51 + 270*c. Find f, given that a(f) = 0.
-11, -1/4, 0
Suppose 0 = 4*k + 12, 0 = -0*q + 4*q - 4*k + 36. Let p be 1/((q/(-33))/4). Solve -3*b**2 - 3*b + p*b + 8 + 5*b**2 = 0.
-2
Let y(m) be the second derivative of -m**4/30 + 14*m**3/15 + 32*m**2/5 - 373*m. Suppose y(t) = 0. What is t?
-2, 16
Let c(l) be the third derivative of l**7/105 - l**6/12 + 3*l**5/10 - 7*l**4/12 + 2*l**3/3 + 4*l**2 - 3*l. Suppose c(r) = 0. What is r?
1, 2
Suppose -5*x + 40 = 0, m - 10*x = -5*x - 38. Find k, given that -5/2*k**3 - 5*k**m + 4 + 2*k + k**4 + 1/2*k**5 = 0.
-2, -1, 1, 2
Factor 9/5 + 8/5*y - 1/5*y**2.
-(y - 9)*(y + 1)/5
Let j(q) = -14*q**2 + 47*q - 15. Let n be j(3). Factor -h + n + 1/4*h**3 + 0*h**2.
h*(h - 2)*(h + 2)/4
Let p(o) be the third derivative of o**6/120 + 2*o**5/15 + o**4/2 - 152*o**2 + 1. Factor p(x).
x*(x + 2)*(x + 6)
Let t = 63 - -108. Let f = t + -169. Factor 3/4*w**3 + 1 + 11/4*w**f + 3*w.
(w + 1)*(w + 2)*(3*w + 2)/4
Let 2312 + 68*z + 1/2*z**2 = 0. Calculate z.
-68
Suppose 3*l + 6*l - 54 = 0. Let r(t) be the second derivative of 1/18*t**3 + 0*t**2 + 0 - 7/180*t**6 - 11/72*t**4 - l*t + 2/15*t**5. Solve r(z) = 0.
0, 2/7, 1
Let x = 4339/2 + -2169. Solve -1/2*q**4 + x*q**2 + 1/2*q**3 - 1/2*q + 0 = 0 for q.
-1, 0, 1
Suppose 0 = 2*n - 4*f + 32, 4*n - f + 31 = -5. Let v = 2 - n. Factor v + 2*z - 14 + 4*z**2 - 2*z.
4*(z - 1)*(z + 1)
Let d(o) = o**3 - o**2 - o + 2. Let f(u) = -4*u**3 + 22*u**2 - 13*u - 10. Let x(m) = -5*d(m) - f(m). Factor x(i).
-i*(i - 1)*(i + 18)
Suppose -6*a + 2*a = -12, -5*g + 2*a + 19 = 0. Suppose -4*q - 4 = -g*q. Factor 3*f**q - 22 - 3*f**2 + 22 - 6*f**3 + 6*f.
3*f*(f - 2)*(f - 1)*(f + 1)
Let w(l) be the second derivative of -l**5/50 - 26*l**4/15 - 676*l**3/15 - l + 28. What is x in w(x) = 0?
-26, 0
Let k = -102 + 33. Let o = k + 69. Factor -12/7*c + o - 4/7*c**2.
-4*c*(c + 3)/7
Let w be 2/2 - 40/(-25 + 5). Solve 1/2*i**w - 1/2 - 1/2*i + 1/2*i**2 = 0 for i.
-1, 1
Let a(g) be the first derivative of -g**3/3 + 3*g**2 - 8*g - 181. Suppose a(k) = 0. What is k?
2, 4
Let h = -4 + 8. Let p(a) = a**3 - 21*a**2 + 62*a - 456. Let c be p(19). Let 1/3*g - 1/3*g**h + c - g**2 + g**3 = 0. What is g?
0, 1
Let u be (10 - 1)*(-22)/(-99). Let y(d) = d**3 - 6*d**2 - 6*d + 1. Let q be y(7). Factor 32*a**2 - q*a**3 + 28*a + 20*a**3 + 3 + 7 - u.
4*(a + 1)**2*(3*a + 2)
Let -12*d - 126 - 2/7*d**2 = 0. What is d?
-21
Let g(w) be the first derivative of -2*w**3/5 + 21*w**2/5 + 48*w/5 - 95. Factor g(y).
-6*(y - 8)*(y + 1)/5
Let a(t) be the third derivative of -t**5/60 - 29*t**4/12 + 59*t**3/6 + 6*t**2 - 34*t. Factor a(q).
-(q - 1)*(q + 59)
Factor 15*x - 8*x + 75*x**2 - 15*x - 100 - 32*x - 70*x**2.
