-23. Let 4/3*v + 1/3*v**z + 4/3 = 0. What is v?
-2
Suppose 0 = z - 2*z + 77. Let o = 391/5 - z. Factor 0*m + 2/5*m**5 - o*m**3 - 4/5*m**2 + 0*m**4 + 0.
2*m**2*(m - 2)*(m + 1)**2/5
Let s(t) = -t**3 + 7*t**2 - 6*t + 2. Let a be s(6). Determine n so that 9 + 5 + 10*n - 2*n**a - 26 = 0.
2, 3
Let c(m) be the third derivative of 39*m**2 + 0 - 1/40*m**6 + 0*m**4 + 0*m + 1/420*m**7 + 0*m**3 - 7/120*m**5. Determine t, given that c(t) = 0.
-1, 0, 7
Factor -45535 + 1458*r - 51972 - 3*r**2 - 79640.
-3*(r - 243)**2
Factor 2/3*k**2 - 50/3*k + 92/3.
2*(k - 23)*(k - 2)/3
Let x(c) be the first derivative of c**6/30 - 2*c**5/15 - 7*c**4/6 - 8*c**3/3 + 6*c**2 - 7. Let y(p) be the second derivative of x(p). Factor y(s).
4*(s - 4)*(s + 1)**2
Factor -11 - 33 + 83*m - 6 - 68*m + 5*m**2.
5*(m - 2)*(m + 5)
Suppose 3*i - 4*g - 17 = 0, -5*g - 13 = 2*i - 3*i. Determine w so that 3 + 168*w**2 - i - 4*w**3 - 172*w**2 = 0.
-1, 0
Let o be 9/(-90)*85 - -10. Let 3/2 - o*g**2 + 3/4*g - 3/4*g**3 = 0. What is g?
-2, -1, 1
Let j(d) be the first derivative of -2*d**5/5 + 49*d**4 - 1534*d**3 - 4900*d**2 - 5000*d - 12. Factor j(l).
-2*(l - 50)**2*(l + 1)**2
Factor -7*k**3 - 78*k**2 - 3*k**3 - 465 + 13*k**3 + 576*k + 8 - 407.
3*(k - 12)**2*(k - 2)
Let y(u) = -9*u**4 - 25*u**3 + 3*u**2 + 9*u - 10. Let b(a) = -a**4 - 2*a**3 - a**2. Let s(l) = -40*b(l) + 5*y(l). What is q in s(q) = 0?
-10, -1, 1
Let a = -800 + 800. Factor -2*t**2 + a + 2*t + 1/2*t**3.
t*(t - 2)**2/2
Factor 4/7*r - 12/7 + 1/7*r**2.
(r - 2)*(r + 6)/7
Suppose 45*f**3 + 57*f**3 + 9*f + 11 - 12*f**2 + 11 - 101*f**3 = 0. Calculate f.
-1, 2, 11
Let z(l) be the first derivative of -5*l**3/3 - 15*l**2/2 + 20*l + 72. Find i such that z(i) = 0.
-4, 1
Let t(f) be the first derivative of f**5/330 - f**4/66 + 35*f**2/2 + 34. Let u(m) be the second derivative of t(m). Let u(c) = 0. What is c?
0, 2
Let x = -23 - -58. Let o = -32 + x. Solve -2/3*q + 0*q**4 + 0 - 2/3*q**5 + 4/3*q**o + 0*q**2 = 0.
-1, 0, 1
Solve 0 + 2/7*f**4 - 8/7*f**3 + 6/7*f**2 + 0*f = 0.
0, 1, 3
Let x(k) = -k**3 + k**2 + k. Let c(z) = 24*z**3 + 128*z**2 - 60*z. Let y(l) = -c(l) - 4*x(l). Let y(o) = 0. Calculate o.
-7, 0, 2/5
Let z(n) be the first derivative of n**5/90 + n**4/18 + n**3/9 + 4*n**2 + 4. Let q(y) be the second derivative of z(y). Solve q(o) = 0 for o.
-1
Let q = -469 - -22513/48. Let g(b) be the third derivative of -2*b**2 + 0*b + q*b**4 - 1/8*b**3 + 0 + 1/240*b**5. Determine n, given that g(n) = 0.
-3, 1
Let h be 0*(5 - -1)/6. Let k be (((-45)/(-10))/9 - h)*0. Factor 1/7*f**4 - 1/7*f**2 + k + 0*f**3 + 0*f.
f**2*(f - 1)*(f + 1)/7
Let x(s) be the third derivative of s**8/1008 - s**7/14 + 19*s**6/12 - 145*s**5/18 + 455*s**4/24 - 49*s**3/2 - 3*s**2 + 10*s. Factor x(v).
