5/10 + 13*p**4/8 + 5*p**3 - p**2 + 52. Determine u, given that i(u) = 0.
-2, -1, 5
Let b = 29 - 29. Suppose 4*o - 2*x - 20 = b, 5*o - x - 4*x = 35. Factor 3*y**2 - 14*y + 75 - 16*y - o*y**2 + 3*y**2.
3*(y - 5)**2
Let i = -1 - -34. Suppose 5*x**4 + i*x - 20*x**3 + 20*x**2 - 33*x = 0. What is x?
0, 2
Let x(v) be the second derivative of 0*v**3 + 0*v**2 - 1/120*v**6 - 1/48*v**4 + 0 + 4*v - 1/40*v**5. Factor x(q).
-q**2*(q + 1)**2/4
Let j = -251/6 - -1291/30. Let h(l) be the first derivative of 8 + 2/5*l**3 - 3/10*l**2 - j*l + 3/20*l**4. Factor h(c).
3*(c - 1)*(c + 1)*(c + 2)/5
Suppose 0 = -4*t - 46 - 6. Let u be -2 - 2/1 - t. Let 6*b + 0 + 1 + u + b**2 - 1 = 0. Calculate b.
-3
Let z(p) be the third derivative of -p**9/8316 - p**8/3080 - p**7/4620 + p**3/3 + 7*p**2. Let l(h) be the first derivative of z(h). Factor l(s).
-2*s**3*(s + 1)*(2*s + 1)/11
Let s(q) be the first derivative of -q**4/4 + 4*q**3/3 - 5*q**2/2 + 2*q - 304. Find g such that s(g) = 0.
1, 2
Suppose -2*n - r = -8, r + 16 = 5*r. Suppose n = k - 1. Solve 6/5*t**k + 0*t + 4/5*t**4 + 2/5*t**2 + 0 = 0 for t.
-1, -1/2, 0
Suppose -5*f + 15 = 5*x, -x - f + 15 = 3*x. Determine l, given that -l**2 + l**5 - 4 - 2*l**4 + 8*l - 5*l**3 - 2*l**x + 3*l**4 + 2*l**4 = 0.
-2, 1
Let z(a) be the second derivative of a**7/189 + 2*a**6/135 - 7*a**5/90 + 2*a**4/27 + 2*a - 71. Let z(r) = 0. Calculate r.
-4, 0, 1
Let p(n) = 4*n + 7. Let s be p(-2). Let c = s - -3. Find u such that 0 - 8/5*u - 42/5*u**3 - 98/5*u**4 + 48/5*u**c = 0.
-1, 0, 2/7
Let i be ((-8398)/(-133))/((-9)/(-14)). Let a = i - 98. Factor a*x**2 + 0 - 2/9*x.
2*x*(x - 1)/9
Find i, given that 0 + 160/7*i - 22/7*i**2 - 2/7*i**3 = 0.
-16, 0, 5
Let t = 1114 + -1110. Let m(g) be the third derivative of 2/105*g**7 + 0*g**6 + 0*g**3 + 0 - 4*g**2 + 0*g**t + 0*g - 1/15*g**5. Factor m(v).
4*v**2*(v - 1)*(v + 1)
Suppose -5*s = -0*s - 3*p + 1137, 0 = 5*s + 2*p + 1117. Let j = s + 1577/7. Factor 2/7*w**2 + j*w**3 + 0 - 2/7*w - 2/7*w**4.
-2*w*(w - 1)**2*(w + 1)/7
Let m(d) be the first derivative of d**4/9 + 12*d + 20. Let z(l) be the first derivative of m(l). Find t such that z(t) = 0.
0
Let -6/7*v**3 + 5/7*v - 4/7*v**2 + 0 + 4/7*v**4 + 1/7*v**5 = 0. Calculate v.
-5, -1, 0, 1
Let x(c) be the second derivative of c**6/75 + 8*c**5/25 + 31*c**4/10 + 46*c**3/3 + 40*c**2 - 13*c - 9. Factor x(j).
2*(j + 2)*(j + 4)*(j + 5)**2/5
Let u = -11024/7 + 1575. Factor 2/7*i + 0 + u*i**2.
i*(i + 2)/7
Let c = -1696/3 - -568. Factor -16/3 + c*d + 7/3*d**2 + 1/3*d**3.
(d - 1)*(d + 4)**2/3
Let a(y) be the first derivative of -16*y**3/9 - 5*y**2 + 4*y/3 + 34. Factor a(x).
-2*(x + 2)*(8*x - 1)/3
Let i(r) = 37*r - 6. Let f be i(7). Suppose 4*p - 5*p + f = 0. Solve -p*b**2 + 253*b**2 + 3*b - 3*b**3 = 0.
