20)/7
Let y(q) be the second derivative of -q**6/120 - q**5/10 + 17*q**4/48 + 17*q**3/2 + 45*q**2/2 + 89*q. Factor y(f).
-(f - 5)*(f + 1)*(f + 6)**2/4
Let l be (-108)/(-57) - (16 - 6426/399). Let v be (-4)/84 + (-1)/(-3). What is r in 10/7*r - v*r**4 - 2/7*r**3 + 6/7*r**l + 4/7 = 0?
-1, 2
Suppose q + 54 - 58 = -4*k, -3*k + 3*q - 12 = 0. Let g(l) be the second derivative of k + 0*l**2 - 14*l + 1/3*l**3 + 1/40*l**5 - 1/6*l**4. Factor g(i).
i*(i - 2)**2/2
Let j(c) be the third derivative of -25*c**6/12 - 101*c**5/12 - 65*c**4/6 - 5*c**3/6 - 724*c**2. Factor j(f).
-5*(f + 1)**2*(50*f + 1)
Let f(m) = -9*m**2 - 3*m - 38. Let y(u) = -3*u**2 - u - 18. Let o(d) = 2*d**2 + d + 17. Let x(c) = 2*o(c) + 3*y(c). Let b(j) = 6*f(j) - 11*x(j). Solve b(w) = 0.
-1, 8
Let g(s) = -9*s**2 - 424*s - 47. Let o be g(-47). Suppose 0 = 25*r - 21*r - 16. Determine i, given that o*i + 0 + 100/7*i**r + 0*i**3 - 16/7*i**2 = 0.
-2/5, 0, 2/5
Let i = 2507 + -2482. Let a(u) be the first derivative of -1/18*u**4 + i - 4/9*u**3 - 4/3*u**2 - 16/9*u. Determine b, given that a(b) = 0.
-2
Let a(c) be the second derivative of -c**8/1120 - 3*c**7/70 - 3*c**6/5 + c**3/6 + 2*c**2 - 2*c - 35. Let k(l) be the second derivative of a(l). Factor k(o).
-3*o**2*(o + 12)**2/2
Let s(c) be the second derivative of -c**6/1440 - c**5/160 - 25*c**3/3 + 78*c. Let i(p) be the second derivative of s(p). Solve i(y) = 0.
-3, 0
Let m(r) be the third derivative of r**7/525 + 179*r**6/300 + 1547*r**5/30 - 8281*r**4/20 + 2819*r**2. Factor m(h).
2*h*(h - 3)*(h + 91)**2/5
Let r(l) = 14*l + 2. Let s be r(0). Factor -6332 + 16*m + 6332 + s*m**2.
2*m*(m + 8)
Let d(b) be the first derivative of 13*b - 1/3*b**3 + 1/10*b**5 + b**2 - 1/6*b**4 + 23. Let c(w) be the first derivative of d(w). Suppose c(k) = 0. Calculate k.
-1, 1
What is c in 434*c + 42*c**2 + 80384*c**3 - 172 + 83*c**2 + 467*c**2 - 80398*c**3 = 0?
-1, 2/7, 43
Let i(k) be the first derivative of 1/2*k**2 + 24 - 11*k + 8/3*k**3. Let a(l) = 3*l**2 - 4. Let j(b) = -11*a(b) + 4*i(b). Let j(f) = 0. What is f?
0, 4
Let k = -392513/2 + 196259. Let 15/2*t + 5 + k*t**2 = 0. Calculate t.
-2, -1
Let p(b) be the second derivative of 1/195*b**6 - 122*b + 98/13*b**4 + 0*b**2 + 21/65*b**5 + 2744/39*b**3 + 0. Determine v so that p(v) = 0.
-14, 0
What is g in 93/8*g + 1/8*g**2 - 47/4 = 0?
-94, 1
Let u(d) be the first derivative of d**3/5 - 21*d**2/5 - 7867. Factor u(l).
3*l*(l - 14)/5
Let s(n) be the second derivative of 0*n**2 + 44*n + 1/30*n**6 + 0*n**4 + 1/20*n**5 + 0*n**3 + 0. Determine q, given that s(q) = 0.
-1, 0
Let r be (-26)/(-806)*(4 + -4). What is b in -15/2*b**4 + 27/2*b**2 - 21/4*b**3 + r - 3/4*b**5 + 0*b = 0?
-9, -2, 0, 1
Solve 24656*a - 50784 + 4/3*a**3 + 1096/3*a**2 = 0 for a.
-138, 2
Let b(l) be the second derivative of -l**6/270 + l**5/27 + 2*l**4/27 - 40*l**3/27 - 109*l**2/2 + 155*l. Let a(y) be the first derivative of b(y). Factor a(d).
