8)*(p + 1)/3
Let y(h) be the first derivative of -9*h**5/20 + 21*h**4/8 - 61*h**3/12 + 7*h**2/2 - h - 44. Suppose y(w) = 0. What is w?
1/3, 2
Let k = 652 + -39119/60. Let u(t) be the third derivative of -k*t**5 - 1/360*t**6 + 0*t - 1/9*t**3 - 4*t**2 + 0 + 1/630*t**7 + 5/72*t**4. Factor u(d).
(d - 1)**3*(d + 2)/3
What is p in -4*p**4 - 4*p**3 - 41*p + 9*p - 103*p**2 + 58*p**2 + 85*p**2 = 0?
-4, 0, 1, 2
Solve 11*r**2 + 41/2*r + 10 + 1/2*r**3 = 0 for r.
-20, -1
Let k be 5*(1 - (-18)/(-20))/(2/3). Factor -15/4*x + 3 + k*x**2.
3*(x - 4)*(x - 1)/4
Let c(y) be the first derivative of -y**4/24 - 21*y**3/2 - 125*y**2/4 - 187*y/6 + 286. Let c(t) = 0. Calculate t.
-187, -1
Let j = -35 + 38. Let r be j - 5 - (90/(-21) + 2). Factor -2/7*c**2 + 4/7*c + 0 + r*c**4 - 4/7*c**3.
2*c*(c - 2)*(c - 1)*(c + 1)/7
Let y be (-1)/2*126/(56/(-4)). Factor 3*u**3 + 0 + y*u**2 - 3/2*u**4 + 0*u.
-3*u**2*(u - 3)*(u + 1)/2
Let q(u) be the first derivative of u**4/60 - u**3/30 - 11*u + 4. Let z(o) be the first derivative of q(o). Solve z(t) = 0 for t.
0, 1
Let n = 11474 - 57178/5. Determine c so that -n + 48/5*c - 3/5*c**2 = 0.
8
Suppose 0 = 4*k + 2*i - 10, -2*i - 9 = -3*k - 3*i. Find h such that 20*h + 4*h**3 - 9*h**3 - 36 - k + 10*h**2 = 0.
-2, 2
Let o = -9460 - -47306/5. Determine k so that -13/5*k**2 - o*k**3 - 1/5*k**4 - 12/5*k - 4/5 = 0.
-2, -1
Let f(a) be the third derivative of a**7/70 - 3*a**6/20 + 9*a**5/20 - a**4/2 - 102*a**2. Factor f(r).
3*r*(r - 4)*(r - 1)**2
Let l = -505 - -283. Let w be l/(-15) + (-2)/(-10). Factor 6*r**4 + 12*r + 24*r**2 + 5*r**4 + w*r**3 - 8*r**4.
3*r*(r + 1)*(r + 2)**2
Let a(n) be the second derivative of -2/9*n**3 + 10*n + 1 - 1/18*n**4 + 1/180*n**6 - 1/252*n**7 + 1/20*n**5 + 0*n**2. Let a(c) = 0. What is c?
-2, -1, 0, 2
Let x(d) = -6*d**5 + 2*d**4 + 10*d**3 + 5*d + 10. Let l(n) = 7*n**5 - 3*n**4 - 10*n**3 - 6*n - 12. Let k(h) = 5*l(h) + 6*x(h). Factor k(t).
-t**3*(t - 2)*(t + 5)
Let b(c) be the first derivative of 18 - 14*c + 2*c**3 - 207*c**2 + 384*c**2 - 197*c**2. Factor b(g).
2*(g - 7)*(3*g + 1)
Let t(m) be the third derivative of -m**5/180 - 5*m**4/36 - 4*m**3/3 + 3*m**2 + 3. Let t(a) = 0. Calculate a.
-6, -4
Let l(k) = -k**2 + 5*k + 8. Let n be l(4). Factor -3*c**2 + 12*c**3 + 0*c**3 - 9*c**3 - 12*c + n.
3*(c - 2)*(c - 1)*(c + 2)
Let f = -1183 - -1183. Let w(z) be the second derivative of 0*z**3 + 0 - 1/60*z**6 - 1/4*z**2 - 8*z + f*z**5 + 1/12*z**4. Find b, given that w(b) = 0.
-1, 1
Let k(o) be the first derivative of -o**2 + 4/7*o + 1 - 4/21*o**3 + 1/2*o**4. Factor k(d).
2*(d - 1)*(d + 1)*(7*d - 2)/7
Let n(c) be the second derivative of c**6/6 - c**5 - 35*c**4/4 - 10*c**3/3 + 70*c**2 - 2*c - 128. Factor n(x).
