2
Let h = 1318/3 + -439. Let u(m) be the first derivative of 2/3*m**3 - 8*m**2 - 1 - 2/5*m**5 + 5/2*m**4 + 8*m - h*m**6. Factor u(g).
-2*(g - 1)**3*(g + 2)**2
Let i = 219 + -214. Let z(b) be the third derivative of 0 + 0*b - 1/24*b**4 + 1/120*b**i + 1/12*b**3 + 4*b**2. Let z(y) = 0. Calculate y.
1
Suppose 98*p + 254*p = 704. Factor -2/5*y**p + 0*y - 8/5*y**5 - 12/5*y**3 - 18/5*y**4 + 0.
-2*y**2*(y + 1)**2*(4*y + 1)/5
Let u(l) be the second derivative of 5*l**4/96 + 17*l**3/48 + 3*l**2/8 + 11*l. Solve u(i) = 0 for i.
-3, -2/5
Let p = 72 + -72. Suppose p*f = -0*f + f. Factor -1/2*j**5 + 0*j**2 + f + 0*j - j**4 - 1/2*j**3.
-j**3*(j + 1)**2/2
Let k(f) = f**3 - 23*f**2 - f + 26. Let r be k(23). Factor 48*l**2 - 16*l - 44*l**r + 8*l**2 - 2*l**4 + 12*l**4.
2*l*(l - 2)**2*(5*l - 2)
Let l be (7 + -5)*(-10)/(-4). Let c be l/(-6)*(-9)/30. Suppose 0*a**2 + 1/4*a**3 + 0 - c*a = 0. What is a?
-1, 0, 1
Suppose -2*t + t = 0. Suppose 5*y + 0*y - 10 = t. Factor -3*r**3 - 6*r**y - 5*r + 2*r + 0*r**3.
-3*r*(r + 1)**2
Suppose 3*s = -15 + 24. Factor 6*y**s + 40*y**5 - 43*y**5 + 3*y**2 - 3*y**3 - 3*y**4.
-3*y**2*(y - 1)*(y + 1)**2
Suppose -m = -4*m + 12. Let c(f) be the first derivative of 8*f - 4 + 44*f - 12*f**2 + 11 - m*f + f**3. What is l in c(l) = 0?
4
Let k be 12 + -12 - (-4 - 1). Suppose -3*x = k*m + 6, -4*m = 2*x + 11 - 5. Find p, given that 32/7*p - 2*p**4 - 50/7*p**2 - 8/7 + 2/7*p**5 + 38/7*p**x = 0.
1, 2
Suppose 0 = 3*b + 2*d - 4*d - 8, 6 = 2*b - 2*d. Solve 3*t**2 + 2*t**b + 10*t**2 - 20*t**2 + 20*t = 0 for t.
0, 4
Let q = 126 + -627/5. Let n = 28166/5 + -5633. What is d in -q*d**2 - n - d + 9/5*d**3 = 0?
-1/3, 1
Let u be (-6)/120*(-84)/238. Let k(n) be the second derivative of u*n**5 - 4/51*n**3 + 0 + 4/17*n**2 + 3*n - 5/102*n**4. Factor k(q).
2*(q - 2)*(q + 1)*(3*q - 2)/17
Factor -7/5*p**4 + 0 + 16/5*p**2 + 0*p - 1/5*p**5 - 8/5*p**3.
-p**2*(p - 1)*(p + 4)**2/5
Let s(h) be the first derivative of 3/5*h**5 + 16 + 0*h - 3*h**2 + 3/2*h**4 - h**3. Factor s(n).
3*n*(n - 1)*(n + 1)*(n + 2)
Let w(a) be the second derivative of a**7/14 - 3*a**6/5 - 3*a**5/20 + 3*a**4/2 - 170*a. Let w(j) = 0. What is j?
-1, 0, 1, 6
Let b(z) be the first derivative of -4*z**2 + 6*z - 14/3*z**3 + 11. Factor b(m).
-2*(m + 1)*(7*m - 3)
Let x(f) be the first derivative of -20 - 1/3*f**6 + 2/5*f**5 + f**4 + 0*f**3 + 0*f**2 + 0*f. Determine k, given that x(k) = 0.
-1, 0, 2
Suppose -14 = -32*w + 25*w. Let h = -184/21 + 66/7. Find p, given that 0 + 2/3*p**3 - h*p - 2/3*p**4 + 2/3*p**w = 0.
-1, 0, 1
Let g = 861 - 4273/5. Let k = -6 + g. Factor 2/5*r**2 - k + 2/5*r - 2/5*r**3.
-2*(r - 1)**2*(r + 1)/5
Let x(v) = v**3 - 43*v**2 - 74*v + 32. Let w(d) = -7*d**3 + 390*d**2 + 665*d - 286. Let o(b) = -6*w(b) - 57*x(b). Factor o(r).
