044*d**2 - 3*d. Let f(g) = -4026*g**3 + 1980046*g**2 - 2*g. Let k(a) = -3*f(a) + 2*h(a). Suppose k(y) = 0. What is y?
0, 995
Let i(z) be the first derivative of -138*z**5 - 3430*z + 13965/2*z**2 - 35/6*z**6 - 49 - 2105/2*z**4 - 5600/3*z**3. Let i(h) = 0. Calculate h.
-7, 2/7, 1
Let c = 17 - 13. Suppose c*r - 12 = 2*r. Factor -2*p**2 + 5*p - 2*p**4 + 8*p - 8*p**3 + r - 2*p**2 - 5*p.
-2*(p - 1)*(p + 1)**2*(p + 3)
Suppose 2*d = -4*a + 9 - 5, -a - 4 = -2*d. What is l in 18*l**2 - 192 - 32*l + 673*l**3 + d*l**2 - 669*l**3 = 0?
-4, 3
Let z(k) be the first derivative of -k**6/15 + 12*k**5/25 - 6*k**4/5 + 4*k**3/3 - 3*k**2/5 - 172. Factor z(l).
-2*l*(l - 3)*(l - 1)**3/5
What is p in 398/3*p - 5/3*p**2 + 160/3 = 0?
-2/5, 80
Suppose 0*p - 18*p + 54 = 0. Factor 10 - 10*u**2 - 5*u - 38*u**3 + 83*u**p - 40*u**3.
5*(u - 2)*(u - 1)*(u + 1)
Let j be 32/(-4) + ((-130)/14 - -13 - -6). Factor -2/7*w**2 - 10/7*w - j.
-2*(w + 2)*(w + 3)/7
Let n = -181 + 183. Let z be (6 + (-87)/15)/(6/45). Suppose -g - z - 1/6*g**n = 0. What is g?
-3
Factor 116/9*q - 16/3 + 2/3*q**3 + 82/9*q**2.
2*(q + 2)*(q + 12)*(3*q - 1)/9
Factor 52/9*h**2 - 64/9 + 136/3*h.
4*(h + 8)*(13*h - 2)/9
Let k = 3738/785 - 622/157. Determine o, given that 0*o**3 + k*o**4 + 0 + 0*o - 4/5*o**2 = 0.
-1, 0, 1
Let l(a) be the third derivative of a**7/2520 - a**6/180 - a**5/24 - 73*a**4/24 + 110*a**2. Let i(j) be the second derivative of l(j). Factor i(y).
(y - 5)*(y + 1)
Let f(g) be the third derivative of g**5/30 + g**3/6 - 269*g**2. Let x(v) = 40*v - 34. Let h(c) = -2*f(c) + x(c). Factor h(m).
-4*(m - 9)*(m - 1)
Suppose 529 + 1775 = -32*u. Let d be u/240*96/(-9). Factor -4/5*q**5 + d + 4*q**3 + 4/5*q**2 - 32/5*q - 4/5*q**4.
-4*(q - 1)**3*(q + 2)**2/5
Let v(p) be the second derivative of p**5/5 + 299*p**4/3 + 14800*p**3 - 45000*p**2 + 156*p + 5. What is j in v(j) = 0?
-150, 1
Let p = 1071487/46 + -23292. Let a = p - -7/23. Suppose -a*x**4 + 21/2*x**3 + 0 - 45/2*x**2 + 27/2*x = 0. Calculate x.
0, 1, 3
Let i(b) be the second derivative of 1 + 0*b**2 + 1/3*b**4 + 0*b**3 + 1/10*b**5 - 1/15*b**6 + 12*b. Determine t, given that i(t) = 0.
-1, 0, 2
Let y(o) be the first derivative of 2*o**3 - 3/2*o**2 + 0*o + 146 - 3/4*o**4. Factor y(z).
-3*z*(z - 1)**2
What is i in 32 + 208/3*i - 4/3*i**5 + 136/3*i**2 - 16/3*i**4 + 4*i**3 = 0?
-2, -1, 3
Let h = 1346 - -19. Let y be (156/h)/(3/60). Factor -y + 88/7*z - 76/7*z**2 + 200/7*z**4 + 250/7*z**5 - 230/7*z**3.
2*(z + 1)**2*(5*z - 2)**3/7
Suppose 9*g + 2 = 7*g - c, -5*g + 5*c = -10. Let x = -2773 - -2775. Factor 3/7 - 6/7*z**x + g*z + 3/7*z**4 + 0*z**3.
3*(z - 1)**2*(z + 1)**2/7
Let x(i) be the second derivative of i**5/20 + 37*i**4/2 + 147*i**3/2 + 110*i**2 - 375*i - 2. Factor x(b).
