for f.
-17, -3, -2, -1, 0
Let n(z) be the second derivative of 1/4*z**4 - 9/40*z**5 + 3/4*z**3 - 2 - 25*z - 15/8*z**2 + 1/40*z**6. Solve n(t) = 0 for t.
-1, 1, 5
Let p = -88894 + 88909. Let 1/4*v**2 + 225 + p*v = 0. What is v?
-30
Let f(g) = 5*g**2 - 31*g. Let d = 164 - 169. Let v(s) = -9*s**2 + 61*s. Let j(o) = d*f(o) - 3*v(o). Factor j(l).
2*l*(l - 14)
Suppose 18*j - 20 = 8*j. Factor 2 + 159*q**j + 102 + 61 + 327*q - 3*q**3.
-3*(q - 55)*(q + 1)**2
Let s(f) be the first derivative of -f**6/57 + 24*f**5/95 - 24*f**4/19 + 128*f**3/57 + 4982. Factor s(z).
-2*z**2*(z - 4)**3/19
Let v(b) be the second derivative of 51*b + 1/4*b**5 + 0*b**3 + 0*b**2 - 5/12*b**4 + 0 - 5/42*b**7 + 1/6*b**6. Find q such that v(q) = 0.
-1, 0, 1
Let a(s) be the third derivative of -s**7/2016 + s**6/1440 - 4*s**4/3 + s**3/3 - 2*s**2 + 1. Let v(w) be the second derivative of a(w). Solve v(y) = 0 for y.
0, 2/5
Suppose 306*z = -17*z + 8*z + 3150. Suppose -15 + 115/2*n + z*n**2 = 0. What is n?
-6, 1/4
Let r = 489/113 - 418811/791. Let k = r - -526. Factor 0*y**3 + 3/7 - k*y**2 + 0*y + 3/7*y**4.
3*(y - 1)**2*(y + 1)**2/7
Suppose 5*m = 3*f - 72, 2*m - 3*f - f + 26 = 0. Let l be 2 - 0*(-4 + (-65)/m). What is q in -8/9*q + 8/9 + 2/9*q**l = 0?
2
Find y such that 180*y**4 + 24167 + 2864*y**3 + 4*y**5 + 37632*y - 5397 + 3182 + 19889*y**2 - 1521*y**2 = 0.
-14, -2, -1
Find c, given that 98 + 296/3*c + 2/3*c**2 = 0.
-147, -1
Let o(f) be the third derivative of 1/1260*f**7 - 1/240*f**6 + 0*f + 0*f**3 - 1/360*f**5 + 0 + 1/72*f**4 + 13*f**2 + 1/2016*f**8. Factor o(b).
b*(b - 1)**2*(b + 1)*(b + 2)/6
Solve -103096*m**3 + 2432 - 25504*m + 23488*m**2 + 18079*m**2 + 47473*m**2 - 1372*m**4 = 0.
-76, 2/7
Let v(t) be the third derivative of -t**6/1020 - 19*t**5/85 - 56*t**4/51 - 1112*t**2. Determine z so that v(z) = 0.
-112, -2, 0
Let v(b) be the third derivative of -b**7/1365 - 17*b**6/390 - b**5/6 - 8*b**4/39 - 21*b**2 - 2*b. Factor v(k).
-2*k*(k + 1)**2*(k + 32)/13
Suppose 527*m - 56 = 519*m. Suppose 57 = 12*k + m*k. What is i in 3/5*i**5 + 0 + 12/5*i**4 + 6/5*i**2 + 0*i + 3*i**k = 0?
-2, -1, 0
Let q = -232 - -387. Let -145*x - 81 + 282*x - x**2 - q*x = 0. Calculate x.
-9
Suppose 44 - 12 = -t - 2*u, 0 = -u + 2. Let z be (9 - (-276)/t)/(4/10). Factor -7/3*k**2 + z*k - 1.
-(k - 1)*(7*k - 3)/3
Let k(r) = 3*r**3 - 93*r**2 - 3*r - 3. Let z(q) = 2*q**3 - q**2 - q - 1. Let s(x) = -k(x) + 3*z(x). Factor s(g).
3*g**2*(g + 30)
Let h(c) be the second derivative of -12/5*c**2 - 21/100*c**5 - 9/10*c**4 - 1/50*c**6 - 20*c + 0 - 2*c**3. Factor h(g).
-3*(g + 1)*(g + 2)**3/5
Let d(h) = h**2 + 7*h - 42. Let i be d(-11). Solve -242 + 554 - 160*k - k**i + 1288 + 5*k**2 = 0 for k.
