9*n + 19 = u. Determine h so that -4/7*h**3 + 2/7*h + 4/7*h**2 + 2/7*h**5 - 2/7*h**n - 2/7 = 0.
-1, 1
Let j(n) = -3*n**2 - 5*n + 7. Let i(o) = 2*o**2 + 3*o - 4. Let s(u) = -5*i(u) - 3*j(u). Let l(c) = c**2 + 24*c - 44. Let q(x) = -l(x) - 4*s(x). Factor q(m).
3*(m - 4)**2
Let p(g) be the second derivative of 0 + 0*g**3 + 0*g**2 + 1/6*g**6 + 0*g**5 - 7*g - 5/12*g**4. Factor p(s).
5*s**2*(s - 1)*(s + 1)
Let w = 9475/1629 + -1002911/215028. Let o = w + 13/108. Factor -2/11*t**5 - 26/11*t + 4*t**2 + o*t**4 + 6/11 - 36/11*t**3.
-2*(t - 3)*(t - 1)**4/11
Let a(m) be the third derivative of m**8/336 + 5*m**7/42 - 53*m**6/120 + 9*m**5/20 + 207*m**2 - m. Factor a(z).
z**2*(z - 1)**2*(z + 27)
Let s(l) = -282*l - 5073. Let t be s(-18). Factor -a**2 - a - 1/4*a**t + 0.
-a*(a + 2)**2/4
Let k(t) be the first derivative of -32*t**6/21 + 208*t**5/35 - 9*t**4 + 45*t**3/7 - 27*t**2/14 + 119. Suppose k(p) = 0. What is p?
0, 3/4, 1
Let z(x) = x + 1. Let w be z(-14). Let o(r) = 2*r + 28. Let s be o(w). Solve -5*c**2 - c**3 + 7*c**4 - 4*c**4 - c**5 + 2*c + 2*c**s = 0.
-1, 0, 1, 2
Let x(u) = -u**4 - 2*u**3 + 2*u**2 + 4*u + 1. Let p(j) = 2*j**4 + 2*j**3 - 3*j**2 - 5*j - 2. Let v(q) = 2*p(q) + 3*x(q). Factor v(k).
(k - 1)**3*(k + 1)
Let g be 7*(-36)/(-126)*2/6. Let s(r) be the first derivative of -g*r**3 - 10 + 0*r**2 + 2*r. Solve s(z) = 0 for z.
-1, 1
Let x(s) be the first derivative of -s**8/168 - s**7/35 - s**6/20 - s**5/30 + 25*s**2 + 47. Let b(t) be the second derivative of x(t). Factor b(m).
-2*m**2*(m + 1)**3
Let m = -29 + 34. Suppose -6*t + 3 = -m*t. Determine k, given that t*k - 3*k**3 + 4 - 3 + 2 - 3*k**2 = 0.
-1, 1
Let y be -2*(1 - 0) - -2. Let w(h) be the first derivative of 0*h**2 + 2/5*h**3 + y*h + 8 + 1/10*h**4. Let w(s) = 0. What is s?
-3, 0
Let i(p) be the third derivative of 0*p - 5/336*p**8 - 1/42*p**7 + 22*p**2 + 0*p**3 + 1/12*p**5 - 5/12*p**4 + 0 + 1/8*p**6. Let i(c) = 0. What is c?
-2, -1, 0, 1
Let r = 83 - 79. Determine d, given that 7*d**r - 5*d**4 - 5*d**2 + 3*d**2 = 0.
-1, 0, 1
Determine v so that 0*v + 0 + 21/8*v**3 - 81/8*v**4 + 15/8*v**5 + 45/8*v**2 = 0.
-3/5, 0, 1, 5
Let c be (-42)/(-15)*(-12)/(-132). Let k(v) be the first derivative of -1/33*v**6 + 15/11*v**2 + 4/33*v**3 + c*v**5 - 1 - 18/11*v - 7/11*v**4. Solve k(a) = 0.
-1, 1, 3
Let a(b) be the third derivative of 384*b**7/245 - 40*b**6/21 + 4*b**5/5 - b**4/14 - b**3/21 - 151*b**2. Factor a(v).
2*(4*v - 1)**3*(18*v + 1)/7
Let m = -270 + 276. Let w(f) be the second derivative of 1/15*f**m + 0*f**2 + 1/10*f**5 + f + 0 - 1/21*f**7 + 0*f**3 - 1/6*f**4. Suppose w(k) = 0. What is k?
-1, 0, 1
Let b(j) be the first derivative of -28/3*j**3 - 16/3*j + 13 - 88/3*j**2. Factor b(c).
-4*(c + 2)*(21*c + 2)/3
Solve 4*d**3 - 6*d**3 - 57*d - 54*d + 113*d = 0 for d.
