f*i**5 + 0*i**2 + 0*i + 2/5*i**3 + 0 + 0*i**4 = 0.
-1, 0, 1
Let f(v) be the third derivative of -v**8/840 + 8*v**7/525 - 7*v**6/100 + 11*v**5/75 - 2*v**4/15 - 6*v**2 + 3. Find k such that f(k) = 0.
0, 1, 2, 4
Factor -4 - 7*o + 24 + 56*o**2 - 29*o**2 - 28*o**2 - 2.
-(o - 2)*(o + 9)
Let d(f) be the third derivative of -f**8/80640 + f**7/20160 + 2*f**5/5 - 25*f**2. Let a(n) be the third derivative of d(n). Factor a(k).
-k*(k - 1)/4
Let p(s) be the second derivative of -1/24*s**3 + 0*s**4 - 1/168*s**7 + 0*s**2 + 0*s**6 + 13*s + 1/40*s**5 + 0. Factor p(d).
-d*(d - 1)**2*(d + 1)**2/4
Let m(a) be the first derivative of -a**8/1120 - a**7/336 - a**6/360 + 4*a**3 + 1. Let t(q) be the third derivative of m(q). Factor t(o).
-o**2*(o + 1)*(3*o + 2)/2
Let s(o) = -69*o + 2. Let b be s(0). Factor 8/11*t + 2/11*t**b + 6/11.
2*(t + 1)*(t + 3)/11
Let n(b) be the first derivative of b**5 + 5*b**4 - 10*b**3 - 10*b**2 + 25*b + 52. Determine t, given that n(t) = 0.
-5, -1, 1
Suppose -2*v + 0*v + 18 = 0. Let z = v + -4. Factor -z*b**2 - b**2 - b + 4*b**2.
-b*(2*b + 1)
Let q(p) = p**2 + 13*p + 22. Let a be q(-12). Let d(b) = b**2 - 11*b + 12. Let r be d(a). Factor 81*i**3 - 2*i - r*i + 2*i**2 + 2*i**2 - 78*i**3.
i*(i + 2)*(3*i - 2)
Let d be (-208)/(-72) - 2/(-18). Determine c so that 15*c**5 - 12*c**3 - 5*c**4 - c**d + 13*c**3 = 0.
0, 1/3
Let v(y) be the third derivative of y**5/15 - y**4/2 - 8*y**3/3 - 74*y**2. Factor v(i).
4*(i - 4)*(i + 1)
Let o(k) be the third derivative of k**6/780 + k**5/195 - 5*k**4/52 - 12*k**3/13 + 82*k**2 - 4*k. Factor o(r).
2*(r - 4)*(r + 3)**2/13
Let j = -290 - -290. Let p**4 + 1/2*p**5 + 0*p**2 + 0 + 1/2*p**3 + j*p = 0. What is p?
-1, 0
Let w(z) = z**3 + 27*z**2 + 31*z + 132. Let y be w(-26). Factor -1/5*o + 0 + 3/5*o**y.
o*(3*o - 1)/5
Let t(r) = -28*r**2 + 79*r - 275. Let p(l) = -10*l**2 + 26*l - 92. Let g(w) = -11*p(w) + 4*t(w). Determine u, given that g(u) = 0.
4, 11
Let x(a) be the first derivative of a**4/18 + 2*a**3/27 - 5*a**2/9 + 2*a/3 + 8. Factor x(s).
2*(s - 1)**2*(s + 3)/9
Let q(p) be the first derivative of 2*p**3/9 + 3*p**2 - 140*p/3 - 48. Find j such that q(j) = 0.
-14, 5
Let c(j) be the second derivative of 0 + 0*j**3 - 3/8*j**4 - 3*j**2 + 4*j + 1/40*j**6 + 1/10*j**5. Let f(l) be the first derivative of c(l). Factor f(n).
3*n*(n - 1)*(n + 3)
Suppose 3*j = -4*t + 22, -j + 14 = -4*j + 5*t. Let m(f) be the first derivative of -14/3*f**3 + 12*f**j + 4 + 8*f. Factor m(v).
-2*(v - 2)*(7*v + 2)
Let d(q) = -10*q - 848. Let n be d(-85). Factor 2/5*x**3 - 6/5 - 2/5*x**2 - n*x.
2*(x - 3)*(x + 1)**2/5
Let m(u) be the second derivative of u**6/15 + 23*u**5/10 + 63*u**4/2 + 637*u**3/3 + 686*u**2 - 82*u. Factor m(k).
2*(k + 2)*(k + 7)**3
Let b = 292 + -290. Let d(j) be the first derivative of -2/5*j**b + 4/15*j**3 + 0*j - 3 - 1/20*j**4. Factor d(h).
