 - 2/7*k**3.
-2*(k + 3)**2*(k + 8)/7
Let f(q) be the first derivative of 5*q**4/2 + 406*q**3/3 + 118*q**2 - 160*q + 885. Solve f(r) = 0 for r.
-40, -1, 2/5
Factor -2/7*f**2 + 6 - 40/7*f.
-2*(f - 1)*(f + 21)/7
Suppose -y + 2*d - 15 = -14, d = 3*y - 12. Determine v so that 25/4*v**3 - 5/4*v**4 - y*v**2 + 0 + 0*v = 0.
0, 1, 4
Let f(j) be the third derivative of -j**8/112 - j**7/21 + j**5/6 + j**4/8 + j**2 - 100*j. Let f(u) = 0. Calculate u.
-3, -1, -1/3, 0, 1
Solve -2/11*p**4 + 0 + 50/11*p**2 + 0*p - 48/11*p**3 = 0 for p.
-25, 0, 1
Let c(h) be the third derivative of h**6/780 + h**5/78 + h**4/26 + 2*h**2 - 22. Determine q so that c(q) = 0.
-3, -2, 0
Solve 11*y**4 + 18*y**4 - 25*y**4 - 4*y**2 = 0.
-1, 0, 1
Let i(p) be the third derivative of p**6/64 - 77*p**5/40 + 181*p**4/64 + 61*p**3/8 + 299*p**2. Factor i(s).
3*(s - 61)*(s - 1)*(5*s + 2)/8
What is t in 20*t**2 - 20*t**4 + 17*t - 11*t**3 + 3*t**3 - 12*t + 3*t = 0?
-1, -2/5, 0, 1
Let y(k) be the third derivative of k**7/1155 + k**6/165 - 3*k**5/55 + 5*k**4/33 - 7*k**3/33 + 94*k**2. Determine a so that y(a) = 0.
-7, 1
Let s(q) = -2*q**4 - 30*q**3 + 10*q**2 + 30*q + 8. Let a(j) = -j**4 - 10*j**3 + 4*j**2 + 10*j + 3. Let b(h) = -8*a(h) + 3*s(h). Factor b(g).
2*g*(g - 5)*(g - 1)*(g + 1)
Suppose 7 = -30*u + 35*u - l, -4*u = -3*l + 1. Factor -10/3*d**3 + 2/3*d + 0 + 8/3*d**u.
-2*d*(d - 1)*(5*d + 1)/3
Suppose 0 = -4*z + 36 - 20. Determine r, given that -4*r**5 - 424 + 4*r**z + 424 = 0.
0, 1
Let n(u) = u**2 - 2*u - 4. Let b be n(-4). Let c = -171 - -173. Factor -14 + 3*w**2 - 7*w + b - c*w.
3*(w - 2)*(w - 1)
Let t be ((-12)/80)/3*(-3)/18. Let v(a) be the third derivative of 5*a**2 + 0*a + 0 - 1/96*a**4 + 0*a**3 + t*a**5 - 1/480*a**6. Factor v(x).
-x*(x - 1)**2/4
Let p(f) be the third derivative of 0*f + 0 + 0*f**3 + 0*f**4 + 3/350*f**7 + 1/560*f**8 + 0*f**6 - 5*f**2 + 0*f**5. Factor p(v).
3*v**4*(v + 3)/5
Let y = -184 + 196. Suppose -4*n + 4*b = y, -8*b = -4*n - 6*b - 6. Suppose 1/2*d**4 + 1/2*d**2 + 0*d + n + d**3 = 0. Calculate d.
-1, 0
Suppose 47 - 11 = 6*a. Let c(s) = s**2 + 8*s + 14. Let o be c(-7). Determine x, given that -3*x + o - 1 - 3*x**5 + a*x**4 - 12*x**2 + x**3 + x**3 + 4*x**3 = 0.
-1, 1, 2
Let j be 68/4 - (3 + 2). Let l be 3/j - (-1)/(-4). Suppose 1/3*f + 1/6*f**2 - 1/6*f**3 + l = 0. What is f?
-1, 0, 2
Let l(o) be the second derivative of 0*o**2 + 1/126*o**7 - 1/6*o**4 + 0 - 1/2*o**3 + 2/15*o**5 + 1/15*o**6 + 30*o. Factor l(t).
t*(t - 1)*(t + 1)*(t + 3)**2/3
Let d(w) be the second derivative of -5*w**4/48 + 25*w**3/4 - 1125*w**2/8 + 6*w - 8. Factor d(v).
-5*(v - 15)**2/4
Let m = 62913/2 - 31456. Suppose 5/2 - 3*f + m*f**2 = 0. Calculate f.
