 - 3*i**2 + 5/2*i = 0.
1, 3
Let a(d) be the third derivative of -d**8/6720 + d**7/1120 - d**6/720 - d**3/2 - 2*d**2. Let n(u) be the first derivative of a(u). Factor n(v).
-v**2*(v - 2)*(v - 1)/4
Let n = -6/65 + 2/5. Factor 6/13*p**2 - 2/13*p - n.
2*(p - 1)*(3*p + 2)/13
Let o(x) be the third derivative of -5*x**8/504 - x**7/45 + x**6/60 + 7*x**5/90 + x**4/18 + 17*x**2. Find b, given that o(b) = 0.
-1, -2/5, 0, 1
Let t = -44549/90 + 495. Let i(v) be the third derivative of 0*v - 7/180*v**5 + v**2 + 1/36*v**4 + 0 + 1/18*v**3 + t*v**6. Factor i(u).
(u - 1)**2*(4*u + 1)/3
Let v = 12 - 16. Let l = v - -6. Determine o so that 1/4*o**l + 1/4*o - 1/4*o**3 - 1/4 = 0.
-1, 1
Let i(f) = -f + 4. Let w be i(2). Let o = 38 - 36. What is h in 5*h + h - 2 - o*h - w*h**2 = 0?
1
Let k(g) be the second derivative of -g**6/75 - g**5/10 - 4*g**4/15 - 4*g**3/15 + 12*g. Factor k(d).
-2*d*(d + 1)*(d + 2)**2/5
Let z(v) be the second derivative of -2*v**6/15 - v**5 - 8*v**4/3 - 8*v**3/3 + 8*v. Suppose z(r) = 0. What is r?
-2, -1, 0
Let i(o) = -o**3 - 28*o**2 - 30*o - 79. Let u be i(-27). Let -9/2*z**u + 15/4*z + 9/4*z**5 + 3*z**4 + 3/2 - 6*z**3 = 0. Calculate z.
-2, -1, -1/3, 1
Factor -2 + 12*d - 5*d**2 + 11 - 15*d**3 + 3*d + 1 - 5*d**4.
-5*(d - 1)*(d + 1)**2*(d + 2)
Factor -16/11 - 24/11*s - 162/11*s**3 + 180/11*s**2.
-2*(3*s - 2)**2*(9*s + 2)/11
Suppose -7*q = -2*q - 950. Let f be 4/14 + q/70. Factor 1/2*k**2 + 9/2 - f*k.
(k - 3)**2/2
Factor 0*j + 1/4*j**3 - 1/2*j**2 + 0.
j**2*(j - 2)/4
Let h(u) be the second derivative of -u**4/6 + 2*u**3/3 - u**2 - 10*u. Factor h(j).
-2*(j - 1)**2
Let d(z) be the second derivative of -z**8/1120 - z**7/560 + z**3/2 - z. Let k(c) be the second derivative of d(c). Factor k(a).
-3*a**3*(a + 1)/2
Let y(f) be the third derivative of -f**7/1050 + f**6/150 + f**5/60 + 22*f**2. Determine i, given that y(i) = 0.
-1, 0, 5
Factor 0*q - 4/7*q**2 + 0 - 2/7*q**4 + 6/7*q**3.
-2*q**2*(q - 2)*(q - 1)/7
Suppose 11*y = -7*y. Factor 0 + 0*i**2 - 3/5*i**3 + 3/5*i**5 + y*i**4 + 0*i.
3*i**3*(i - 1)*(i + 1)/5
Suppose -5*h + 11 = 2*f + 1, -3*f + 5 = 5*h. Suppose 3*o = 3*r + 12, h*o + 0*o + r = -4. Factor 1/5*q**3 - 1/5*q + o + 1/5*q**4 - 1/5*q**2.
q*(q - 1)*(q + 1)**2/5
Suppose -136 - 27*g**4 - 15*g**5 + 136 - 9*g**3 + 3*g**2 = 0. Calculate g.
-1, 0, 1/5
Suppose 3 = -l + 4. Let f = 2 + l. Factor 0*u**2 + 4*u**2 + 2*u**f + 0*u + 2*u.
2*u*(u + 1)**2
Factor -10/7*g**3 + 0*g**2 - 2/7*g**4 + 0 + 0*g.
-2*g**3*(g + 5)/7
Let q be (-25)/225 - 28/(-90). Factor q*g**4 + 0*g**3 - 1/5*g**2 + 0 + 0*g.
g**2*(g - 1)*(g + 1)/5
Let n(j) = j**2 - j - 1. Let b(c) = 5*c**2 - 7*c - 6. Let t(v) = b(v) - 6*n(v). Let m(l) = -6*l**2 - 4*l + 2. Let q(h) = -m(h) + 4*t(h). Factor q(k).