20
Let c = 47379/2 + -23689. Let v(g) be the first derivative of -2*g**3 + c*g**4 - 2*g + 4 + 3*g**2. Factor v(z).
2*(z - 1)**3
Let h(q) = 160*q - 640. Suppose -12 = 12*d - 15*d. Let x be h(d). Factor 8/3*b**3 + x + 20/3*b**4 + 0*b + 0*b**2 - 4*b**5.
-4*b**3*(b - 2)*(3*b + 1)/3
Let q(y) be the third derivative of -y**5/60 - 15*y**4/8 + 34*y**3/3 + 2*y**2 - 132*y. Let f(t) = -42*t + 69. Let s(x) = 4*f(x) - 3*q(x). What is c in s(c) = 0?
3, 8
Let l(w) = -w**5 - w**3 + w - 2. Let m(y) = 14*y**5 + 40*y**4 + 104*y**3 + 40*y**2 - 109*y - 62. Let p(u) = 9*l(u) + m(u). Find t such that p(t) = 0.
-4, -2, -1, 1
Let v(z) be the first derivative of -21/5*z + 14 + z**3 - 3/5*z**2. Let v(u) = 0. What is u?
-1, 7/5
Determine p, given that -165*p**4 - 1620385*p**2 - 2645*p**3 + 1838736*p - 212927*p**2 - 3524*p**3 + 749*p**3 + 161*p**4 = 0.
-678, 0, 1
Let i(k) = k**3 + 4*k**2 - 5*k - 17. Let v be i(-4). Factor -225 - 88*p - v*p**2 + 2*p**2 + 118*p.
-(p - 15)**2
Let n(j) be the first derivative of 35/4*j**4 + 30*j + 42 + 20/3*j**3 - 85/2*j**2. Determine v so that n(v) = 0.
-2, 3/7, 1
Let c(f) be the third derivative of -f**8/1176 + 8*f**7/735 + f**6/20 - 4*f**5/105 - 5*f**4/21 - 3*f**2 + 4*f - 21. Let c(q) = 0. Calculate q.
-2, -1, 0, 1, 10
Let c(a) = -15*a**3 + 35*a**2 + 440*a - 472. Let k(h) = -102*h**3 + 246*h**2 + 3081*h - 3306. Let w(x) = -27*c(x) + 4*k(x). Factor w(d).
-3*(d - 20)*(d - 1)*(d + 8)
Let a(f) = 6*f**2 - 5891*f + 1440534. Let z(u) = 2*u**2 - 1964*u + 480176. Let x(b) = -4*a(b) + 11*z(b). What is t in x(t) = 0?
490
Suppose -d = -2*t + 5*t - 1966, 4*t + 5*d = 2603. Suppose -4*y - t = -5*s, -s - 3*y = y - 117. Factor -7*x + 28*x**2 + 32 - s*x + 16*x.
4*(x - 4)*(7*x - 2)
Factor 29*f**4 - 3*f**3 + 12*f + 0*f**2 + 27*f**4 - 87*f**4 + 28*f**4 + 12*f**2.
-3*f*(f - 2)*(f + 1)*(f + 2)
Suppose -119*d**2 + d**5 + 145*d**4 + 39*d**2 + 7*d**3 - 197*d**3 - 16*d**5 = 0. Calculate d.
-1/3, 0, 2, 8
Let n = -4078 + 6260. Let i = n - 28306/13. Find x such that i*x**2 + 46/13*x - 18/13*x**3 + 8/13 = 0.
-1/3, 4
Let m(h) be the second derivative of -h**5/20 - 17*h**4/12 - 19*h**3/3 + 28*h**2 + 1017*h. Factor m(d).
-(d - 1)*(d + 4)*(d + 14)
Let v(w) = w**3 + w**2 + 11*w + 55. Let p be v(-3). Let b(c) be the second derivative of -c**3 + 0*c**2 + 0 + 0*c**5 - 3/4*c**p + 1/10*c**6 - 13*c. Factor b(g).
3*g*(g - 2)*(g + 1)**2
Suppose 463*m - 1736 = 456*m. Let w = -248 + m. Factor 1/4*h**5 + 0*h**2 + 0*h - 1/4*h**4 + w + 0*h**3.
h**4*(h - 1)/4
Let o(v) be the second derivative of -v**7/504 + v**6/72 + 5*v**5/8 - 6*v**4 + 29*v - 1. Let g(u) be the third derivative of o(u). Determine x so that g(x) = 0.
-3, 5
Suppose 0 = c - 5*q - 5, 0 = 2*c - 8*c + q + 1. Let b(z) be the second derivative of 3/5*z**5 + 0*z**2 - 3/4*z**4 - 1/2*z**3 - 27*z + c. Factor b(h).
