l(i) be the first derivative of i**6/24 - i**5/5 - 3*i**4/8 + i**3/3 + 5*i**2/8 - 133. Solve l(w) = 0.
-1, 0, 1, 5
Let t be 12/(-90) - (-7266)/(-45). Let o = t + 162. Factor 0 - 2/5*a**3 + 2/5*a + o*a**4 - 2/5*a**2.
2*a*(a - 1)**2*(a + 1)/5
Let b(g) be the second derivative of -1/3*g**4 + 4*g**2 - 2/3*g**3 + 0 + 10*g. Factor b(q).
-4*(q - 1)*(q + 2)
Let v(x) be the first derivative of -x**5/20 + 3*x**4/8 - 2*x**3/3 - 3*x**2/4 + 9*x/4 + 127. Factor v(z).
-(z - 3)**2*(z - 1)*(z + 1)/4
Let j(o) be the first derivative of 2*o**6/15 - 2*o**5/5 + 4*o**3/3 - 2*o**2 + 8*o + 10. Let i(k) be the first derivative of j(k). Factor i(x).
4*(x - 1)**3*(x + 1)
Let o(y) be the first derivative of 6561*y**4/14 - 1944*y**3/7 + 432*y**2/7 - 128*y/21 - 387. Suppose o(n) = 0. Calculate n.
4/27
Let p be 4/(-8) - (-4)/(-8). Let x be -3 - p*138/36. Determine b, given that 0 + 3/2*b**3 + 0*b + 2*b**4 + x*b**5 + 1/3*b**2 = 0.
-1, -2/5, 0
Let v(s) be the third derivative of -s**6/1620 + s**4/27 + 11*s**3/6 + 23*s**2. Let h(j) be the first derivative of v(j). Factor h(d).
-2*(d - 2)*(d + 2)/9
Factor -y + 225*y**5 + 7 + 2*y**3 + 224*y**5 + 7*y**4 - 450*y**5 - 14*y**2.
-(y - 7)*(y - 1)**2*(y + 1)**2
Suppose 7*a + 3*y + 50 = 3*a, 2*a - 3*y = -34. Let h = a - -23. Solve -3*q**4 - q + h*q**2 + 2*q + 5*q = 0 for q.
-1, 0, 2
Let f(h) be the first derivative of 2*h**3/3 + 23*h**2 + 44*h - 120. Factor f(i).
2*(i + 1)*(i + 22)
Factor 5*b - 73*b**2 + 30 + 38*b**2 + 30*b**2.
-5*(b - 3)*(b + 2)
Let w(x) be the third derivative of x**6/30 + 4*x**5/15 - 7*x**4/2 - 5*x**2 + 1. Solve w(l) = 0.
-7, 0, 3
Let z be (-1 + (-13)/(-12))/((-55)/(-880)). Factor 4/3*s**2 - 8/3*s + z.
4*(s - 1)**2/3
Let l = 1120 - 1116. Let w(s) be the third derivative of -10*s**2 - 1/315*s**7 + 0*s**3 - 1/36*s**l + 0*s + 1/90*s**5 + 1/180*s**6 + 0. Factor w(h).
-2*h*(h - 1)**2*(h + 1)/3
Find t, given that 30 - 50*t**2 - 10*t**2 + 5*t**5 - 10*t**3 + 5*t + 7*t**2 + 30*t**4 - 7*t**2 = 0.
-6, -1, 1
Let c(f) be the second derivative of f**5/5 - 28*f**4/3 + 442*f**3/3 - 676*f**2 + 62*f - 3. Solve c(z) = 0.
2, 13
Let m(c) be the second derivative of c**6/135 + c**5/90 - 2*c**4/27 - 4*c**3/27 - 473*c - 2. Factor m(b).
2*b*(b - 2)*(b + 1)*(b + 2)/9
Suppose -6*m = -2*m - 48. Let r(b) be the first derivative of 0 + 5 - b**4 + m*b**3 + 35*b + 73*b - 54*b**2. Suppose r(x) = 0. What is x?
3
Let u(l) = 2*l**2 - 4*l. Suppose d - 196 = 4*p, d - p + 57 = 250. Let y(m) = -m**2 + d - 192. Let v(s) = u(s) + 4*y(s). Determine z, given that v(z) = 0.
-2, 0
Factor 7/2*a**5 + 6*a**4 + 3/2*a**3 + 0 - a**2 + 0*a.
a**2*(a + 1)**2*(7*a - 2)/2
Let j(k) = -k**2 - 2*k + 2. Let r(n) be the second derivative of -n**4/12 + n**3/6 + n**2/2 - 5*n + 3. Let t(d) = j(d) - 2*r(d). Factor t(o).
o*(o - 4)
Let m = 552 - 548. Let g(w) be the second derivative of -1/25*w**5 + 0 - 4/15*w**3 + 0*w**2 - w - 1/5*w**m. Factor g(k).