2*(k - 1)*(k + 1)
Find y such that 5*y**2 - 45*y**2 + 0 - 25*y + 10 + 5*y**2 = 0.
-1, 2/7
Suppose 3*f + k = 201, k + 2*k + 145 = 2*f. Suppose 2*i - f = -s - 3*s, -4*s + 4*i + 56 = 0. Solve s*w - 5*w**2 - 1 - 1 - 27*w**2 = 0 for w.
1/4
Let o(j) be the third derivative of -1/24*j**3 + 1/240*j**5 + 0*j**4 + 0*j + 0 + 5*j**2. Factor o(w).
(w - 1)*(w + 1)/4
Let v(d) be the second derivative of -1/9*d**3 + 0 + 0*d**2 + 1/9*d**4 - d - 1/30*d**5. Factor v(z).
-2*z*(z - 1)**2/3
Let q(z) be the third derivative of -z**5/60 - z**4/12 + z**3/2 - 29*z**2. Suppose q(i) = 0. Calculate i.
-3, 1
Suppose 4*t - 9*t + 30 = 0. Let d(i) be the first derivative of 2/15*i**3 - 2 + 6/25*i**5 + 0*i - 3/10*i**4 + 0*i**2 - 1/15*i**t. Factor d(r).
-2*r**2*(r - 1)**3/5
Let u(q) be the second derivative of q**8/320 - 23*q**7/840 + q**6/40 + q**4/6 + 5*q. Let x(c) be the third derivative of u(c). Let x(b) = 0. What is b?
0, 2/7, 3
Let z(a) = 44*a**4 - 8*a**3 - 10*a**2. Let c(s) = 5*s**4 - s**3 - s**2. Let i(r) = -52*c(r) + 6*z(r). Suppose i(g) = 0. What is g?
-2, 0, 1
Let x(r) be the second derivative of 1/7*r**3 - 1/7*r**2 + 0 - 1/14*r**4 + 1/70*r**5 - 3*r. Find o, given that x(o) = 0.
1
Let x(b) be the third derivative of b**5/30 + 13*b**4/24 - 16*b**3/3 - 5*b**2. Let p(m) = 3*m**2 + 27*m - 63. Let d(k) = -5*p(k) + 9*x(k). Solve d(o) = 0.
3
Let s(v) be the first derivative of -3*v**5/40 - v**4/8 - 6*v + 8. Let u(f) be the first derivative of s(f). Solve u(g) = 0.
-1, 0
Let d be (18/(-12))/(1/4*-3). Let 0*k**d - 2/7*k**3 + 2/7*k + 0 = 0. Calculate k.
-1, 0, 1
Let s(w) be the second derivative of 5*w**4/6 - 5*w**3/2 - 5*w**2 + 2*w. Factor s(n).
5*(n - 2)*(2*n + 1)
Let p(v) = 13*v**2 + 64*v + 24. Let o(f) = -25*f**2 - 128*f - 48. Let k(i) = -6*o(i) - 10*p(i). Solve k(d) = 0 for d.
-6, -2/5
Factor -7*b**2 + 15*b**2 + 28*b**4 + 36*b**3 + 544 - 544.
4*b**2*(b + 1)*(7*b + 2)
Let z(b) = -4*b**2 - 2*b + 6. Let i(p) be the third derivative of -p**5/12 - p**4/12 + 7*p**3/6 + 4*p**2. Let w(v) = 5*i(v) - 6*z(v). Factor w(s).
-(s - 1)**2
Suppose 32 = 5*c - 3. Let h = -7 + c. Factor 0 - 45/2*k**4 + 25/2*k**5 + 12*k**3 - 2*k**2 + h*k.
k**2*(k - 1)*(5*k - 2)**2/2
Let d be 0/(-5) + (-4)/(-22). Let k = 16/33 + d. Let -2/3*a**2 + 2/3*a + 2/3*a**4 + 0 - k*a**3 = 0. Calculate a.
-1, 0, 1
Let f(b) be the third derivative of -1/45*b**6 + 0 - 1/252*b**7 - b**2 + 0*b - 1/36*b**3 - 1/20*b**5 - 1/18*b**4. Factor f(v).
-(v + 1)**3*(5*v + 1)/6
Let x = -1961/77 - -288/11. Let v(g) be the first derivative of -x*g**2 + 2 + 1/14*g**4 - 2/35*g**5 + 4/7*g + 2/7*g**3. Find b such that v(b) = 0.
-2, 1
Let t(f) = -2*f - 42. Let h be t(-23). Let k(y) be the third derivative of 0*y + 0 + 0*y**3 + y**2 + 1/90*y**5 + 0*y**h. Factor k(r).
2*r**2/3
Let y = 36 + -32. Let s(p) be the first derivative of 0*p**2 - 3/25*p**5 + 3 + 0*p - 1/5*p**3 - 3/10*p**y. What is t in s(t) = 0?