-h*(h - 2)**2/5
Suppose 12 = 8*u - 5*u. Factor 3*t**5 - 3*t**u - 5*t**5 - 4*t**3 - 3*t**4.
-2*t**3*(t + 1)*(t + 2)
Let o = -1/928 + 465/928. Solve -1/2*g - o*g**3 - g**2 + 0 = 0.
-1, 0
Let n(r) be the first derivative of -9 - 5*r + 1/8*r**4 + 1/8*r**2 + 1/20*r**5 + 1/120*r**6 + 1/6*r**3. Let d(k) be the first derivative of n(k). Factor d(g).
(g + 1)**4/4
Let o(i) be the first derivative of -i**4/21 - 46*i**3/63 - 11*i**2/21 - 109. Factor o(j).
-2*j*(j + 11)*(2*j + 1)/21
Let t(v) = -21*v**2 + 47*v + 2. Let f(c) = 2*c**2 + c + 2. Let h(n) = -6*f(n) - 3*t(n). Solve h(y) = 0.
-2/17, 3
Suppose -340*t + 343*t - j - 3 = 0, 11 = 4*t + j. Factor -4/11*p - 2/11 - 2/11*p**t.
-2*(p + 1)**2/11
Let i = 11873719/185 - 64182. Let l = 5/37 + i. Solve 2/5*m + 0 + l*m**3 + 4/5*m**2 = 0 for m.
-1, 0
Let o = 14794 + -59169/4. Solve -o*i**3 - 9/2*i**2 - 5*i - 2 - 1/4*i**4 = 0.
-2, -1
Let q(m) = 14*m**3. Let h be q(-1). Let r = -12 - h. Factor 3*o**3 + 9*o**r - 5*o**2 - 5*o**3.
-2*o**2*(o - 2)
Let a(b) be the first derivative of b**6/480 + b**5/80 + b**4/32 - 5*b**3 - 18. Let u(f) be the third derivative of a(f). Factor u(j).
3*(j + 1)**2/4
Let a(o) be the first derivative of 5 + 0*o + 5/2*o**2 + 1/3*o**3 + 1/90*o**5 + 1/9*o**4. Let b(m) be the second derivative of a(m). Solve b(y) = 0 for y.
-3, -1
Let p(l) be the third derivative of -l**5/60 + 7*l**4/8 + 11*l**3/3 + 20*l**2. Let p(q) = 0. What is q?
-1, 22
Let v be (-1761)/(-18) + (-36)/(-8) + -4. Let a = v + -98. What is s in 1/6*s**3 - 1/6*s - a + 1/3*s**2 = 0?
-2, -1, 1
Let w(y) be the second derivative of 3*y**5/20 - 27*y**4/4 - 14*y**3 + 167*y. Factor w(z).
3*z*(z - 28)*(z + 1)
Factor -50*f**3 - 346*f**2 + f**4 + 220*f**2 - 2*f**4 - 373*f**2 - 126*f**2.
-f**2*(f + 25)**2
Suppose 7*i - 16 = 12. Factor 25*l + 2*l**3 + 0*l**i + l**4 - 25*l.
l**3*(l + 2)
Let v(z) be the first derivative of z**3/9 + 4*z**2/3 + 16*z/3 + 70. Factor v(a).
(a + 4)**2/3
Let q be (-5 - -5)*3/12. Suppose 2*b - 9 + 3 = 0. Factor -p + 2*p - b*p**2 - 7*p + q*p**2.
-3*p*(p + 2)
Suppose 6*i + 5*i = 44. Suppose i*d = -2*f - d - 6, d - 2 = -2*f. Find t such that -f*t**2 - 7/2*t + 1 = 0.
-2, 1/4
Determine a so that 4/7*a**2 - 2/7*a**3 - 4/7 + 2/7*a = 0.
-1, 1, 2
Factor x**4 + 0*x - 4/3*x**3 - 4/3*x**2 + 0.
x**2*(x - 2)*(3*x + 2)/3
Let b(f) = 5*f**5 - 27*f**3 + 34*f**2 - 12*f. Let c(a) = 6*a**5 - 2*a**4 - 26*a**3 + 34*a**2 - 12*a. Let j(h) = -4*b(h) + 3*c(h). What is d in j(d) = 0?
-6, 0, 1
Let w = 2/25 + 221/50. Let v(d) be the first derivative of -9/4*d**4 - 11 - d**3 + w*d**2 + 3*d. Factor v(r).
-3*(r - 1)*(r + 1)*(3*r + 1)
Let m = -2227/11 - -203. Determine n, given that m + 2/11*n**4 + 24/11*n**2 + 12/11*n**3 + 20/11*n = 0.
-3, -1
Let z(p) be the first derivative of 2*p**3/3 - 9*p**2/2 - 5*p - 323. What is v in z(v) = 0?
