3*(c + 1)/2
Let u(i) be the third derivative of 3*i**6/200 - 11*i**5/50 + 37*i**4/40 - i**3 - 136*i**2. Find r such that u(r) = 0.
1/3, 2, 5
Let k(n) = 5*n**3 - 8*n**2 + 7*n. Suppose 5*z = 4*z - 15. Let r(d) = 35*d**3 - 55*d**2 + 50*d. Let q(m) = z*k(m) + 2*r(m). Suppose q(c) = 0. Calculate c.
0, 1
Let b(o) be the third derivative of -o**8/1344 + o**7/60 - o**6/10 - 7*o**5/120 + 49*o**4/96 - 289*o**2. Find d, given that b(d) = 0.
-1, 0, 1, 7
Let b = 4 + -1. Let h be (-5 - 7)/(8/(-4)). Determine j so that -b*j**2 - 3*j**4 + h*j**2 + 0*j**4 = 0.
-1, 0, 1
Let n(y) be the second derivative of -y**8/336 - y**7/84 + y**6/24 + y**3/2 - 26*y. Let b(x) be the second derivative of n(x). Factor b(g).
-5*g**2*(g - 1)*(g + 3)
Let x be 3/(-4)*(-4 + 0). Determine b, given that -150*b**3 - 7*b**2 - 125*b**4 - 2*b - 3*b - x*b - 53*b**2 = 0.
-2/5, 0
Let c(y) be the first derivative of -8 - 1/12*y**4 + 1/18*y**6 + 2/15*y**5 - 2/9*y**3 + 0*y**2 + 0*y. Factor c(u).
u**2*(u - 1)*(u + 1)*(u + 2)/3
Let u(v) be the second derivative of 4*v**5/15 - 7*v**4/6 - 4*v**3/3 - 17*v**2/2 + 2*v. Let r(d) be the first derivative of u(d). Let r(c) = 0. Calculate c.
-1/4, 2
Let k(n) = -n**2 - n - 1. Let b(t) = -7*t**2 - 3*t - 6. Let r(m) = b(m) - 6*k(m). Let s be r(2). Solve 5 + f**3 - 1 - 6*f**2 + 0*f**3 + 3*f**s = 0.
-1, 2
Let q = 10 + -7. Factor -3*l**3 + 7*l**q - 21 + 21 - 4*l**2.
4*l**2*(l - 1)
Let c(f) be the first derivative of 3*f**5/20 - 27*f**4/16 - f**3/4 + 27*f**2/8 + 23. Let c(m) = 0. Calculate m.
-1, 0, 1, 9
Solve -168 + 35*p + 18 + 8*p - 17*p + 39*p - 5*p**2 = 0.
3, 10
Let t(q) be the third derivative of -5*q**8/1176 - 4*q**7/245 + 11*q**6/420 + 23*q**5/105 + 3*q**4/7 + 8*q**3/21 - 16*q**2 + 7. Solve t(o) = 0.
-2, -1, -2/5, 2
Let m(o) be the first derivative of 1/2*o**4 + 0*o + 0*o**2 - 2/3*o**3 + 6. Factor m(p).
2*p**2*(p - 1)
Let p = -35 + 38. Let v(w) = 2*w**3 - w**2 - 3. Suppose 13 = -3*k + k + 3*z, z + 4 = -k. Let u(c) = 4*c**3 - c**2 - 5. Let m(i) = k*v(i) + p*u(i). Factor m(t).
2*t**2*(t + 1)
Let z(a) be the second derivative of -a**5/4 - 5*a**4/3 + 95*a**3/6 - 35*a**2 - 29*a. Factor z(w).
-5*(w - 2)*(w - 1)*(w + 7)
Factor 200*n - 2*n**2 - 96*n - 4 - n**3 - 97*n.
-(n - 1)**2*(n + 4)
Let p(h) = 2*h**2 - h. Let t(u) = -u**2 - 1. Let y(j) = -p(j) - t(j). Let d(c) = 2*c**2 - 4*c - 4. Let r(i) = -d(i) - 4*y(i). Factor r(q).
2*q**2
Let l be 23/7 - (-46)/(-161). Factor -14*t - 2317*t**3 - 5 + 17 + 2319*t**l.
2*(t - 2)*(t - 1)*(t + 3)
Factor 3 + 3/4*s - 3/8*s**2.
-3*(s - 4)*(s + 2)/8
Let k = -125 + 128. Suppose -b = -1 - 1. Let 3*p**2 + p**k - 2*p - 5*p**3 + p**b + 2*p**3 = 0. Calculate p.