1, 5
Let n(h) = -6*h**3 + 4*h**2 - h + 3. Let u(m) = 9*m**2 + 6 + 2 - m - 3 - 13*m**3. Suppose 0 = 2*q + 5 + 5. Let r(k) = q*n(k) + 3*u(k). Factor r(b).
-b*(b - 1)*(9*b + 2)
Let k(d) be the third derivative of -d**5/60 - 5*d**4/24 - d**3 + 102*d**2. Factor k(q).
-(q + 2)*(q + 3)
Let f(w) be the first derivative of -2*w**3/21 - w**2 - 467. Factor f(v).
-2*v*(v + 7)/7
Let w be -3 - (-3 - (-15)/(-5)). Factor 12*v**3 + 6*v**w + 7*v**3 - 24*v**3 - v.
v*(v - 1)*(v + 1)
Solve 4/3*d**4 + 6*d**2 + 2/3 + 10/3*d + 14/3*d**3 = 0 for d.
-1, -1/2
Factor -2/15 + 0*d + 2/15*d**2.
2*(d - 1)*(d + 1)/15
Let o(k) be the second derivative of k**9/5040 + k**8/1400 - k**7/1050 - 5*k**4/6 - 11*k. Let a(s) be the third derivative of o(s). Solve a(f) = 0.
-2, 0, 2/5
Solve -6/5 - 2/5*v - 3/10*v**4 - 1/10*v**5 + 1/2*v**3 + 3/2*v**2 = 0 for v.
-3, -2, -1, 1, 2
Let b(a) be the second derivative of -a**4/12 - a**3/6 + 32*a - 2. What is c in b(c) = 0?
-1, 0
Let l(f) be the first derivative of -15*f**6/2 - 16*f**5 + 5*f**4 + 135. Factor l(q).
-5*q**3*(q + 2)*(9*q - 2)
Suppose 0 = -2*t + 3*u + 15, 2*u = -5*t - 4 - 6. Let m(z) be the first derivative of -z**3 + 9/2*z**2 + t*z - 4. Factor m(y).
-3*y*(y - 3)
Let m = -4/3271 + 39280/22897. Find f, given that -76/7*f**2 - m*f**3 - 16/7*f + 48/7 = 0.
-6, -1, 2/3
Factor 20/9 - 2/9*r**2 - 2*r.
-2*(r - 1)*(r + 10)/9
Let l(r) = -2*r**3 + r**2 + 10*r - 10. Let i(x) = -x**3 + x - 1. Let k(z) = -3*i(z) + 3*l(z). Suppose k(t) = 0. Calculate t.
-3, 1, 3
Let w(r) = -r**2 - 10*r - 19. Let h be w(-7). Suppose n**2 + 7*n**2 + 5*n**2 + 5*n - 8*n**h = 0. What is n?
-1, 0
Let q = 5243/7012 - -4/1753. Factor -q*c**3 + 0 + 2*c**2 - c.
-c*(c - 2)*(3*c - 2)/4
Let -39/5*g**3 + 0 - 42/5*g**2 + 3/5*g**4 + 0*g = 0. Calculate g.
-1, 0, 14
Let r(z) be the third derivative of -z**5/270 + z**4/12 - 8*z**3/27 - 5*z**2 + z. Solve r(g) = 0 for g.
1, 8
Factor 0 - 28/9*z**3 - 64/9*z**2 + 0*z + 2/9*z**4.
2*z**2*(z - 16)*(z + 2)/9
Let g = -24 + 20. Let f be (g - (-770)/189)/(2/6). Solve f*z - 2/9*z**2 - 2/9*z**3 + 2/9 = 0 for z.
-1, 1
Let d(s) = -s**3 - 6*s**2 - 5*s - 10. Let x be d(-6). Solve -12*u + 3*u**4 + 7*u**4 + x*u**5 - 12*u**2 + 2*u**4 + 9*u**3 - 17*u**5 = 0 for u.
-2, -1, 0, 1
Let h(y) be the second derivative of -y**7/11340 - y**6/810 - y**5/135 + 5*y**4/4 + 10*y. Let z(a) be the third derivative of h(a). Factor z(f).
-2*(f + 2)**2/9
Let n = 84 - 77. Suppose 3*j = -3*m - m + 18, -n = -2*j - m. Factor 0 - j*v**2 + 1/3*v**3 + 3*v.
v*(v - 3)**2/3
Suppose 46/5 + 48/5*s + 2/5*s**2 = 0. Calculate s.
-23, -1
Determine g so that -62/3*g**2 - 400/9 + 32/9*g**3 - 2/9*g**4 + 460/9*g = 0.
2, 4, 5
Let x(a) be the first derivative of -5*a**3/3 + 45*a**2/2 + 149. Determine n, given that x(n) = 0.
0, 9
Let m(l) = -2*l**2 + 1. Let p(j) = -j**3 - 15*j**2 - 8*j + 1. Let a(t) = -10*m(t) + 2*p(t). Factor a(d).