-1, 0, 1
Let a(u) be the first derivative of 3*u**5/10 - 27*u**4/2 + 162*u**3 - 97. Let a(c) = 0. Calculate c.
0, 18
Suppose 0 = -l - l - 0*l. Let i be 15*(l + 4/10) - 3. Factor 5/4*c + 5/2*c**2 + 1/4 + 5/4*c**4 + 1/4*c**5 + 5/2*c**i.
(c + 1)**5/4
Let d(z) = 10*z**3 - 4*z**2 - 18*z + 4. Let r(c) = 7*c**3 - 3*c**2 - 12*c + 3. Suppose -5*v - 8 = -6*v. Let a(k) = v*r(k) - 5*d(k). Suppose a(n) = 0. What is n?
-1, 2/3, 1
Let r(l) be the third derivative of l**9/70560 + l**8/70560 - l**7/8820 + l**5/15 - 3*l**2. Let u(o) be the third derivative of r(o). Solve u(k) = 0 for k.
-1, 0, 2/3
Let z(k) = -3*k**2 - 6*k + 7*k + 2 + 2*k**2 - 3. Let t(d) = -d**2 + 6*d + 2. Let g(h) = 5*t(h) - 10*z(h). Factor g(l).
5*(l + 2)**2
Let 5*h**2 - 41*h - 34*h + 15*h - 140 = 0. What is h?
-2, 14
Let w(v) = v**2 - 2. Let j be w(-3). Suppose 3 = -2*y + j. Factor 2 - 6*m**y + 7*m**2 + m - 4*m.
(m - 2)*(m - 1)
Find o, given that 10 + 6 + 22*o**2 + 8*o**3 - 21*o - 4*o**4 - 11*o - 10*o**2 = 0.
-2, 1, 2
Solve 1/6*g**3 + 1/6*g**2 - 1/6*g - 1/6 = 0 for g.
-1, 1
Let l(q) = 10*q**3 - 12*q**2 + 6*q + 12. Let v(g) = 32*g**3 - 36*g**2 + 17*g + 39. Let h(j) = 13*l(j) - 4*v(j). Factor h(r).
2*r*(r - 5)*(r - 1)
Let a(m) be the third derivative of m**6/3 - 3*m**5/10 + m**4/12 + 2*m**2 - 48*m. Factor a(j).
2*j*(4*j - 1)*(5*j - 1)
Solve -16/7*l + 2/7*l**2 - 18/7 = 0.
-1, 9
Let z(w) be the first derivative of 16/5*w + 484/15*w**3 + 15 + 88/5*w**2. Let z(d) = 0. Calculate d.
-2/11
Let d be 4/5*(-20)/(-8). Suppose 3 = d*v - 3. What is t in -2*t**4 - 3*t + 6*t**3 - 16*t**2 - 13*t**3 - v*t**3 - 5*t = 0?
-2, -1, 0
Let a(n) = n**2 - n + 1. Let r(g) = 0*g - 7*g + 6 + 1436*g**2 - 1428*g**2. Let q(y) = -35*a(y) + 5*r(y). Factor q(j).
5*(j - 1)*(j + 1)
Let p(d) = 5*d + 1. Let z be p(1). Let z*w**3 + 4 - w**2 - w**2 - 2*w**4 + 0*w**3 - 6*w = 0. Calculate w.
-1, 1, 2
Let w(m) = -12*m**3 - 6*m**2 - 10. Let z(q) = q**3 + q**2 + 1. Let o(t) = 2*w(t) + 20*z(t). Factor o(r).
-4*r**2*(r - 2)
Let b(v) be the third derivative of -2*v**6/15 - 131*v**5/15 - 95*v**4/6 + 64*v**3/3 + 634*v**2. Factor b(w).
-4*(w + 1)*(w + 32)*(4*w - 1)
Let w(n) be the second derivative of -n**7/14 + n**6/5 + 3*n**5/5 - n**4/2 - 3*n**3/2 - 62*n. Determine r, given that w(r) = 0.
-1, 0, 1, 3
Suppose q + 3*q = 72. Factor -28*o**2 + 9*o + 13*o**2 + q*o**2.
3*o*(o + 3)
Solve 5*t**5 + t**3 + 0 + 0*t - 21/2*t**4 + 0*t**2 = 0 for t.
0, 1/10, 2
Let y(m) = m**2 + 13*m - 13. Let i be 7/(2/7 + 187/(-238)). Let j be y(i). Factor j + 5/3*o**2 + 1/3*o**3 + 7/3*o.
(o + 1)**2*(o + 3)/3
Let b = 34 - 16. Suppose 3*m - 2*m - r = 0, 5*m + 4*r - b = 0. What is a in -1 - 4*a**2 + 3*a**m + 4*a**2 + 3*a + a**2 = 0?