-1/2, 5
Let i(f) be the third derivative of -5*f**8/336 - f**7/14 - f**6/8 - f**5/12 + 9*f**2 + 4. Solve i(b) = 0.
-1, 0
Factor 0 + 3*a**2 + 5*a + 1/4*a**3.
a*(a + 2)*(a + 10)/4
Find i, given that 17*i - 5*i**2 + 6*i**5 + 8*i**4 - 21*i - 17*i**2 - 24*i**3 - 6*i**4 + 2*i**5 = 0.
-1, -1/4, 0, 2
Let d(i) be the first derivative of -5*i**4/3 + 83*i**3/9 - 12*i**2 + 3*i + 1068. Solve d(g) = 0.
3/20, 1, 3
Let v(q) be the second derivative of -q**6/72 + q**5/8 - 5*q**4/12 + 23*q**3/6 + 19*q. Let t(x) be the second derivative of v(x). Let t(g) = 0. Calculate g.
1, 2
Let j(v) be the first derivative of v**6 + 14*v**5/15 - 11*v**4/6 - 14*v**3/9 + 2*v**2/3 - 11. Let j(p) = 0. Calculate p.
-1, 0, 2/9, 1
Let i(z) be the second derivative of -z**6/90 + z**5/12 - z**4/12 - z**3/2 - 13*z + 5. Factor i(v).
-v*(v - 3)**2*(v + 1)/3
Let r be ((-3420)/63)/10 - 12/(-2). Let 0 - 4/7*a**2 + 0*a - r*a**5 + 4/7*a**4 + 4/7*a**3 = 0. What is a?
-1, 0, 1
Suppose 5*i + 140 = -4*m, 0 - 56 = 2*m - i. Let j be 15/m - (-7)/2. Factor -4/5*h**j + 1/5*h**4 - 2/5*h + h**2 + 0.
h*(h - 2)*(h - 1)**2/5
Suppose -1254 = 29*u - 1254. Factor -50/3*w**5 + 30*w**4 - 16*w**3 + 0 + 8/3*w**2 + u*w.
-2*w**2*(w - 1)*(5*w - 2)**2/3
Let z = 356/477 + -16/53. Factor 0 + 7/9*h**3 + z*h**4 - 2/9*h**2 + 0*h.
h**2*(h + 2)*(4*h - 1)/9
Let t(n) be the first derivative of n**3/12 - n**2/8 - n/2 + 95. Determine y, given that t(y) = 0.
-1, 2
Let t(h) be the first derivative of -h**6/40 + h**5/4 - 3*h**4/8 + 14*h**3/3 + 19. Let u(f) be the third derivative of t(f). Determine c so that u(c) = 0.
1/3, 3
Let q(t) be the first derivative of 3*t**4/7 + 13*t**3/7 - 39*t**2/14 - 12*t/7 + 50. Factor q(y).
3*(y - 1)*(y + 4)*(4*y + 1)/7
Let h = 7045 + -7040. Solve -9*y**3 + 0 + 6*y**4 - 3/2*y**h + 6*y**2 - 3/2*y = 0 for y.
0, 1
Let d(p) = 2*p**2. Let y be d(-1). Let f(c) = c**3 - 3*c**2 + 5*c - 3. Let h(k) = 2*k**3 - 4*k**2 + 5*k - 3. Let a(q) = y*h(q) - 3*f(q). Factor a(i).
(i - 1)**2*(i + 3)
What is o in -33/8*o**2 - 3/8*o**3 + 9/2*o + 0 = 0?
-12, 0, 1
Suppose 4 = 2*u - h + 1, -2*h = 3*u - 8. Suppose 5*w = f + 13, -4 = 2*w - u*f - 6. Let -2*i**3 + i**3 + 3*i**w + 3*i - 5*i**3 = 0. What is i?
-1, 0, 1
Suppose 3*j - 12 = -2*j - n, -3*j - 4 = -5*n. Solve -4*z**3 + 2*z**3 - 27*z**2 - 2*z + 23*z**j = 0 for z.
-1, 0
Factor -60/17*h + 2/17*h**2 + 450/17.
2*(h - 15)**2/17
Let x(w) = 4*w**2 + 3*w - 3. Let n(h) = -h**2 - h + 1. Let v be 6 + (0/(-1))/1. Let z(o) = v*n(o) + 2*x(o). Solve z(y) = 0.
0
Let y be (0 - -1)*(-8 + 3). Let t be 0/((0 + 10)/y). Suppose 3/4*b**4 - 3/4*b + 9/4*b**2 + t - 9/4*b**3 = 0. What is b?
0, 1
Suppose 1/2*r**3 + 2*r + 0 - 5