-4*k*(k + 1)*(k + 2)/5
Let v = -223 + 223. Let m(r) be the first derivative of v*r + 1/3*r**2 + 1 + 4/9*r**3 + 1/6*r**4. Find w such that m(w) = 0.
-1, 0
Let m(y) be the second derivative of 1/36*y**4 - 1/3*y**2 + 1 + 23*y + 1/18*y**3. Factor m(c).
(c - 1)*(c + 2)/3
Factor -105*t**3 - 2*t**4 + 2*t + 438*t**2 - 153*t**3 + 148 + 116*t**3 - 444*t.
-2*(t - 1)**3*(t + 74)
Let n(f) = -6*f + 108. Let x be n(17). Let m(q) be the second derivative of -5*q - 3/10*q**x - 3/10*q**5 - 3/2*q**2 + 1/7*q**7 + 0 + 0*q**3 + q**4. Factor m(w).
3*(w - 1)**3*(w + 1)*(2*w + 1)
Let r be 22/44 + (-279)/566. Let x = r - -4805/849. Suppose -5/3*q**2 - x*q - 2 = 0. Calculate q.
-3, -2/5
Let n(a) be the first derivative of -2*a**5/55 - a**4/11 + 2*a**3/33 + 2*a**2/11 - 88. Suppose n(j) = 0. What is j?
-2, -1, 0, 1
Suppose -5*x + 32 = -2*z, 0*x + 2*z = x. Factor -x*i - i + 15*i - 2*i - 4*i**2.
-4*i*(i - 1)
Let j(q) be the third derivative of q**8/6720 - q**7/840 + q**6/360 - 4*q**3/3 - 6*q**2. Let b(f) be the first derivative of j(f). Factor b(k).
k**2*(k - 2)**2/4
Suppose -58 = -2*n + 46. Suppose 2*m - n = -2*m. Factor -9*y**3 + 4 - 5*y + m*y**3 + y - 4*y**2.
4*(y - 1)**2*(y + 1)
Factor 36/7*a**4 + 9*a**3 + 3/7*a**5 + 30/7*a**2 + 0 + 0*a.
3*a**2*(a + 1)**2*(a + 10)/7
Let v(t) = 7*t**3 + 2*t**2 + 7*t + 6. Let l(q) = q**2 + q. Let k be l(-3). Let g(a) = a**3 + a + 1. Let i(j) = k*g(j) - v(j). Factor i(p).
-p*(p + 1)**2
Let y(x) be the second derivative of x**7/140 + x**6/20 + 3*x**5/40 - x**4/4 - x**3 + 5*x**2 + 3*x. Let g(a) be the first derivative of y(a). Factor g(z).
3*(z - 1)*(z + 1)*(z + 2)**2/2
Let x(h) = 6*h**2 + 3*h - 25. Let g be x(8). Factor -5*p**3 - 388*p**4 + 0*p**3 + g*p**4.
-5*p**3*(p + 1)
Let o = 2/977 - -965/5862. Factor p**3 + 2/3*p**4 + 0 + 1/6*p**5 + o*p + 2/3*p**2.
p*(p + 1)**4/6
Suppose 4 = -19*v - 2*v + 23*v. Factor -1/2*b**v + 1/6*b**4 + 2/3*b + 2/3 - 1/3*b**3.
(b - 2)**2*(b + 1)**2/6
Suppose 29 + 13 = 6*b. Factor -14*a - 3 + 4*a**2 + b*a**2 - 5*a**2 - 9.
2*(a - 3)*(3*a + 2)
Factor -8*n**2 - 2/3*n**3 - 32*n - 128/3.
-2*(n + 4)**3/3
Suppose 5*h + 2*n = 27, 3*h + 2*n = -h + 20. Suppose 0 = -4*y + 62 + 46. Let 0 - y*f**2 + 18*f - h + 4 = 0. What is f?
1/3
Let a be (-1371)/(-12) + 7 - 2/8. Factor 129*g - 232*g + 4*g**2 + 5 + a*g + 3.
2*(g + 4)*(2*g + 1)
Factor -22*y + 67/3 - 45*y**2 - 2/3*y**3.
-(y + 1)*(y + 67)*(2*y - 1)/3
Let c = 41 + -35. Determine q so that 4*q**3 + 465*q + 33*q**4 - 492*q + c + 23*q**3 - 39*q**2 = 0.
-1, 2/11, 1
Let c be (-6 - -46)*(4 - 3). Factor 8*i**4 + 24*i**2 - 52*i**3 - 26*i + c*i**4 - 16*i**5 + 22*i.
-4*i*(i - 1)**2*(2*i - 1)**2
Let g(b) be the second derivative of -3*b**5/20 + 3*b**4/2 - 11*b**3/2 + 9*b**2 + 2*b + 8. Factor g(a).