5*(x - 7)*(x - 1)*(x + 2)**2
Let y be 4/3*(3 + 3). Suppose -5*i + 19 = 2*l - 0*i, 4*i - y = 2*l. Factor 4*x + 15*x**l + 9*x - 2*x - 5*x.
3*x*(5*x + 2)
Suppose 7*y - 14 = -0. Let l(o) be the first derivative of -4 + 0*o**4 - 2/9*o**3 + 26/15*o**5 + 4/3*o**6 + 0*o + 0*o**y. Find q such that l(q) = 0.
-1, -1/3, 0, 1/4
Let i(p) be the first derivative of 2*p**5/5 - p**4 - 8*p**3 + 40*p**2 - 64*p + 244. Factor i(y).
2*(y - 2)**3*(y + 4)
Solve -3/4*i**5 + 3*i + 0 - 15/4*i**2 - 9/4*i**3 + 15/4*i**4 = 0 for i.
-1, 0, 1, 4
Let x(y) = y**3 + 23*y**2 + 17*y - 56. Let n be x(-22). Let w = 273/5 - n. Determine q so that -3*q + w*q**2 + 12/5 = 0.
1, 4
Let z be (0/(-9))/(1 + 1). Let u(a) be the third derivative of 1/20*a**5 + 0 + 0*a**4 + 2*a**2 + z*a - 2/3*a**3 + 1/120*a**6. Factor u(g).
(g - 1)*(g + 2)**2
Let k(i) be the second derivative of i**5/220 + 17*i**4/132 + 2*i**3/3 + 14*i**2/11 - 61*i. Factor k(n).
(n + 1)*(n + 2)*(n + 14)/11
Let o(y) be the third derivative of 5/3*y**3 + 0*y - 1/21*y**4 + 1/1260*y**6 - 9*y**2 + 0*y**5 + 0. Let q(f) be the first derivative of o(f). Factor q(h).
2*(h - 2)*(h + 2)/7
Let v(h) be the first derivative of -5/12*h**4 + 3/2*h**2 - 1/60*h**6 + 0*h + 2/3*h**3 + 5 + 2/15*h**5. Let x(a) be the second derivative of v(a). Factor x(n).
-2*(n - 2)*(n - 1)**2
Let k(y) be the first derivative of -9/5*y - 31 + 1/5*y**3 - 3/5*y**2. Factor k(i).
3*(i - 3)*(i + 1)/5
Let z = 4209 - 4209. Factor z - 1/4*c**4 + 1/8*c**5 + 1/4*c**2 + 0*c - 1/8*c**3.
c**2*(c - 2)*(c - 1)*(c + 1)/8
Let x be 56/21 + 4/(-6). Let 2*v**2 + 3 + 10*v**x + 24*v - 9*v = 0. What is v?
-1, -1/4
Let f(d) be the first derivative of -d**6/45 - 8*d**5/75 - d**4/30 + 4*d**3/15 + 128. Solve f(j) = 0 for j.
-3, -2, 0, 1
Suppose -q - 4*q + 1 = -3*a, -5*q - 2 = -4*a. Suppose d = -x + 10, 0 = 5*x + 2*d + 2*d - 45. Factor -6*c**4 + c**4 + 2*c**3 + 6*c**3 - 13*c**3 + x*c**q + 5*c.
-5*c*(c - 1)*(c + 1)**2
Let g(i) be the first derivative of -2*i**3/45 - 8*i**2/15 - 8*i/5 + 3. Factor g(s).
-2*(s + 2)*(s + 6)/15
Let r(p) = -13*p**2 + 226*p - 160. Let z(h) = 180*h**2 - 3165*h + 2240. Let l(n) = 85*r(n) + 6*z(n). Find v such that l(v) = 0.
4/5, 8
Let m be 21/(-28) + (-526)/(-8). Find n, given that -70*n + 5*n**2 + 117 - m + 120 + 73 = 0.
7
Let p be 60/56 - 3*((-16)/(-8))/12. Factor -60/7*v + p*v**3 - 24/7*v**2 - 32/7.
4*(v - 8)*(v + 1)**2/7
Let h(y) be the third derivative of -1/360*y**6 + 13*y**2 - 1/9*y**3 - 1/45*y**5 + 0 + 0*y - 5/72*y**4. Factor h(d).
-(d + 1)**2*(d + 2)/3
Let k(m) be the first derivative of m**5/35 + 5*m**4/28 + 3*m**3/7 + m**2/2 + 2*m/7 + 315. Factor k(t).
(t + 1)**3*(t + 2)/7
Suppose 3*s + 7 = 7. Let r be 8/12 - ((-30)/(-63))/5. Suppose r*x**2 + s - 2/7*x**3 + 0*x = 0. Calculate x.