(b + 1)**2*(b + 220)
Let z(l) be the second derivative of -46/5*l**5 + 2*l - 50/3*l**3 - 20*l**4 + 0*l**2 - 12 - 8/5*l**6 - 2/21*l**7. Factor z(a).
-4*a*(a + 1)**2*(a + 5)**2
Let i(q) = 613*q**2 + 5*q - 6. Let k(x) = 715*x**2 + 5*x - 6. Let u(v) = 7*i(v) - 6*k(v). Let u(t) = 0. What is t?
-6, 1
Determine v so that -3/2*v**3 + 15*v**2 + 624*v + 0 = 0.
-16, 0, 26
Let r be -7 + (-144)/(-16) + (-3)/9. Let v(k) be the first derivative of 15/2*k**2 - r*k**3 + 13 - 10*k. Factor v(n).
-5*(n - 2)*(n - 1)
Let h(o) = -25*o**2 + 39*o - 79. Let u(j) = -64713*j - 25 - 1 + 64726*j - 9*j**2. Let b(d) = 4*h(d) - 11*u(d). Factor b(n).
-(n - 10)*(n - 3)
Let a be ((-1300)/(-26) - 47)/((-15)/(-2)). Factor 0 - a*g**4 + 0*g + 4/5*g**3 - 2/5*g**2.
-2*g**2*(g - 1)**2/5
Let x be (-2)/8*(-8)/(-3) - (210 + -218). Factor x*f - 1/3*f**2 - 121/3.
-(f - 11)**2/3
Determine f so that -57337308*f**3 - 12478*f + 35 + 1703595*f**2 - 3 - 33426*f + 14838765*f**2 = 0.
2/1431, 2/7
Suppose x + 10 = 3*m, -6*m = -2*m + 5*x + 12. Factor -13*o - 55*o**m - 19*o**3 + 20 - 26*o**3 + 93*o.
-5*(o - 1)*(o + 2)*(9*o + 2)
Let m = -190977 + 1336843/7. Factor 0 + 4/7*x**4 + 2/7*x**5 + 0*x**3 - m*x**2 - 2/7*x.
2*x*(x - 1)*(x + 1)**3/7
Let l(o) be the second derivative of 1/84*o**4 + o - 1/21*o**3 - 3 + 1/14*o**2. Factor l(k).
(k - 1)**2/7
Determine j, given that -16*j**2 + 3*j**2 + 59*j**3 - 7*j + 2*j**4 - 54*j**3 + 3*j + 3*j**2 + 8 - j**5 = 0.
-2, -1, 1, 2
Let w(b) be the first derivative of b**4/32 - 11*b**3/12 + 109*b**2/16 + 33*b/2 - 2306. Factor w(a).
(a - 12)*(a - 11)*(a + 1)/8
Let q = 133833 + -401498/3. Find k such that -4/3*k - q*k**2 - 1 = 0.
-3, -1
Let b = -87285 - -87287. Factor -2*c**2 + 1/7*c**3 - 1/7*c + b.
(c - 14)*(c - 1)*(c + 1)/7
Let z = -4526 - -3182. Let d = -1342 - z. Factor -6/5 - 2/5*m**d + 8/5*m.
-2*(m - 3)*(m - 1)/5
Let f(v) be the first derivative of -4*v**5/5 - 7*v**4 + 4*v**3/3 + 14*v**2 - 599. Determine s so that f(s) = 0.
-7, -1, 0, 1
Let 232*b - 392 + 11*b**5 + 192*b**4 - 10*b**5 + 3*b**5 + 120*b**2 + 740*b - 688*b**2 - 208*b**3 = 0. Calculate b.
-49, -2, 1
Let m(l) be the first derivative of -2*l**3/3 - 42*l**2 + 86*l - 141. Suppose m(y) = 0. Calculate y.
-43, 1
Determine m so that -1/5*m**2 - 73/5 + 74/5*m = 0.
1, 73
Let k(u) = 2*u**3 - 122*u**2 + 167*u - 2818. Let p be k(60). Suppose -2499/2*l - 987*l**p - 285*l**3 - 3/2*l**5 - 1029/2 - 69/2*l**4 = 0. What is l?
-7, -1
Let k(u) be the second derivative of -u**5/50 - 3*u**4/10 + 19*u**3/5 + 13*u**2 - 2*u + 756. Factor k(o).
-2*(o - 5)*(o + 1)*(o + 13)/5
Suppose 105*v + 2 - 2 = 61*v - 37*v. Factor v + 2/5*t**4 + 8/5*t**2 + 2*t**3 + 0*t.
2*t**2*(t + 1)*(t + 4)/5
Suppose -2*z = -4*d + 96, -2*d - 5*z = 2*d - 68. Let u be (-1 + -10)*(d + -23). Suppose -u*t**2 + 8*t**2 + 0*t**2 - 3*t = 0. What is t?