-1, 1/4
Let o(b) be the third derivative of -b**6/720 + b**5/5 - 9*b**4 + 106*b**2. Solve o(p) = 0 for p.
0, 36
Let z(w) be the second derivative of 41*w + 2/3*w**3 + 3/2*w**2 + 1/12*w**4 + 0. Factor z(j).
(j + 1)*(j + 3)
Let f(g) be the second derivative of g**4/2 + 23*g**3/2 + 45*g**2 + 625*g. Factor f(o).
3*(o + 10)*(2*o + 3)
Let u(k) = -2*k**3 + 74*k**2 + 85*k - 332. Let c be u(38). Solve c*w - 50 - 1/2*w**2 = 0.
10
Let w(f) be the third derivative of f**5/60 + 7*f**4/12 + 13*f**3/6 - 23*f**2 - 4. Factor w(x).
(x + 1)*(x + 13)
Let u be 8/2*(-72)/(-16). Factor -u*g**2 + 35*g**2 - 37*g - 43*g + 20 + 58*g**2.
5*(3*g - 2)*(5*g - 2)
Suppose 12*r = 99 - 363. Let p = r + 22. Factor 0 - 1/4*k**5 + 0*k**2 - 1/4*k + p*k**4 + 1/2*k**3.
-k*(k - 1)**2*(k + 1)**2/4
Factor 0 + 0*l - 1/6*l**2 - 1/6*l**4 + 1/3*l**3.
-l**2*(l - 1)**2/6
Solve -48/7*i + 4/7*i**3 + 64/7 + 0*i**2 = 0 for i.
-4, 2
Suppose 55*n = -3*p + 56*n - 6, 30 = -5*p + 5*n. Factor 3/2*r**2 - 9/2*r**4 + p*r**3 + 3*r**5 + 0 + 0*r.
3*r**2*(r - 1)**2*(2*r + 1)/2
Let l = -67 + 71. Let a(g) be the second derivative of 0*g**3 + 7*g + 0*g**2 + 1/54*g**l + 1/189*g**7 + 0 - 1/90*g**5 - 1/135*g**6. Suppose a(p) = 0. What is p?
-1, 0, 1
Let v(l) be the third derivative of l**5/12 - 65*l**4/24 + 10*l**3 + 5*l**2 + 56*l. Let v(y) = 0. What is y?
1, 12
Let c(z) = 7*z**3 - 37*z**2 - 83*z - 47. Let k(u) = -9*u**3 + 38*u**2 + 83*u + 48. Let x(b) = -6*c(b) - 5*k(b). Let x(n) = 0. What is n?
-7, -3, -2/3
Let t(s) be the third derivative of 13/12*s**4 - 2*s**3 + 0*s + 0 + 38*s**2 + 1/6*s**5. Find h such that t(h) = 0.
-3, 2/5
Let t = -1233933/209 + 5904. Let r = 642/1045 - t. Suppose 0 - r*a - 3/5*a**2 = 0. Calculate a.
-1, 0
Let y(p) be the second derivative of -p**5/30 - p**4/6 + p**3 + 3*p**2/2 - 19*p. Let h(s) be the first derivative of y(s). Factor h(v).
-2*(v - 1)*(v + 3)
Let n(s) = 9*s**2 - 288*s + 275. Let d(b) = 8*b**2 - 286*b + 275. Let j(z) = 4*d(z) - 3*n(z). Suppose j(x) = 0. What is x?
1, 55
Let n(x) be the second derivative of x**7/21 - 56*x**6/15 + 363*x**5/5 + 812*x**4/3 + 841*x**3/3 + 712*x. Let n(g) = 0. Calculate g.
-1, 0, 29
Suppose -218 + 20 = -6*z. Let t = z - 31. Factor 3/7*f**t - 12/7 + 0*f.
3*(f - 2)*(f + 2)/7
Let m be 21/30*12/7. Let r be ((-918)/(-15))/17 - 2*1. Determine g so that -r + m*g**2 - 8/5*g = 0.
-2/3, 2
Let z(q) be the first derivative of q**4/20 - 4*q**3/15 - q**2/2 - 49. Find i, given that z(i) = 0.
-1, 0, 5
Let w(i) be the third derivative of -1/280*i**7 + 1/240*i**6 - 7*i**2 + 0*i**4 + 0 + 0*i + 0*i**3 + 1/240*i**5. Factor w(a).
-a**2*(a - 1)*(3*a + 1)/4
Let f = -6 - -8. Factor -9*d**4 + 4*d**4 + 3*d**2 + f*d**2.
-5*d**2*(d - 1)*(d + 1)
Let r(a) be the second derivative of a**7/7560 + a**6/2160 - a**5/60 + a**4/3 + 15*a. Let y(d) be the third derivative of r(d). Factor y(o).
(o - 2)*(o + 3)/3
Let l(d) be t