(v - 21)**2*(v - 1)**3/3
Let q(b) = 2*b**2 + 12*b - 10. Let y be q(-7). Find s such that 3*s**3 + 6 + 2*s**y - 9*s**2 + 5*s**4 - 5*s**4 - 3*s + s**4 = 0.
-2, -1, 1
Let t = -2363/3 - -7881/10. Let a = -1/10 + t. Factor -a*n**2 + 1/3*n**4 - 1/3*n**3 + 0 + 1/3*n**5 + 0*n.
n**2*(n - 1)*(n + 1)**2/3
Suppose 0 = 17*q - 22*q + 50. Let h be (-1 + 11)*5/q. Suppose 16*y**4 - 20*y**2 + 9*y**5 + 4 + 0*y**2 - 3*y**h - y - 5*y = 0. What is y?
-2, -1, 1/3, 1
Let r(k) be the second derivative of 1/10*k**5 - 1/12*k**4 + 0 + 1/15*k**6 - 5/12*k**3 + 1/84*k**7 - 1/2*k**2 + 9*k. Determine x so that r(x) = 0.
-2, -1, 1
Let f(q) be the third derivative of -q**5/12 + 65*q**4/24 - 10*q**3 + 13*q**2 - 6. Determine c, given that f(c) = 0.
1, 12
Factor -1426 + 146 + 2094*m**2 - 2131*m**2 + m**3 + 6*m + 410*m.
(m - 16)**2*(m - 5)
Let w(s) = s**5 + s**3 + 2*s**2 + 1. Let v(g) = -6*g**5 + 38*g**4 + 116*g**3 + 72*g**2 - 5. Let k(u) = -3*v(u) - 15*w(u). Find y such that k(y) = 0.
-2, -1, 0, 41
Let b(q) be the first derivative of 1/24*q**4 + 0*q**2 - 6 - 1/6*q**3 - 12*q. Let v(z) be the first derivative of b(z). Factor v(s).
s*(s - 2)/2
Let o(r) be the first derivative of 23 + 3/11*r**4 - 2/55*r**5 + 12/11*r**2 - 26/33*r**3 - 8/11*r. Suppose o(c) = 0. What is c?
1, 2
Let r = 96 - 128. Let b be 15/((-15)/(-2)) - r/(-18). Determine n, given that -2/9*n**4 + 0 + b*n**2 - 2/9*n + 2/9*n**3 = 0.
-1, 0, 1
Let n(f) be the second derivative of -f**7/10 + 37*f**6/50 - 177*f**5/100 + 7*f**4/4 - 3*f**3/5 - 171*f. Suppose n(p) = 0. What is p?
0, 2/7, 1, 3
Let -1139 - 2088*m**2 + 542 - 1931 + 321*m - 2880 - 8017*m + 196*m**3 - 4*m**4 = 0. Calculate m.
-2, -1, 26
Factor 84*n**3 + 0 + 3/4*n**5 + 441*n**2 + 0*n - 75/4*n**4.
3*n**2*(n - 14)**2*(n + 3)/4
Let y = -1610 + 1613. Let m(x) be the second derivative of 1/255*x**6 + 12*x + 1/51*x**y + 0*x**2 + 3/170*x**5 + 1/34*x**4 + 0. Let m(r) = 0. Calculate r.
-1, 0
Factor 464*q**2 - 31*q - 46 - 98 - 467*q**2 - 40*q - 7*q.
-3*(q + 2)*(q + 24)
Let a(i) be the first derivative of 3*i**5/10 - 6*i**4 + 23*i**3 + 108*i**2 + 243*i/2 + 41. Find j, given that a(j) = 0.
-1, 9
Let n(g) be the first derivative of 48 + 2/3*g**3 + 1/2*g**4 + 0*g - 2*g**2. Factor n(z).
2*z*(z - 1)*(z + 2)
Suppose 2*w = 2*q + w - 7, -5*w + 7 = 4*q. Let h(o) be the first derivative of 4*o - o**4 - 8 - 4/3*o**q + 2*o**2. Suppose h(a) = 0. Calculate a.
-1, 1
Let b(a) be the first derivative of 4*a**5/35 + 2*a**4 + 76*a**3/7 + 152*a**2/7 + 128*a/7 + 43. Factor b(v).
4*(v + 1)**2*(v + 4)*(v + 8)/7
Find z such that 1/4 + 1/4*z**3 - 1/4*z**2 - 1/4*z = 0.
-1, 1
Let w(h) be the first derivative of h**5/25 + 27*h**4/20 - h**3/15 - 27*h**2/10 - 176. Factor w(c).
c*(c - 1)*(c + 1)*(c + 27)/5
What is t in -3*t - 45*t**2 - 15*t + 26*t**3 - 249*t**4 - 1 + 246*t**4 + 1 = 0?