-1, 0
Let d(u) be the first derivative of 7/3*u**2 - 78 + 10/9*u + 8/27*u**3. Factor d(a).
2*(a + 5)*(4*a + 1)/9
Let m(x) = 5*x**2 - 2995*x + 11940. Let p(h) = -8*h**2 + 4991*h - 19904. Let i(j) = 17*m(j) + 10*p(j). Let i(c) = 0. What is c?
4, 197
Let q = -12280/43 - -111208/387. Factor 0*g - q*g**2 + 2/9*g**4 - 4/9*g**3 + 0.
2*g**2*(g - 4)*(g + 2)/9
Let l(t) be the second derivative of -t**5/20 + 2*t**4/3 + 10*t**3/3 - 991*t. Suppose l(b) = 0. What is b?
-2, 0, 10
Let c(b) be the first derivative of 2/3*b**6 + 31 - 2*b**4 + 2*b**2 + 0*b**3 + 0*b**5 + 0*b. Suppose c(p) = 0. What is p?
-1, 0, 1
Let n(j) = -j**3 + 7*j**2 - 5*j + 8*j - 2*j - 7. Let w be n(5). Factor 220*m**2 + 47*m**3 + 70*m**3 - 224*m - 17*m**3 + w.
4*(m + 3)*(5*m - 2)**2
Let j = -11126/105 - -2578/21. Factor -4/5*o**2 - j - 8*o.
-4*(o + 3)*(o + 7)/5
Suppose -41 = 194*y + 4 - 477 - 538. Find d, given that -5*d**2 - 47/3*d**3 + 35/3*d**4 + 3*d - 2*d**y + 0 = 0.
-1/2, 0, 1/3, 3
Let f(v) be the first derivative of 275*v**3 + 411*v**2 - 3*v - 2988. Solve f(k) = 0.
-1, 1/275
Let g(r) be the first derivative of r**3/2 - 129*r**2/2 - 261*r/2 - 576. Let g(n) = 0. What is n?
-1, 87
Solve 209*z - 206 + 216*z**2 + 124*z - 196*z**3 - 137*z - 10*z**4 = 0 for z.
-103/5, -1, 1
Factor 54*f + 225*f + 95 - 99*f**2 + 30*f**3 + 254*f**2 - 59*f.
5*(f + 1)**2*(6*f + 19)
Solve 1 + 17/8*y**2 - 1/8*y**5 - 5/8*y**4 - 1/8*y**3 + 11/4*y = 0 for y.
-4, -1, 2
Let p be 14/(-7) - ((-2584)/(-133) + -28). Factor 2/7*s**3 - 88/7 + p*s**2 + 40/7*s.
2*(s - 1)*(s + 2)*(s + 22)/7
Let l(s) be the second derivative of -1/108*s**4 - 5*s + 14 + 5/54*s**3 + 1/3*s**2. Determine n, given that l(n) = 0.
-1, 6
Let l(a) be the first derivative of 3*a**6/200 - 3*a**5/4 + 125*a**4/8 - 10*a**3/3 - a - 133. Let d(r) be the third derivative of l(r). Factor d(p).
3*(3*p - 25)**2/5
Let a = 2589/83 - 23997/913. Determine b, given that 58/11*b**2 - 20/11*b - a*b**3 + 2/11*b**5 + 14/11*b**4 + 0 = 0.
-10, 0, 1
Let f(v) be the first derivative of 0*v + 0*v**3 - 1/7*v**4 + 0*v**2 - 4/35*v**5 - 33. Factor f(r).
-4*r**3*(r + 1)/7
Let v = 820369/1640734 - 1/820367. Factor -13/2*k**2 - 35/2*k - v*k**3 + 49/2.
-(k - 1)*(k + 7)**2/2
Suppose 985*d - 5668 = -1728. What is x in 51/2*x**2 + 15/2*x**d - 23*x**3 + 2 - 12*x = 0?
2/5, 2/3, 1
Let c(l) = l**4 - l**3 + l**2. Let z(v) = 50*v**3 - 160*v**2 + 185*v - 70. Let k(p) = -p**2 - p + 61. Let s be k(-8). Let a(y) = s*c(y) - z(y). Factor a(n).
5*(n - 7)*(n - 2)*(n - 1)**2
Solve 11*t**3 + 20*t**4 - 7*t**3 - 9*t**3 + t**4 = 0.
0, 5/21
Let s be (3/((-99)/12))/((-18)/(-16) + (-13965)/8360). Determine m, given that -11/6*m**2 - 5/3*m - s*m**3 - 1/2 = 0.
-1, -3/4
Factor -8*g + 2862*g**3 - 2884*g**3 + 69*g**2 + 15*g**2 - 168 + 49*g**2 + 