0, 1
Let y(u) be the first derivative of u**6/60 + u**5/25 + u**4/40 - 201. Factor y(i).
i**3*(i + 1)**2/10
Solve -60 + 25*r**2 + 5*r**3 - 3*r**3 + 4*r**3 + 5*r**3 - 16*r**3 + 40*r = 0.
-2, 1, 6
Factor -4 + 4 - 64*h**3 + 842*h**2 - 4*h**4 - 954*h**2.
-4*h**2*(h + 2)*(h + 14)
Let u(m) = -m**3 - 7*m**2 - 6*m + 2. Let i be u(-5). Let p be 51/i - 1 - -4. Factor -p + 4/3*b - 8/3*b**2.
-(4*b - 1)**2/6
Let t(k) = 3*k + 10. Let l be t(-3). Let h be l - (3 - -5)/(-4). Find i, given that -9/5*i**h + 7/5*i**2 - 3/5*i**5 + 12/5*i - 11/5*i**4 + 4/5 = 0.
-2, -1, -2/3, 1
Let x(u) = u**2 + 23*u - 327. Let f be x(-33). Determine i so that 24/5*i**f + 2*i**4 - 5*i + 1/5*i**5 + 0 - 2*i**2 = 0.
-5, -1, 0, 1
Let y(q) = 6*q**5 + 3*q**4 + 3*q**2 - 3*q - 3. Let l(n) = 3*n**5 + 2*n**4 + n**3 + 2*n**2 - 2*n - 2. Let r(h) = -3*l(h) + 2*y(h). Factor r(x).
3*x**3*(x - 1)*(x + 1)
Let g(m) be the first derivative of 12/11*m - 41 - 14/11*m**2 + 1/55*m**5 + 23/33*m**3 - 2/11*m**4. Factor g(q).
(q - 3)*(q - 2)**2*(q - 1)/11
Let x(p) be the third derivative of p**9/22680 - p**8/10080 - 5*p**4/24 + 20*p**2. Let z(d) be the second derivative of x(d). Factor z(v).
2*v**3*(v - 1)/3
Suppose -f + 212 = 208. Let c(p) = -p**3 + 2*p**2 + 7*p + 8. Let n be c(f). Factor -1/2*k**2 - 3*k + k**3 + 1/4*k**n + 9/4.
(k - 1)**2*(k + 3)**2/4
Suppose -2*p + 46 + 64 = 0. Let k(z) = -125*z**3 - 15*z**2 + 125*z + 70. Let f(u) = 9*u**3 + u**2 - 9*u - 5. Let q(i) = p*f(i) + 4*k(i). Factor q(r).
-5*(r - 1)*(r + 1)**2
Let o(d) be the second derivative of -d**4/54 - 38*d**3/27 - 361*d**2/9 + 3*d. Factor o(s).
-2*(s + 19)**2/9
Let i(l) be the first derivative of -15*l**4/4 - 20*l**3/3 + 25*l**2/2 + 10*l - 255. Let i(a) = 0. Calculate a.
-2, -1/3, 1
Let c(k) = k**2 - 30*k - 3. Let a be c(31). Let l be a/(-70) + (-2)/(-2). Determine o so that 1/5*o**2 + 4/5*o + l = 0.
-3, -1
Let d(l) be the first derivative of 10/3*l**3 + 15/2*l**2 + 11 + 0*l - 5/4*l**4. Let d(v) = 0. Calculate v.
-1, 0, 3
Determine o, given that -4*o**5 + 1/2*o - 63/4*o**4 - 27/4*o**2 - 19*o**3 + 0 = 0.
-2, -1, 0, 1/16
Let b = 0 + 2. Let v be (-9)/3 - (-4)/8 - (-24 + 20). Determine o, given that 3/4*o**b - 9/4*o + v = 0.
1, 2
Let u(v) = -8*v**3 - 2*v**3 - 3*v**3 - 5*v**4 + v**2 - 3*v**5 - 4*v**4. Let f(b) = -b**3 + b**2. Let c(j) = -4*f(j) + u(j). Factor c(h).
-3*h**2*(h + 1)**3
Suppose 0 = 6*y - 11 - 7. Let k(n) be the first derivative of 1/2*n + 1/8*n**4 + 1/2*n**3 - y + 3/4*n**2. Solve k(t) = 0 for t.
-1
Suppose 3/8*r**2 - 3/4*r + 3/4*r**3 + 0 - 3/8*r**4 = 0. What is r?
-1, 0, 1, 2
Factor 2/11*f**4 + 70/11*f**3 + 0 + 256/11*f**2 + 248/11*f.
2*f*(f + 2)**2*(f + 31)/11
Let s(y) be the second derivative of y**6/24 - 93*y**5/80 + 11*y**4/4 + 17*y**3/6 + y - 15. Factor s(p).
p*(p - 17)*(p - 2)*(5*p + 2)/4
Let n(d) be the second derivative of -1/6*d**4 - 19*d + 0*d**3 + d**2 + 0. Factor n(h).