-1, 0
Suppose -2*l - 1 = -l - 3*v, -4*v - 55 = 3*l. Let m(p) = -p - 11. Let w be m(l). What is h in 10/3*h**4 + 20*h**w + 46/3*h**3 - 16/3 + 8/3*h = 0?
-2, -1, 2/5
Let h(w) = w**3 + w**2. Suppose -4 = -0*t + 4*t. Let o be h(t). Suppose 0*j**3 - 1/3*j**5 + 1/3*j**4 + o*j + 0 + 0*j**2 = 0. What is j?
0, 1
Let z = 1 - -2. Factor -4*d**3 - d**2 - 4*d**3 + 1 + 2*d**z + 5*d**3 + d.
-(d - 1)*(d + 1)**2
Suppose 0 = -2*x, -5*l + 3*x + 12 = -3. Factor t**5 + 3*t**3 + 3*t**4 + 2*t**5 - l*t**2 - 6*t**5.
-3*t**2*(t - 1)**2*(t + 1)
Let x(c) be the third derivative of -c**5/15 - c**4/3 - 2*c**3/3 - 6*c**2. Find d, given that x(d) = 0.
-1
Let u = 34 - 4. Let f be (u/9 - 3)/1. Factor 1/3*m**4 + 2/3*m**3 + f*m**2 + 0*m + 0.
m**2*(m + 1)**2/3
Let w(o) = o - 3. Let a be w(6). Suppose 4*p - 2*j = 16, -6*p + a*j = -3*p - 15. Factor 2*v**p - v**2 + 2*v**4 + v**4 - 4*v**4.
-v**2*(v - 1)**2
Let h(l) = l**3 + 3*l**2 - 6*l - 6. Let q be h(-4). Solve -k**3 - 4*k**4 + 2*k**4 - q*k**5 + 2*k**2 + 3*k**3 = 0 for k.
-1, 0, 1
Let p = 2 - -1. Let c be p/(-5) - 69/(-15). Suppose 2*m**3 + 4*m + 4*m**3 + c + 20*m**2 + 14*m = 0. What is m?
-2, -1, -1/3
Suppose 2*l = -3*v - 1, 3*l - l + 8 = 4*v. Let i(w) = -2*w**2 + 6*w. Let u(a) = a - 1. Let z(c) = v*i(c) - 4*u(c). Factor z(y).
-2*(y - 2)*(y + 1)
Let n be (-2)/(-50)*5/10. Let z(r) be the second derivative of 1/15*r**4 + n*r**5 + 4*r + 0 + 1/15*r**3 + 0*r**2. Factor z(s).
2*s*(s + 1)**2/5
Let h be 9 + -10 + 1*(-21)/(-20). Let x(m) be the second derivative of -1/3*m**3 + 1/4*m**4 + 0 - h*m**5 + 0*m**2 + 3*m. Factor x(l).
-l*(l - 2)*(l - 1)
Factor -2*c**3 + 5*c**5 + 4*c**2 + 40 - 5*c**4 - 2*c**5 + 2*c**2 - c - 41.
(c - 1)**3*(c + 1)*(3*c + 1)
Let t(o) = o**3 - 11*o**2 - 13*o + 14. Let s be t(12). Find n such that -9*n**s - 3*n**3 - 266 - 5*n + 263 - 4*n = 0.
-1
Let i(r) be the third derivative of 0 + 0*r**4 + 0*r**3 + 0*r + 3*r**2 - 1/60*r**5 + 1/60*r**6 - 1/210*r**7. Find t such that i(t) = 0.
0, 1
Factor -36*j**2 + 3*j**3 + 39*j - 375 - 35*j**2 + 26*j**2 + 186*j.
3*(j - 5)**3
Let d(y) = -4*y**2 - y + 2. Let z(g) = -7*g**2 - g + 3. Let b(t) = 10*d(t) - 6*z(t). What is h in b(h) = 0?
1
Let d(p) = -2*p**3 + 2*p**2 - 2*p. Let g be d(2). Let f = g + 18. Factor 27*c**2 + f*c**4 + 4*c**5 - c**5 + 3*c**4 + 9*c**3 - 24*c**2.
3*c**2*(c + 1)**3
Let s be (-12)/(-10) + (-8)/10. Factor 2/5*u - s*u**3 + 0*u**2 + 0.
-2*u*(u - 1)*(u + 1)/5
Let c(i) be the second derivative of -i**4/30 - 2*i**3/15 - i**2/5 + 8*i. Solve c(b) = 0.
-1
Let j = -16/33 + 106/231. Let u = 160/231 + j. Determine l so that 2/3 - u*l**2 + 0*l = 0.
-1, 1
Let d(h) = -2*h - 20. Let y be d(-14). Let v be 15/12 + 2/y. Factor u**2 + 1/2*u**5