5*(x - 10)*(x + 2)
Suppose 3*h - 8 = -i - 0*h, 5 = -2*i + h. Let w(t) = -t**2 + 4*t. Let v(k) = -k**2 + 1. Let c(q) = i*w(q) + 4*v(q). Factor c(m).
-(m + 2)*(3*m - 2)
Let z be -2*(-4)/16*2. Let s be 20*(z - (-4)/(-20)). Factor -6*r**3 - 8*r**3 + s*r**3 + 2*r + 4*r**2.
2*r*(r + 1)**2
Let z(u) be the second derivative of 3*u**4 - 7*u**3/2 + 3*u**2/2 + 3*u + 5. Determine y so that z(y) = 0.
1/4, 1/3
Let s = -1152 - -1156. Let c(m) be the third derivative of 12*m**2 + 0 + 1/630*m**7 + 1/36*m**5 + 0*m**3 - 1/90*m**6 - 1/36*m**s + 0*m. Solve c(f) = 0 for f.
0, 1, 2
Let s = -170 - -166. Let h be 6*-1*s/12. Let -2/3*m**h + 2/3 + 0*m = 0. What is m?
-1, 1
Let c be 17/4 + 0*(-14)/(-140). Let n(z) be the first derivative of -11/2*z**2 + 7*z**3 - c*z**4 + 2*z + z**5 + 6. Factor n(d).
(d - 1)**3*(5*d - 2)
Let j(c) be the first derivative of 5/3*c**3 - 4 + 1/5*c**5 - c**4 - c**2 + 0*c. Find x such that j(x) = 0.
0, 1, 2
Let h(r) be the second derivative of r**6/18 + 43*r**5/60 + 17*r**4/6 + 16*r**3/9 - 16*r**2/3 + 60*r. Factor h(o).
(o + 1)*(o + 4)**2*(5*o - 2)/3
Let z be (42/60)/((-322)/(-345)). Solve 0 + 3/2*o**2 - 3/2*o**4 + 0*o - 3/4*o**5 + z*o**3 = 0 for o.
-2, -1, 0, 1
Let g(f) be the third derivative of f**6/24 + 29*f**5/12 + 275*f**4/24 + 45*f**3/2 + 10*f**2 - 36. Find s such that g(s) = 0.
-27, -1
Let y(t) be the first derivative of 5*t**6/6 + 19*t**5 - 215*t**4/2 + 670*t**3/3 - 455*t**2/2 + 115*t - 3. Factor y(a).
5*(a - 1)**4*(a + 23)
Suppose -13*l = -8*l - 155. Suppose l*s = 8*s. Find g such that 1/2*g + 1/4*g**4 - 1/4 + s*g**2 - 1/2*g**3 = 0.
-1, 1
Let h(i) be the second derivative of i**5/80 - i**3/24 - 18*i. Find f such that h(f) = 0.
-1, 0, 1
Let j = -35 + 77. Solve 39*b**2 - 6 - 79*b**2 + j*b**2 - 2*b - 2*b = 0.
-1, 3
Let p = 122/99 - 4/33. Let 2/3*u**2 - p*u**3 + 0*u - 4/9*u**4 + 0 = 0. What is u?
-3, 0, 1/2
Let b(m) be the third derivative of -m**8/2800 + m**7/350 - m**6/120 + m**5/100 + m**3 + 10*m**2. Let v(s) be the first derivative of b(s). Factor v(y).
-3*y*(y - 2)*(y - 1)**2/5
Let r be -30*6/42*-7. Let y(t) = -5*t + 153. Let d be y(r). Factor -8/7*p**4 - 2/7 + 2*p - 30/7*p**2 + 26/7*p**d.
-2*(p - 1)**3*(4*p - 1)/7
Let r(y) be the second derivative of y**5/240 - y**4/24 + y**3/8 - 9*y**2 - 16*y. Let v(s) be the first derivative of r(s). Find f such that v(f) = 0.
1, 3
Let u = -348 - -1678/5. Let i = u + 293/20. Factor 0*n**3 + 0 + 3/4*n**4 + 3/2*n - i*n**2.
3*n*(n - 1)**2*(n + 2)/4
Suppose 20*m - 22*m = -4. Let x be m/(-6)*(2 + (-65)/10). Factor -3/2*l + 3/2*l**3 + x*l**2 - 3/2.
3*(l - 1)*(l + 1)**2/2
Let d be (-6)/(-5) + (-15)/(-50). Factor 7/2*b + 3 - d*b**2.
-(b - 3)*(3*b + 2)/2
Let h(n) be the third derivative of -n**7/210 + n**6/40 - n**5/60 - n**4/8 + n**3/3 + 31*n**2 + 5. Factor h(q).
-(q - 2)*(q - 1)**2*(q + 1)
Let s(c) = c**2. Let p(g) = 4*g**3 + 20*g**2 - 20*g. Let h(o) = -p(o) + 4*s(o). Factor h(k).