-3*(r - 9)*(r + 2)*(5*r - 2)
Let d be 2/4 - 33/(-6). Suppose 1 = 2*i - h, -h - 7 = -d*i + i. Factor 0 - 5*n**4 - 5 + 10*n**i + 0*n**4.
-5*(n - 1)**2*(n + 1)**2
Let c(m) be the second derivative of m**6/10 - 9*m**5/2 - 31*m**4/4 + 140*m. Determine l, given that c(l) = 0.
-1, 0, 31
Let d be (4/22)/((-9)/(-99)). Let a(k) be the second derivative of 0*k**d - 1/40*k**5 + 0 - 1/8*k**4 - 1/6*k**3 + 5*k. Suppose a(b) = 0. What is b?
-2, -1, 0
Factor -25/4*y + 1/4 - 29*y**2.
-(4*y + 1)*(29*y - 1)/4
Suppose 24 = 9*i - i. Factor 6*t - 5*t**i + 3*t - 5*t**2 + 5 - 4*t.
-5*(t - 1)*(t + 1)**2
Let d(j) be the second derivative of j**5/15 + j**4/9 - 8*j**3/9 - 8*j**2/3 - 3*j + 62. Factor d(t).
4*(t - 2)*(t + 1)*(t + 2)/3
Let r = 4 - 2. Suppose 4*x + r*g = -10, g = 2*g + 5. Factor -1/4*n**2 - 1/4*n**3 + x + 1/4*n**4 + 1/4*n.
n*(n - 1)**2*(n + 1)/4
Let w(u) be the third derivative of -3*u**8/136 + 167*u**7/595 - 439*u**6/1020 + 9*u**5/34 - 7*u**4/102 + 39*u**2. What is o in w(o) = 0?
0, 2/7, 1/3, 7
Let j(d) be the third derivative of -d**8/151200 - d**7/18900 - d**6/5400 + 7*d**5/30 - 15*d**2. Let l(n) be the third derivative of j(n). Solve l(z) = 0 for z.
-1
Let x(z) be the first derivative of 40/3*z**3 + 6*z + 7/5*z**5 + 23/3*z**4 + 8*z**2 + 5. Let h(c) be the first derivative of x(c). Determine n so that h(n) = 0.
-2, -1, -2/7
Let w = 1266 + -1260. Let p(u) be the second derivative of 2*u**2 + 0 + 2/3*u**3 + w*u + 1/12*u**4. Solve p(j) = 0.
-2
Let z(w) be the third derivative of 343*w**8/120 - 98*w**7/3 + 1617*w**6/10 - 2268*w**5/5 + 3159*w**4/4 - 4374*w**3/5 - 217*w**2. Factor z(s).
2*(s - 2)*(7*s - 9)**4/5
Let x(g) be the third derivative of 1/21*g**7 - 1/6*g**5 + 5/336*g**8 + 0 + 0*g**3 + 16*g**2 + 0*g**6 + 0*g - 5/24*g**4. Factor x(q).
5*q*(q - 1)*(q + 1)**3
Let j(c) be the second derivative of -c**6/45 + 2*c**5/9 - 17*c**4/36 + 4*c**3/9 - 3*c**2 + 14*c. Let g(d) be the first derivative of j(d). Factor g(n).
-2*(n - 4)*(2*n - 1)**2/3
Let q(u) be the second derivative of -7/75*u**5 + 0 + 0*u**2 + 1/35*u**7 - 2/15*u**4 + 8/45*u**3 + 1/15*u**6 + 9*u. Solve q(n) = 0 for n.
-2, -1, 0, 2/3
Let b(l) = -72*l**2 + 430*l + 12. Let h be b(6). Suppose -5/2*n**4 + h*n + 0*n**3 + 0 + 5/2*n**2 = 0. What is n?
-1, 0, 1
Suppose 2*z - 15 + 3 = 2*l, 4*z - 20 = 3*l. Suppose -3*v = z*v - 20. Solve 2/9 + 0*f**3 + 0*f + 2/9*f**v - 4/9*f**2 = 0.
-1, 1
Let o(c) = -2*c**4 - 8*c**3 - 2*c**2 + 9*c - 6. Let l(t) = -4*t**4 - 16*t**3 - 4*t**2 + 19*t - 10. Let k(w) = 3*l(w) - 5*o(w). Factor k(i).
-2*i*(i - 1)*(i + 2)*(i + 3)
Suppose 7*s - 6*s = -9, 4*i = -s + 7. What is o in 2/11*o**i + 4/11*o**3 + 0*o + 0 + 0*o**2 - 2/11*o**5 = 0?
-1, 0, 2
Let n(g) be the second derivative of 0*g**3 + 0*g**5 - 11*g + 1/2*g**2 + 0 - 1/6*g**4 + 1/30*g**6. Let n(b) = 0. What is b?