-1, 0, 1
Let f be ((-21)/35)/((-1)/5). Factor 7*z**3 + 3*z**3 + 5*z**4 + 9*z**f + 5*z**5 - 29*z**3.
5*z**3*(z - 1)*(z + 2)
Factor -8/5*s + 1/5*s**3 - 7/5*s**2 + 0.
s*(s - 8)*(s + 1)/5
Suppose 10*s - 13*s = -9. Suppose 3*l - l + 10 = 4*g, 0 = s*g - 3*l - 15. Factor -4/7*a**2 - 2/7*a - 2/7*a**3 + g.
-2*a*(a + 1)**2/7
Let j(y) be the second derivative of y**5/20 - y**4/12 + 2*y**3/3 + 17*y. Let w be j(0). Factor -1/2*c - 1/2*c**5 + 0*c**2 + w + 0*c**4 + c**3.
-c*(c - 1)**2*(c + 1)**2/2
Find q such that 241*q + q**4 + 35*q**3 - 13*q**4 - 11*q**3 + 249*q**2 + 54 - 16*q = 0.
-3, -1/2, 6
Suppose -4*t + p + 13 = 0, -7*p - 14 = -4*t - 5*p. Factor 0*c + 0 + 0*c**2 - 1/2*c**4 + 0*c**t.
-c**4/2
Factor 3 - 1/4*j**4 + 3/4*j**2 + 5*j - 3/2*j**3.
-(j - 2)*(j + 1)**2*(j + 6)/4
Let c = -38 - -43. Suppose -7*g + t = -2*g, 5*g + c*t = 0. Determine a, given that g - 2/7*a**5 + 2/7*a**2 + 6/7*a**4 - 6/7*a**3 + 0*a = 0.
0, 1
Let c = 670 + -2635/4. Suppose d = 4*h - 13, 5*h - 4*h + 3 = -d. Let -c*t**3 + 5/2*t**h + 0*t**4 + 27/4*t**5 - 2 + 5*t = 0. Calculate t.
-1, 2/3
Factor -1444/3 - 1/3*h**2 + 76/3*h.
-(h - 38)**2/3
Let c(s) be the third derivative of s**6/60 + s**5/30 - s**4/6 - 12*s**2 - 2. Determine p, given that c(p) = 0.
-2, 0, 1
Suppose -2/7*s**4 + 2*s**2 + 0*s + 0 - 12/7*s**3 = 0. Calculate s.
-7, 0, 1
Let m(x) be the second derivative of x**5/30 + x**4/102 + 5*x**2 - 11*x. Let r(y) be the first derivative of m(y). Find v such that r(v) = 0.
-2/17, 0
Let r(n) be the second derivative of -11*n + 55/4*n**4 + 1/6*n**6 + 0 + 5/2*n**5 + 40*n**2 + 100/3*n**3. Suppose r(u) = 0. Calculate u.
-4, -1
Let r(n) = 8*n - 44. Let f(y) = y**2 + 7*y - 2. Let j be f(-8). Let k be r(j). What is w in -1/2*w**3 + 0 - 1/2*w**2 + 1/2*w**k + 1/2*w = 0?
-1, 0, 1
Let g(y) be the first derivative of 0*y**2 - 33 - 16*y + 28/3*y**3 + 3*y**4. Factor g(s).
4*(s + 1)*(s + 2)*(3*s - 2)
Factor -1/4*r**3 - 209/4*r - 53/2*r**2 - 26.
-(r + 1)**2*(r + 104)/4
Let g(n) be the first derivative of 7/20*n**4 + 24 + 0*n**2 + 1/5*n**3 + 4/25*n**5 + 0*n. Factor g(c).
c**2*(c + 1)*(4*c + 3)/5
Let i(u) be the third derivative of u**6/60 + 133*u**5/30 + 374*u**4 + 1452*u**3 + 2*u**2 + 250. Solve i(n) = 0.
-66, -1
Let b(q) = q**2 - 189*q - 4608. Let a(o) = 2*o**2 - 188*o - 4608. Let c(u) = 3*a(u) - 4*b(u). Factor c(z).
2*(z + 48)**2
Let v(q) be the first derivative of q**4/8 + 37*q**3/12 + 45*q**2/2 + 81*q/4 - 85. Solve v(y) = 0.
-9, -1/2
Let o(k) be the third derivative of -k**5/60 - 11*k**4/4 + 11*k**2 + k. Determine c so that o(c) = 0.
-66, 0
Let r be (-202)/(-6) + (-135)/81. Let u = r - 28. Factor -3/2*p**u + 0*p - 3/2*p**2 + 3*p**3 + 0.