-4*(d - 5)*(d - 2)*(d + 2)/9
Determine l so that 40 - 447*l**2 + 16*l**3 + 1052*l**2 + 94*l + l**4 - 536*l**2 = 0.
-10, -4, -1
Suppose -m - 4*i = -44, 9*i - 30 = 6*i. Factor -3/5*b**m + 0*b**2 + 0 + 0*b - 9/5*b**3.
-3*b**3*(b + 3)/5
Let r = 10046 + -10045. Let p(t) be the first derivative of 1/25*t**5 + r + 0*t - 2/5*t**2 + 3/20*t**4 + 0*t**3. Suppose p(n) = 0. Calculate n.
-2, 0, 1
Let k(t) = -4*t**2 + 40*t + 7. Let j be k(10). Let p be j/1 + (-69)/6 + 6. Factor 3/2*n**3 + p*n**2 + 1/2*n + 1/2*n**4 + 0.
n*(n + 1)**3/2
Let o(c) be the third derivative of c**6/960 - c**5/40 - 7*c**3/6 - 5*c**2 - 2*c. Let f(x) be the first derivative of o(x). Solve f(s) = 0.
0, 8
Let c(o) be the third derivative of 1/20*o**5 + 21/2*o**4 + 4*o + 0 + 882*o**3 + 9*o**2. Find l such that c(l) = 0.
-42
Suppose 0 = -15*s - 335 + 890. What is g in s - 4*g - 3*g**2 - 37 + g = 0?
-1, 0
Let n(i) = -132*i + 399. Let u be n(3). Factor 3/2 - 19/6*d**2 - 4/3*d - 1/3*d**u.
-(d + 1)*(d + 9)*(2*d - 1)/6
Let c(d) be the first derivative of d**5/20 - 7*d**4/20 + 4*d**3/5 - 12*d**2 + 2*d + 88. Let q(i) be the second derivative of c(i). Factor q(k).
3*(k - 2)*(5*k - 4)/5
Let u(y) be the second derivative of -4*y**6/255 + 37*y**5/170 - 41*y**4/102 + 8*y**3/51 + 27*y - 19. Determine q, given that u(q) = 0.
0, 1/4, 1, 8
Suppose -149*i = -143*i - 18. Let 355*c**3 - 181*c**i - 184*c**3 - 2*c**4 - 12*c**2 = 0. What is c?
-3, -2, 0
Let s(w) = 8*w + 316. Let v be s(-28). Let j be 805/v*(-6)/(-15). Factor -j*k + 0 + 1/2*k**2.
k*(k - 7)/2
Let i(x) be the third derivative of 1/15*x**5 + 1/35*x**6 - 141 + 0*x - 2/105*x**7 - 13/84*x**4 + 1/1176*x**8 + 0*x**3 - x**2. Solve i(k) = 0 for k.
-1, 0, 1, 13
Let c = 2029 + -2024. Let g(s) be the third derivative of -1/240*s**6 - 25/48*s**4 + 0 - 25*s**2 - 1/12*s**c + 0*s + 0*s**3. Factor g(t).
-t*(t + 5)**2/2
Let l be 0/(-2)*(-70)/210. Suppose l = 39*z - 4*z - 70. Factor 0*w + 1/3*w**z + 0.
w**2/3
Let x(l) be the first derivative of 4*l**3/3 - 126*l**2 - 3256*l + 6111. Factor x(z).
4*(z - 74)*(z + 11)
Suppose 0 = 42*f + 3*b - 326631, -6064*f + 6063*f - 4*b + 7828 = 0. What is v in -73/2*v**3 - 6912 - f*v - 900*v**2 - 1/2*v**4 = 0?
-24, -1
Factor -164/3 + 166/3*r - 2/3*r**2.
-2*(r - 82)*(r - 1)/3
Let k(m) = -m**2 + 27*m - 45. Let s be k(25). Let z(u) be the third derivative of 2/5*u**3 + 0 + 15*u**2 - 1/150*u**s + 0*u - 1/60*u**4. What is r in z(r) = 0?
-3, 2
Determine o, given that -2*o**4 + 17/2*o**3 - 635/2*o + 75 + 68*o**2 = 0.
-6, 1/4, 5
Let v(i) = -20*i**2 - 11165*i + 11230. Let y(g) = -11*g**2 - 5580*g + 5618. Let n(r) = -3*v(r) + 5*y(r). Factor n(m).
5*(m - 1)*(m + 1120)
Let w(l) be the third derivative of 0*l + 1/12*l**4 + 1/45*l**6 + 62*l**2 + 0*l**3 - 13/180*l**5 + 1 - 1/630*l**7. Solve w(h) = 0.