-1, 1
Factor 3*n**2 + 56 + 18*n + 20*n - 2*n**2 + n**2 - 16*n.
2*(n + 4)*(n + 7)
Let g(n) = 5*n**2 - 5. Let s(x) = -x - 6. Let u be s(13). Let t = u + 16. Let c(i) = -2*i**2 + 2. Let v(o) = t*g(o) - 5*c(o). Suppose v(j) = 0. Calculate j.
-1, 1
Let b(t) be the second derivative of 2*t**6/15 - 59*t**5/5 + 899*t**4/3 - 1682*t**3/3 - 2*t + 32. Factor b(h).
4*h*(h - 29)**2*(h - 1)
Let x(d) be the first derivative of 3/28*d**4 - 1 - 2/7*d**3 + 0*d + 3/14*d**2. Factor x(l).
3*l*(l - 1)**2/7
Suppose 80 - 20*q**4 + 5*q + 185*q - 1094*q**2 + 92*q**3 + 123*q**3 + 629*q**2 = 0. What is q?
-1/4, 1, 2, 8
Factor 1/3*a - 1/3*a**3 + 1/3*a**2 - 1/3.
-(a - 1)**2*(a + 1)/3
Let s(v) be the second derivative of -v**7/231 + v**6/11 + v**5/55 - 5*v**4/11 - v**3/33 + 15*v**2/11 - 2*v - 12. What is r in s(r) = 0?
-1, 1, 15
Let a(v) be the third derivative of 0 - v**4 + 0*v + 3/10*v**5 - 12*v**2 + 4/3*v**3. Factor a(w).
2*(3*w - 2)**2
Let r(c) = -c**2 - 3*c + 10. Let j be r(-5). Suppose j = -2*b + 6, 4*b - 31 + 9 = -5*o. Find f, given that -o + 0 - 12*f**3 - 3*f - 15*f**2 + 2 = 0.
-1, -1/4, 0
Let t(w) be the second derivative of -5*w**4/12 + 160*w**3/3 + 330*w**2 - 590*w. Factor t(l).
-5*(l - 66)*(l + 2)
Suppose 2 = -4*d - h + 5, 4*h - 12 = -d. Let r(v) be the third derivative of 1/60*v**4 + d*v + 0 + 1/100*v**6 + 4*v**2 + 2/75*v**5 + 0*v**3. Factor r(z).
2*z*(z + 1)*(3*z + 1)/5
Suppose -2*u + 8 = -8. Suppose 2*i - 4*i - 2*a + 8 = 0, 4*a = u. Factor 10 - 3*v**i - 9 + 2*v**2.
-(v - 1)*(v + 1)
Find s such that 312 - 736*s + 99*s - 429*s - 4065*s**2 + 146*s - 12 + 275*s**3 = 0.
-2/5, 2/11, 15
Let c(h) be the third derivative of -h**7/1050 + h**6/600 + h**5/150 + 7*h**2 - 2*h. Factor c(w).
-w**2*(w - 2)*(w + 1)/5
Let p(o) be the third derivative of o**7/280 + o**6/30 - o**5/40 - o**4/2 + 25*o**3/6 - 8*o**2. Let t(a) be the first derivative of p(a). Factor t(q).
3*(q - 1)*(q + 1)*(q + 4)
Let l(y) = y**3 + 7*y**2 + 33*y - 9. Let w(x) = 4*x**2 + 16*x - 4. Let c(o) = -4*l(o) + 9*w(o). Factor c(d).
-4*d*(d - 3)*(d + 1)
Suppose -a - x - 616 = 1303, a - 3*x = -1935. Let d = -32681/17 - a. Factor -d*j**2 + 16/17*j + 8/17.
-2*(j - 2)*(5*j + 2)/17
Let f(v) = -v**5 - v**4 - v**3 + v**2 - v + 3. Let r(o) = 8*o**5 + 17*o**4 + 7*o**3 - 4*o**2 + 4*o - 12. Let q(a) = 12*f(a) + 3*r(a). Let q(t) = 0. What is t?
-3, -1/4, 0
Let b(r) = 2*r**2 - 20*r + 17. Let q be b(14). Let s = 131 - q. Factor 4/5 - 2/5*v**s - 2/5*v.
-2*(v - 1)*(v + 2)/5
Let g(w) be the second derivative of 9*w - 3/16*w**5 + 0 + 3/4*w**2 + 1/40*w**6 + 9/16*w**4 - 7/8*w**3. What is k in g(k) = 0?
1, 2
Let -255*r + r**3 + 102*r - 176*r**2 + 59*r - 12 + 31*r**3 = 0. What is r?
-1/4, 6
Let b(o) be the first derivative of -2*o**5/15 - o*