-3*p**2*(p - 1)**2/2
Let h(y) be the third derivative of -y**8/1008 + 2*y**7/315 - y**6/360 - y**5/30 - 2*y**2 + 3. Determine u so that h(u) = 0.
-1, 0, 2, 3
What is u in 274*u + 14*u**3 + 0*u**3 - 5 + 44 + 8 + 13 + 228*u**2 = 0?
-15, -1, -2/7
Let y(h) be the third derivative of -h**6/480 + 59*h**5/240 + h**4/96 - 59*h**3/24 - 2*h**2 + 34*h. Let y(w) = 0. Calculate w.
-1, 1, 59
Let y(r) be the second derivative of 2*r**6/15 + 9*r**5/5 + 8*r**4 + 40*r**3/3 - 16*r + 2. Factor y(t).
4*t*(t + 2)**2*(t + 5)
Let v = -3688271/11 - -335555. Let m = 258 - v. Find c, given that -16/11*c**2 - 18/11*c**5 + m + 14/11*c + 60/11*c**4 - 4*c**3 = 0.
-1/3, 1, 2
Let m(y) be the second derivative of y**6/24 + 5*y**5/16 - 125*y**4/48 - 25*y**3/24 + 15*y**2 + 19*y + 12. Suppose m(c) = 0. What is c?
-8, -1, 1, 3
Determine o so that 15*o**4 + 4711 - 9*o**3 - 4711 - 11*o**2 - 3*o**5 - 16*o**2 = 0.
-1, 0, 3
Let x = 372 + -370. Let r(m) be the first derivative of 3/2*m**x + m + 1/4*m**4 + m**3 - 3. Solve r(c) = 0.
-1
Let -4/5*h**2 - 118336/5 - 1376/5*h = 0. What is h?
-172
Let c(v) be the second derivative of v**4/3 + 56*v**3/3 - 173*v. Factor c(m).
4*m*(m + 28)
Let p(m) be the third derivative of -50*m**2 + 0*m - 1/12*m**3 - 5/96*m**4 + 0 - 1/120*m**5. What is r in p(r) = 0?
-2, -1/2
Solve -183*j**2 + 182*j + 194*j**2 + 730*j - 733*j**2 - 288 = 0 for j.
12/19
Let t(j) = j**2 + 1. Let c(i) = 2*i**2 - 3*i - 3. Let v(o) = c(o) + 2*t(o). Suppose q - 3 = -1. Let m(u) = u - 1. Let r(d) = q*m(d) - v(d). Factor r(z).
-(z - 1)*(4*z - 1)
Suppose 275 + 8 + 26 = 103*v. Suppose v + 7/2*f**2 - 1/2*f**3 + 13/2*f - 1/2*f**4 = 0. What is f?
-2, -1, 3
Let z(b) be the third derivative of b**9/241920 + b**8/13440 + b**7/4032 - b**5/15 + 6*b**2. Let q(k) be the third derivative of z(k). Factor q(d).
d*(d + 1)*(d + 5)/4
Let l(v) be the third derivative of -1/33*v**4 - 1/55*v**5 - 1/33*v**3 + 0 + 0*v + 5*v**2 - 1/1155*v**7 - 1/165*v**6. Let l(a) = 0. Calculate a.
-1
Solve 612 + 44 + 170*f**3 - 18*f**3 + 4*f**4 + 16*f - 336*f**2 - 156*f**2 = 0.
-41, -1, 2
Let d(k) be the second derivative of 3/100*k**5 + 1/20*k**2 - 1/10*k**3 + 0 - 20*k - 1/120*k**4. Suppose d(a) = 0. What is a?
-1, 1/6, 1
Suppose 0 = 5*v + z - 21, -3*v + z = 3 - 14. Factor 20*s**v + 4*s**5 - 17*s**3 - 11*s**3 - 20*s**2 + 59*s - 35*s.
4*s*(s - 1)**2*(s + 1)*(s + 6)
Suppose 7*g - 36 = 3*g - 4*o, 3*g - 31 = -4*o. Let k(l) be the third derivative of -1/2*l**4 + 0*l + 0 - 3/2*l**3 - 1/20*l**g - 5*l**2. Factor k(q).
-3*(q + 1)*(q + 3)
Let f(k) = -k**2 + 2*k. Let j be f(2). Let o(a) = a**2 + 15*a - 16. Let t be o(1). Factor 0*m**2 - 2/9*m**3 + t + j*m + 2/9*m**4.
2*m**3*(m - 1)/9
Let a(u) be the first derivative of -u**6/960 - u**5/40 - u**4/4 - 7*u**3/3 + 6. Let h(n) be the third derivative of a(n). What is j in h(j) = 0?
-4
Let g(z) = 2*z**3 - 6*z**2 