-2*(h - 1)*(h + 1)
Let i be 306/32*6/(-45). Let r = 23/8 + i. Solve 2/5*k**2 + 0*k - r = 0 for k.
-2, 2
Factor -13/4*i**3 + 1/4*i**5 - 7/4*i**2 + 0 + 0*i - 5/4*i**4.
i**2*(i - 7)*(i + 1)**2/4
Let h(x) be the first derivative of x**3/9 - 5*x**2 + 75*x + 245. Factor h(g).
(g - 15)**2/3
Let a(d) be the second derivative of d**6/20 + 9*d**5/16 + 13*d**4/8 + 3*d**3/8 - 15*d**2/4 + 8*d - 29. Find x such that a(x) = 0.
-5, -2, -1, 1/2
Let o(n) be the third derivative of n**8/2240 - n**7/120 + n**6/30 + 2*n**5/5 - n**4/2 - 13*n**2. Let p(x) be the second derivative of o(x). Factor p(l).
3*(l - 4)**2*(l + 1)
Let c(s) = 45 + 6*s - 6 + 35. Let q be c(-12). Factor 0*a + 2/3*a**q + 0.
2*a**2/3
Let f(o) = 10*o**2 - 3*o - 2. Let u be f(-1). Suppose 2*d = -u + 25. Factor d*i**3 - 2*i - 12*i**3 + 3*i + 4*i**3.
-i*(i - 1)*(i + 1)
Let q = 6 - 4. Let i be 47/((-1269)/243) + (-412)/(-44). Factor -i*j - 2/11*j**q - 2/11.
-2*(j + 1)**2/11
Let v(k) be the first derivative of -k**3/4 + 12*k + 215. Determine q so that v(q) = 0.
-4, 4
Let x = -27994/5 + 5602. Solve -14/5*r + 2/5*r**2 - x = 0.
-1, 8
Let a = -456 - -459. Let l(s) = s**2 - s - 2. Let i be l(-2). Solve -t**2 - 4*t**3 + 0*t**3 + i*t**a - t**3 = 0 for t.
-1, 0
Let s be 3*(-2 - -1) + 10455/3321. Let n(z) be the first derivative of 1/6*z**4 + 2/45*z**5 + 0*z + s*z**3 - 1 + 0*z**2. Factor n(f).
2*f**2*(f + 1)*(f + 2)/9
Let k(n) be the third derivative of n**8/2016 + n**7/420 - n**6/240 - 7*n**5/360 + n**4/24 + 440*n**2. Determine d so that k(d) = 0.
-3, -2, 0, 1
Let a(b) be the first derivative of b**7/210 - b**6/75 - b**5/100 + b**4/30 - 23*b - 18. Let f(m) be the first derivative of a(m). Solve f(u) = 0 for u.
-1, 0, 1, 2
Let j(z) be the second derivative of z**10/20160 - z**9/5040 + z**7/840 - z**6/480 - 7*z**4/4 + 7*z. Let d(k) be the third derivative of j(k). Factor d(h).
3*h*(h - 1)**3*(h + 1)/2
Let d(i) be the first derivative of i**4 - 112*i**3/3 + 54*i**2 - 544. Factor d(n).
4*n*(n - 27)*(n - 1)
Factor 2/9*x**2 - 212/9*x + 5618/9.
2*(x - 53)**2/9
Let p(j) be the second derivative of -j**7/63 + 2*j**6/15 - 13*j**5/30 + 2*j**4/3 - 4*j**3/9 - 29*j. Factor p(y).
-2*y*(y - 2)**2*(y - 1)**2/3
Let a = 115 - -9. Factor 245*q**2 - 119*q**2 + q - a*q**2 - 3*q.
2*q*(q - 1)
Let h = -134 + 136. Factor -2*y**h - 4/7*y + 0.
-2*y*(7*y + 2)/7
Let z be ((-10)/6)/((-183)/549). Let j(f) be the third derivative of 3/8*f**3 + 1/80*f**z + 1/8*f**4 + 0*f + 0 + 11*f**2. Factor j(k).
3*(k + 1)*(k + 3)/4
Let h(b) be the first derivative of b**3/2 - 21*b**2/4 + 15*b + 242. What is k in h(k) = 0?
2, 5
Let q = -1/15 - -2/15. Let l(p) be the third derivative of 1/120*p**4 - p**2 + 1/300*p**5 - q*p**3 + 0*p + 0. Factor l(j).
(j - 1)*(j + 2)/5
Let o = 24 + -19. Suppose 0*p**5 - 48