-3*(a - 3)*(a - 2)*(a - 1)
Let k(z) = -4*z - 3 - 9 + 0*z + 3. Let n be k(-5). Factor 6*q**4 - 2*q**2 + n*q**2 - 9*q**4 + 0*q**4 + 6*q.
-3*q*(q - 2)*(q + 1)**2
Let g(u) be the second derivative of 8*u**7/21 + 22*u**6/15 - 11*u**5/5 - 46*u**4/3 - 40*u**3/3 + 16*u**2 + u - 233. Suppose g(m) = 0. What is m?
-2, -1, 1/4, 2
Factor 4/7*v**2 + 0 - 1/7*v**3 + 5/7*v.
-v*(v - 5)*(v + 1)/7
Factor 0*d**3 + 2/9*d**4 + 4/9*d - 2/3*d**2 + 0.
2*d*(d - 1)**2*(d + 2)/9
Let b(a) be the second derivative of 5/2*a**4 + 4/7*a**2 + 0 - 3*a - 12/7*a**3 - 10/7*a**5. Factor b(g).
-2*(4*g - 1)*(5*g - 2)**2/7
Suppose 2*v - 3*h = -0*v + 12, -23 = -5*v + 4*h. Suppose 3*j + v*j - 12 = 0. Determine x so that 28/5*x**j - 6*x**4 + 2/5 + 14/5*x - 18/5*x**5 + 4/5*x**3 = 0.
-1, -1/3, 1
Suppose 0 = 5*m - 5. Let r = 7 - m. Suppose 8*f**4 - 1 - 24*f**4 + 2*f**2 + 3*f**2 - 24*f**3 + 6*f - r*f**2 = 0. What is f?
-1, 1/4
Let m(g) be the first derivative of g**4/20 + 7*g**3/5 + 39*g**2/10 + 19*g/5 - 16. Factor m(y).
(y + 1)**2*(y + 19)/5
Let u(y) be the first derivative of -y**4/27 + 8*y**3/27 - 2*y**2/3 - 27*y + 1. Let x(r) be the first derivative of u(r). Factor x(m).
-4*(m - 3)*(m - 1)/9
Let s be ((-288)/10)/((-103)/1236). Find w, given that s*w - 2592/5 + 48/5*w**3 - 2/5*w**4 - 432/5*w**2 = 0.
6
Suppose 16 + 2/3*o**4 + 76/3*o**2 + 22/3*o**3 + 104/3*o = 0. What is o?
-6, -2, -1
Suppose 21*q = -15*q + 72. Factor 0*r + 0 + 8/11*r**q - 8/11*r**3 + 2/11*r**4.
2*r**2*(r - 2)**2/11
Let o be ((-4)/(-10))/((-2)/(-70)). Suppose f - o = -f. Factor -15*z - 2*z**4 + z - z**3 - 2*z**3 - 4 - 18*z**2 - f*z**3.
-2*(z + 1)**3*(z + 2)
Let r be (-200)/110*264/(-144). Determine l so that 0 - 28/9*l**3 - 2/3*l**2 + 4/9*l + r*l**4 = 0.
-2/5, 0, 1/3, 1
Let w(a) be the first derivative of -a**6/9 + 4*a**5/9 - a**4/18 - 4*a**3/9 - 7. Let w(j) = 0. What is j?
-2/3, 0, 1, 3
Let x(i) be the third derivative of i**8/2520 - i**6/180 + i**4/45 + 172*i**2. What is v in x(v) = 0?
-2, -1, 0, 1, 2
Let p(o) be the first derivative of 15*o**4/4 + 8*o**3 + 3*o**2/2 - 6*o + 503. Suppose p(i) = 0. What is i?
-1, 2/5
Let a be (-544)/(-144) - 4/(-18). Factor -73*x**2 + 2*x**3 + 0*x**3 - a*x + 71*x**2.
2*x*(x - 2)*(x + 1)
Let n(u) = -16*u**2 - 6*u - 10. Let q(z) be the second derivative of 5*z**4/12 + z**3/3 + 3*z**2/2 + 14*z. Let r(w) = -3*n(w) - 10*q(w). Factor r(t).
-2*t*(t + 1)
Suppose 0 = -7*b + 10*b - 9. Factor 3*f**b + 2*f**4 - 4*f**3 + 2*f**2 - 3*f**4 + 0*f**4.
-f**2*(f - 1)*(f + 2)
Let y(v) be the third derivative of -v**8/504 + 13*v**7/1260 - 7*v**6/360 + v**5/72 + 4*v**2 + 35. Determine z so that y(z) = 0.
0, 1, 5/4
Factor -38*h + 115/3 - 1/3*h**2.
-(h - 1)*(