*m. Find j, given that q(j) = 0.
-1/14, 2/5
Suppose -i + 0*m = 2*m - 2, 5*i + 3*m - 10 = 0. Let l - 16*l**2 + 18*l**i - 2*l**3 + l - 2*l**4 = 0. What is l?
-1, 0, 1
Let c(y) be the third derivative of 0*y + 0 + 0*y**3 - 1/8*y**4 - 1/112*y**8 - 1/5*y**5 - 3/20*y**6 - 10*y**2 - 2/35*y**7. What is r in c(r) = 0?
-1, 0
Find x, given that 64 + 1/