0, 2
Factor 5/3*b**2 - 188/3*b - 76/3.
(b - 38)*(5*b + 2)/3
Let j(u) be the first derivative of -u**5/35 - u**4/14 + u**3/7 + 2*u**2/7 - 4*u/7 - 20. Factor j(i).
-(i - 1)**2*(i + 2)**2/7
Let m(z) be the second derivative of z**5/4 + 25*z**4/2 + 415*z**3/6 + 135*z**2 - 2*z + 507. Solve m(h) = 0 for h.
-27, -2, -1
Factor -29160*d**2 - 297*d**5 - 270*d**4 + 591*d**5 - 289*d**5 + 4860*d**3.
5*d**2*(d - 18)**3
Let z(a) be the first derivative of -a**3 + 1/20*a**5 + 0*a - a**2 + 3 + 1/8*a**4. Let d(m) be the second derivative of z(m). Factor d(q).
3*(q - 1)*(q + 2)
Let u(j) = -5*j**3 + 50*j**2 - 125*j + 25. Let f(z) = -1. Let m(c) = -25*f(c) - u(c). Determine l, given that m(l) = 0.
0, 5
Solve -21*s**4 + 25 - 12*s**3 - 5*s + s - 25 + 12*s**2 + 25*s**4 = 0.
0, 1
Factor 5/6*m**4 - 20/3*m**3 - 25*m**2 - 55/6 - 80/3*m.
5*(m - 11)*(m + 1)**3/6
Let w(k) be the second derivative of k**6/50 - 9*k**5/50 - 6*k**4/5 - 13*k**3/5 - 27*k**2/10 - 25*k. Find p such that w(p) = 0.
-1, 9
Let l(n) = -n**3 - 38*n**2 - 67*n + 182. Let v be l(-36). Find k, given that -1/2*k**v + 2*k - 2 = 0.
2
Let c(x) be the first derivative of 1/6*x**3 - 1/12*x**4 - 3 + 4*x + 0*x**2. Let v(q) be the first derivative of c(q). Factor v(w).
-w*(w - 1)
Let f(l) = -l**3 + l**2 + 3*l. Let y be f(2). Solve q + 2*q**3 + q + q**3 - 2*q**3 - 3*q**y = 0 for q.
0, 1, 2
Factor 22/21*d + 26/21*d**2 + 8/21*d**3 + 4/21.
2*(d + 1)*(d + 2)*(4*d + 1)/21
Let x(a) be the third derivative of 0*a**3 + 0 - 18*a**2 + 2/21*a**4 + 0*a - 1/70*a**6 + 0*a**5 - 2/735*a**7. Factor x(o).
-4*o*(o - 1)*(o + 2)**2/7
Suppose -k = 1 - 4. Let q be (-9)/(-5) - k/(-15). Determine x so that 14*x**q - 10*x**2 - x**2 = 0.
0
Let c = 11 + -6. Suppose -4*l = -c*u - 9 - 7, u + 5*l = 20. Determine n, given that 4*n + 0 + n**2 + 2 + n**2 + u*n**2 = 0.
-1
Let s(v) = 11*v + 49. Let j be s(12). Let i = j + -178. Solve 3/2*d**4 + 6*d - 21/4*d**i + 9/4*d**2 - 3 = 0.
-1, 1/2, 2
Factor 440*g + 75*g**2 - 40 + 28 - 32 - 16.
5*(g + 6)*(15*g - 2)
Let k(g) = 20*g**2 - 6496*g + 874792. Let o(z) = 7*z**2 - 2166*z + 291597. Let q(d) = 3*k(d) - 8*o(d). Determine c, given that q(c) = 0.
270
Let j(l) be the third derivative of 7*l**5/60 - l**4/8 - l**3/6 + 17*l**2. Let u(v) = 76*v**2 - 32*v - 12. Let c(s) = -32*j(s) + 3*u(s). Factor c(w).
4*(w - 1)*(w + 1)
Let z be -4 - 5/(15/(-552)). Let u = z + -538/3. Let 0 + 4/3*q**3 + 0*q**2 - 2/3*q**5 + 0*q**4 - u*q = 0. Calculate q.
-1, 0, 1
Let c(z) be the second derivative of z**9/1512 - z**8/168 + 2*z**7/105 - z**6/45 - 5*z**3/3 + 12*z. Let b(j) be the second derivative of c(j). Factor b(k).
2*k**2*(k - 2)**2*(k - 1)
Let t(h) be the third derivative of h**8/11760 + 2*h**7/2205 - 5*h**4/24 - 18*h**2. Let k(y) be the second derivative of t(y). Factor k(u).
4*u**2*(u + 4)/7
Let s(o) be the third derivative of o**8/420 - 2*o**7/525