3*h*(h - 1)*(4*h + 1)
Suppose -61*h + 86*h = -30150. Let x = h - -3620/3. Factor -x*y**2 + 0 + 1/3*y**3 + 1/3*y.
y*(y - 1)**2/3
Let a(z) be the first derivative of 8*z**2 - 1/5*z**5 + 0*z**3 - z**4 - 30*z + 21. Let f(o) be the first derivative of a(o). Factor f(k).
-4*(k - 1)*(k + 2)**2
Suppose 0 = -11*h + 694 + 10647. Let c = h + -1027. Factor 0 - 2/3*w**3 - 1/3*w**c + 0*w - 1/3*w**2.
-w**2*(w + 1)**2/3
Let h = -16731 - -16750. Let b(d) be the first derivative of 0*d**2 + 1/3*d**3 - 1/5*d**5 - 1/8*d**4 + 1/12*d**6 + 0*d + h. Determine p so that b(p) = 0.
-1, 0, 1, 2
Let s(l) be the first derivative of 3*l**5/25 + 81*l**4/2 + 18493*l**3/5 + 10854*l**2 + 53868*l/5 + 6315. Find b, given that s(b) = 0.
-134, -1
Let r(c) be the third derivative of -c**8/672 - 37*c**7/420 + 13*c**6/40 - 422*c**2. Factor r(b).
-b**3*(b - 2)*(b + 39)/2
Let z(a) be the first derivative of a**6/30 - 27*a**5/25 - 89*a**4/20 - 11*a**3/5 + 44*a**2/5 + 12*a + 97. Find r such that z(r) = 0.
-2, -1, 1, 30
Let p(x) = -4*x**2 + 69*x - 10. Let a(g) = 17*g**2 - 140*g + 21. Let o(y) = 4*a(y) + 9*p(y). Determine h, given that o(h) = 0.
-2, 3/32
Let b(j) be the second derivative of j**5/40 + 687*j**4/8 + 471969*j**3/4 + 324242703*j**2/4 + 7*j + 392. Find r such that b(r) = 0.
-687
Suppose 26*h - 483 = 765. Suppose -h - 191*s**3 + 378*s**3 - 96*s + 3*s**4 - 181*s**3 - 45*s**2 = 0. Calculate s.
-4, -1, 4
Let a(v) be the first derivative of 0*v + 5/4*v**4 - 5*v**3 + 47 + 5*v**2. Factor a(c).
5*c*(c - 2)*(c - 1)
Factor -1025*d**3 - 804*d + 30 - 682*d - 1338*d + 1859*d - 2020*d**2.
-5*(d + 1)**2*(205*d - 6)
Suppose 3*u = 2*u - 1. Let b be (-87)/(-58)*(u - 19/(-3)). Factor 2*q**2 + 46 + 0*q**3 - b*q**3 - 48 + 8*q.
-2*(q - 1)*(q + 1)*(4*q - 1)
Let j(q) be the third derivative of -q**6/40 - 19*q**5/20 - 214*q**2 - 6. Factor j(u).
-3*u**2*(u + 19)
Let r(o) = -25*o**4 + 127*o**3 + 18*o**2 - 1836*o - 2528. Let x(i) = -9*i**4 + 42*i**3 + 6*i**2 - 612*i - 843. Let m(l) = 3*r(l) - 8*x(l). Solve m(j) = 0 for j.
-2, 5, 14
Let p be 0*(-2 + (-4 - -5)). Suppose z + 6*z - 28 = p. Determine n so that n**3 + 0*n + 0*n**4 + 8*n**2 - 4*n**4 - 4*n - 4*n**z + 3*n**5 = 0.
-1, 0, 2/3, 1, 2
What is l in -35*l + 40 + 15/2*l**2 = 0?
2, 8/3
Let z(m) be the second derivative of m**7/12600 + m**6/3600 - m**5/300 - 155*m**4/12 + 17*m + 3. Let r(n) be the third derivative of z(n). Factor r(l).
(l - 1)*(l + 2)/5
Let n(s) be the third derivative of 1/420*s**6 - 1/28*s**4 + 0*s**3 - 18*s**2 + 0 + 1/420*s**5 + 0*s. Let n(w) = 0. What is w?
-2, 0, 3/2
Let h be 2/37 - -377*32/61568. Factor 0 + h*y**4 + 1/4*y - 1/4*y**2 - 1/4*y**3.
y*(y - 1)**2*(y + 1)/4
Let u(y) be the second derivative of -y**4/3 + 40*y**3/3 + 138*y**2 + 553*y. Find r such that u(r) = 0.
-3, 23
Let u(l) = -463*l + 5. Let n