-2*(d + 1)*(d + 2)**2
Let c(l) = 9*l**5 + 6*l**4 - 6*l**2 + 9*l. Let b(p) = p**5 + p**4 + p**3 - p**2 + p. Let s = -2 + 1. Let o(g) = s*c(g) + 6*b(g). Factor o(w).
-3*w*(w - 1)**2*(w + 1)**2
Let 0 + 18/11*m**3 - 2/11*m**5 + 0*m**4 + 0*m + 0*m**2 = 0. Calculate m.
-3, 0, 3
Let u be 9/((-63)/14) - 63/(-30). Let b(k) be the second derivative of 0*k**2 + 0 + 0*k**4 - 9*k + 0*k**3 + 1/30*k**6 - u*k**5. Factor b(j).
j**3*(j - 2)
Let z be (-57)/76 + (-11)/(-4). Factor -4*f**2 - 3*f**z + 0*f**2 - 4 + 11*f**2.
4*(f - 1)*(f + 1)
Let d(h) be the first derivative of -h**6/1800 + h**5/200 - h**4/60 - h**3/3 - 3. Let f(s) be the third derivative of d(s). Factor f(t).
-(t - 2)*(t - 1)/5
Let m be ((-1500)/(-24))/(-25)*(-8)/5. Let x(a) be the first derivative of 4/3*a - 10 - 1/3*a**3 + 1/12*a**m + 0*a**2. Factor x(p).
(p - 2)**2*(p + 1)/3
Let y(a) be the first derivative of 2*a**5/45 + 5*a**4/18 - 2*a**3/27 - 5*a**2/9 + 7. Find w, given that y(w) = 0.
-5, -1, 0, 1
Let u(d) be the first derivative of -2*d**3/15 - d**2/5 + 24*d/5 - 127. Factor u(n).
-2*(n - 3)*(n + 4)/5
Suppose 4*h + 3 = 11. Let l be -1 + 1 - h/(-5). Factor l*p**3 + 2/5*p**2 - 2/5 - 2/5*p.
2*(p - 1)*(p + 1)**2/5
Let f(l) be the third derivative of 7*l**6/4 + 37*l**5/12 - 35*l**4/24 - 5*l**3/3 + 2*l**2 + 112*l. Let f(g) = 0. What is g?
-1, -1/6, 2/7
Suppose -3*u = 4*o + u + 16, 5*o + 56 = 4*u. Let x = o - -8. What is q in -6/7*q**2 - 2/7*q + 6/7*q**4 + x + 10/7*q**3 - 8/7*q**5 = 0?
-1, -1/4, 0, 1
Let y(a) be the second derivative of 0 + 0*a**2 - 5/8*a**4 - 3/40*a**5 - 3/4*a**3 + 22*a + 1/20*a**6. Suppose y(q) = 0. What is q?
-1, 0, 3
Let c(g) = -25*g**2 + 10*g - 1. Let q(u) = u + 1. Let k be q(1). Suppose 5*b - 1 = 14. Let p(s) = 25*s**2 - 10*s + 1. Let n(o) = b*p(o) + k*c(o). Factor n(j).
(5*j - 1)**2
Let f(l) be the first derivative of -5*l**3/3 - 475*l**2/2 - 199. Find j such that f(j) = 0.
-95, 0
Suppose -51 = -24*m + 21. Let o(w) be the first derivative of -2*w**2 - 2/3*w**m - 2*w - 6. Find l, given that o(l) = 0.
-1
Let v(w) be the third derivative of -5/96*w**4 + 0*w + 17*w**2 + 0 + 7/240*w**5 - 1/12*w**3. Factor v(q).
(q - 1)*(7*q + 2)/4
Suppose 5*x - 6*x + 3 = 0. Suppose -r + l = -3*l, 0 = -4*r - x*l. Find h, given that 4/5*h**2 - 4/5*h**4 + 2*h**3 + r - 2*h**5 + 0*h = 0.
-1, -2/5, 0, 1
Let r(w) be the first derivative of w**4/3 + 4*w**3/3 - 5*w + 4. Let z(m) be the first derivative of r(m). Factor z(b).
4*b*(b + 2)
Let b be 4575/(-315) + 14 - (-6)/9. Find j such that 0 + 3/7*j**3 + 2/7*j - b*j**4 + 5/7*j**2 - 1/7*j**5 = 0.
-1, 0, 2
Suppose -3*h + 4*s + 26 = -s, 12 = 2*h - 2*s. Factor 39*y - 39*y - 4*y**h.
-4*y**2
Factor 18*o - 40*o**3 + 25*o**2 + 27*o - 19*o**4 - 15*o + 4*o**4.
-5*o*(o - 1)*(o + 3)*(3*o + 2)
Let n be (