-4*k*(k - 1)*(k + 5)
Factor -48*b**2 + 96*b**2 - 61*b**3 + 18*b**4 - 8*b + 3*b**3.
2*b*(b - 2)*(b - 1)*(9*b - 2)
Let i(g) be the first derivative of -1/9*g**3 + 0*g - 1/3*g**6 + 0*g**2 + 9 + 13/24*g**4 - 17/30*g**5. Let i(u) = 0. Calculate u.
-2, 0, 1/4, 1/3
Let l(p) = -9*p**2 + 85*p + 52. Let x be l(10). Solve -15/2*w + 5 + 5/2*w**x = 0.
1, 2
Let i(y) be the second derivative of -y**6/255 + 69*y**5/170 + 35*y**4/51 - 291*y. Factor i(z).
-2*z**2*(z - 70)*(z + 1)/17
Let d(a) be the second derivative of 1/3*a**4 + 0 - 2/15*a**6 + 2*a + 0*a**5 + 0*a**2 + 1/21*a**7 - 1/3*a**3. Factor d(w).
2*w*(w - 1)**3*(w + 1)
Determine b, given that -126/5*b + 0 + 2/5*b**2 = 0.
0, 63
Let u(g) be the second derivative of -10*g**7/21 + 3*g**6/2 + 13*g**5/2 - 145*g**4/4 + 170*g**3/3 - 30*g**2 - 69*g. Determine v so that u(v) = 0.
-3, 1/4, 1, 2
Let d(x) = 31 - 16*x - 19*x + 45*x - 13*x. Let t be d(9). Factor -2/3*a + 8/3*a**2 - 2/3*a**5 + 0 + 8/3*a**t - 4*a**3.
-2*a*(a - 1)**4/3
Let f(u) = 11*u + 14*u**2 - u**2 + 13*u**3 - 12*u**3 - 9. Let i be f(-12). Determine l so that -1/5*l + 1/5*l**4 + 3/5*l**2 - 3/5*l**i + 0 = 0.
0, 1
Let n = 27 - -18. Let k be 3/n*(4 + -1). Determine l so that 0 + 0*l - 1/5*l**3 - k*l**2 = 0.
-1, 0
Let n = 221918/97083 - 2/13869. Let -17/7*a**3 - 4/7*a + 5/7*a**4 + n*a**2 + 0 = 0. Calculate a.
0, 2/5, 1, 2
Suppose 4*q + 3*w = 15, 0 = -q + 7*w - 6*w + 2. Factor -2 - 13/2*k**2 - q*k**3 - 1/2*k**4 - 6*k.
-(k + 1)**2*(k + 2)**2/2
Let q(g) be the second derivative of g**7/315 - g**6/15 + 3*g**5/5 - 3*g**4 + 9*g**3 + 5*g**2 - 12*g. Let h(t) be the first derivative of q(t). Factor h(d).
2*(d - 3)**4/3
Let l(m) be the third derivative of m**6/1440 - m**5/240 - m**4/32 + m**3/2 + 40*m**2. Let h(k) be the first derivative of l(k). Suppose h(f) = 0. What is f?
-1, 3
Suppose 865*w = 868*w - 5*k + 10, -5*w + k + 20 = 0. What is o in -2/13*o**4 + 0 + 2/13*o**w + 0*o**2 + 0*o + 0*o**3 = 0?
0, 1
Let k = 1300 - 1294. Let m(r) be the third derivative of 0*r + 0 + 1/50*r**5 + 1/75*r**k - 2*r**2 - 3/20*r**4 + 2/15*r**3. Factor m(w).
2*(w - 1)*(w + 2)*(4*w - 1)/5
Let a(u) be the third derivative of -5*u**8/112 + 53*u**7/63 - 41*u**6/12 + 16*u**5/3 - 125*u**4/72 - 5*u**3 + 437*u**2. What is i in a(i) = 0?
-2/9, 1, 9
Let g(i) be the first derivative of -3*i**5/5 - 15*i**4/2 - 17*i**3 - 12*i**2 - 107. Factor g(t).
-3*t*(t + 1)**2*(t + 8)
Let k(c) be the second derivative of -c**7/273 + c**6/39 - 3*c**5/65 + c + 583. What is p in k(p) = 0?
0, 2, 3
Let w(u) be the first derivative of -7*u**6/54 - 43*u**5/45 - 7*u**4/4 + u**3 + 3*u**2 + 121. Solve w(m) = 0 for m.
-3, -1, 0, 6/7
Suppose -3*s + 5*v + 18 = 0, -2*s + 6*s - 1 = -v. Suppose -s = -12*g - 1. Suppose 5/8*r**