-1/3, 0, 3, 6
Let c(g) be the second derivative of g**5/240 - g**4/96 - g**3/12 - 21*g**2/2 + 27*g. Let p(x) be the first derivative of c(x). Solve p(j) = 0 for j.
-1, 2
Let m = -96 + 99. Let r(t) be the third derivative of -6*t**2 + 1/180*t**6 - 1/108*t**4 + 1/135*t**5 + 0 + 0*t + 0*t**m. Factor r(d).
2*d*(d + 1)*(3*d - 1)/9
Let u = -1672/9 + 1696/9. Let -28/3*o - 49/6 - u*o**2 = 0. What is o?
-7/4
Suppose 4*l + 34 = 82. Suppose 2*o + o - l = 0. Factor -6*h**3 + 2*h**2 - 4*h**o - 4*h**2 - h**4 - 2*h**5 - h**4.
-2*h**2*(h + 1)**3
Let w = 6366/119 - 372/7. Factor 14/17*b + 10/17*b**2 + 2/17*b**3 + w.
2*(b + 1)**2*(b + 3)/17
Factor 33*z + 21*z - 4*z**2 + 28 - 352 + 18*z.
-4*(z - 9)**2
Let r = 210 - 206. Let q(f) be the first derivative of -7/16*f**4 - 1/6*f**3 + 1/2*f - r + 7/8*f**2. Suppose q(l) = 0. Calculate l.
-1, -2/7, 1
Factor -9*a - 3*a**5 - 3 + 9 - 9*a**2 + 6*a**3 + 6*a**3 + 3*a**2.
-3*(a - 1)**3*(a + 1)*(a + 2)
Let z(v) = v**3 + 5*v**2 - 4*v + 4. Let a(b) = 2*b**3 + 6*b**2 - 5*b + 5. Suppose -r + 3 = -4*r. Let h be (r + 5)/2*-2. Let j(t) = h*a(t) + 5*z(t). Factor j(q).
-q**2*(3*q - 1)
Let a(j) be the second derivative of -49*j**4/24 - 77*j**3/6 - 121*j**2/4 - 92*j. Factor a(f).
-(7*f + 11)**2/2
Let u(c) be the second derivative of -c**8/80640 - c**7/30240 + c**6/1728 - c**5/480 + 5*c**4/12 + c. Let i(x) be the third derivative of u(x). Factor i(a).
-(a - 1)**2*(a + 3)/12
Let o(i) be the second derivative of 0 - 1/50*i**5 + i - 7/15*i**3 - 3/5*i**2 - 1/6*i**4. Factor o(b).
-2*(b + 1)**2*(b + 3)/5
Let j be ((-2)/(-24))/(26/(624/36)). Let z(v) be the first derivative of 5 - 2/9*v**2 - 2/27*v**3 + 0*v + j*v**4. Factor z(p).
2*p*(p - 2)*(p + 1)/9
Factor -324 + 26*q + 17*q + 11*q + 36*q + 32*q**2 + 2*q**3.
2*(q - 2)*(q + 9)**2
Let z = 71 + -69. Solve 5*v**2 - 6*v**2 - 2*v**3 - 9*v**z = 0 for v.
-5, 0
Let n(t) be the first derivative of 0*t**2 + 0*t + 1/240*t**6 - 4 + t**3 + 0*t**5 - 1/16*t**4. Let y(j) be the third derivative of n(j). Solve y(p) = 0.
-1, 1
Let k = -8096/3 - -8098/3. Suppose -8 + k*l**2 - 8/3*l = 0. Calculate l.
-2, 6
Let v be -4 + 2 - (-1 - 1). Suppose -3*r + 4*p - 2 = v, -2*p = -5*r + 3*r. Let 6/7*s + 3/7*s**r + 3/7 = 0. What is s?
-1
Factor -8/3*d + 0 + 2*d**2 + 2/3*d**3.
2*d*(d - 1)*(d + 4)/3
Let t = -48 + 57. Suppose -12 = -p - t. Find z such that -2/5*z**p + 2/5 - 6/5*z + 6/5*z**2 = 0.
1
Let p(t) be the first derivative of 1/4*t**2 - 18 - 1/18*t**3 - 1/3*t. Factor p(b).
-(b - 2)*(b - 1)/6
Let m be ((-1)/(-2))/(390/828*2). Let u = m + -2/65. Determine p so that p**3 - 1/2*p + 1/2*p**4 - p**2 - u*p**5 + 1/2 = 0.
-1, 1
Let w(a) be the third derivative of -1/228*a**4 + 0*a - 37*a**2 + 2/285*a**5 + 0*a**3 + 0. Factor w(h).
2*h*(4*h - 1)/19
Let q(t) be the 