0, 1, 6
Factor 640/11*m + 64/11*m**3 - 416/11 - 336/11*m**2 - 2/11*m**4.
-2*(m - 26)*(m - 2)**3/11
Let c(y) = -2*y**2 + 2*y + 32. Let h be c(0). Let j be 2/(-4*(-4)/h). Find a, given that 29*a**5 - 7*a - 3*a - 35*a**j + 35*a**2 - 4*a**5 - 15*a**3 = 0.
-1, 0, 2/5, 1
Factor 3*y**2 + 1784*y - 113882 - 85034 - 7*y**2.
-4*(y - 223)**2
Suppose -3*c - 3*i + 18 = -2*i, -34 = -5*c - 3*i. Let y(s) be the second derivative of 0*s**3 - 38*s + 0*s**4 + 0*s**2 - 1/50*s**c + 1/75*s**6 + 0. Factor y(j).
2*j**3*(j - 1)/5
Suppose 5*q - n - 258 = 140, 3*q - 250 = -5*n. Factor -430*p**2 + 218*p**2 + q*p + 208*p**2.
-4*p*(p - 20)
Let a(q) be the first derivative of 2/9*q**3 - 8/3*q**2 + 14/3*q - 18. Let a(x) = 0. What is x?
1, 7
Let t(y) be the second derivative of y**4/60 - y**3/10 - 14*y**2/5 - 11*y - 47. Find j such that t(j) = 0.
-4, 7
Suppose 8*g - 172 - 28 = 0. Suppose 79 + g = 4*k. Let -18 + k - 72*c + 43*c**5 + 250*c**2 - 151*c**5 + 342*c**4 - 420*c**3 = 0. Calculate c.
1/3, 1/2, 2/3, 1
Find h such that -81*h**3 - 134*h**2 - 306*h**2 - 523*h**2 + 79*h**3 + 29*h**2 = 0.
-467, 0
Let f(y) be the second derivative of y**6/315 - 13*y**5/210 + 11*y**4/63 - 446*y. Factor f(a).
2*a**2*(a - 11)*(a - 2)/21
Let v(g) be the first derivative of g**4/20 + 41*g**3 + 47124*g**2/5 - 94864*g/5 - 3241. Solve v(h) = 0 for h.
-308, 1
Let a be (-4520)/(-825) + 25/15. Let n = -72/11 + a. Determine d so that -1/5*d**2 + n*d - 2/5 = 0.
1, 2
Let h(r) = 7*r**5 + 7*r**4 - 86*r**3 + 81*r**2 + 9*r. Let p(g) = 12*g**5 + 13*g**4 - 173*g**3 + 163*g**2 + 15*g. Let m(z) = 5*h(z) - 3*p(z). Factor m(y).
-y**2*(y - 7)*(y - 1)*(y + 12)
Let z be 2 - 4 - (1 + (-3 - -2)). Let s be (-18)/15 - z - 0. Factor -4/5*b + 4/5*b**2 + s*b**3 - 4/5*b**4 + 0.
-4*b*(b - 1)**2*(b + 1)/5
Factor -73*w**3 - 387*w**3 + 2513*w**4 + 455*w**2 + 2518*w**4 - 5026*w**4.
5*w**2*(w - 91)*(w - 1)
Factor -90 + 19*o**2 + 1/4*o**3 + 283/4*o.
(o - 1)*(o + 5)*(o + 72)/4
Let i(v) = -5*v**4 - 190*v**3 - 1145*v**2 - 1545*v. Let z(k) = -15*k**4 - 570*k**3 - 3433*k**2 - 4636*k. Let w(d) = -14*i(d) + 5*z(d). Factor w(o).
-5*o*(o + 2)*(o + 5)*(o + 31)
Let h be (12/(-36))/(2*(-49)/1680). Solve 18/7*o**2 - 2/7*o**3 + 0 - h*o = 0.
0, 4, 5
Suppose -5*m = 5*b - 15, -5*b - 1072 = 4*m - 1085. Factor 8/7*r**3 + 12/7*r + 0 + 22/7*r**m - 2/7*r**4.
-2*r*(r - 6)*(r + 1)**2/7
Let s(q) be the first derivative of 1/8*q**4 + 267 - 3/2*q**2 + 0*q + 5/6*q**3. Factor s(h).
h*(h - 1)*(h + 6)/2
Suppose -18 = 2*r - 24. Suppose -2*l = -3*q + 9, -r*q + 20 = 2*l - 1. Factor -32*o**2 + 6*o**3 - 78*o**5 + 18*o**l + 76*o**5.
-2*o**2*(o - 2)*