 - v(c). Let g(n) = 0. What is n?
-5, -1, 1/3, 8
Suppose 2*a + 4*i = 12, 32 - 26 = 3*a + 2*i. Let q(n) be the third derivative of -1/48*n**4 + a + 0*n + 0*n**3 - 20*n**2 + 1/120*n**5. Factor q(c).
c*(c - 1)/2
Let f be 44/8 + -7 + 49/(-12). Let k = f - -27/4. Determine i so that 7/6*i**3 - 1/3 - k*i - 3/2*i**4 + 11/6*i**2 = 0.
-1, -2/9, 1
Let i(p) be the third derivative of 2*p**7/21 + 23*p**6/24 + 19*p**5/6 + 65*p**4/24 - 5*p**3 - 74*p**2. Suppose i(h) = 0. What is h?
-3, -2, -1, 1/4
Let c = -1159 + 1166. Let l be 2/c + 0 + (2 - 0). Factor 0*p + 0 - 4/7*p**4 + l*p**3 + 0*p**2.
-4*p**3*(p - 4)/7
Let c(n) = -43*n**2 - 57*n + 232. Let b(m) = -5*m**2 + m. Let d(l) = -18*b(l) + 2*c(l). Solve d(u) = 0.
4, 29
Let u(v) = 11*v**2 + 39*v + 34. Let o(d) = 52*d**2 + 194*d + 170. Let p(t) = t**2 - t - 14. Let y be p(-6). Let z(k) = y*u(k) - 6*o(k). Let z(s) = 0. What is s?
-17, -1
Let t be (-37905)/2660*4/(-114). Suppose -1/2*s + 7/2*s**2 - 1 - 5/2*s**4 - t*s**3 + s**5 = 0. What is s?
-1, -1/2, 1, 2
Let c(k) be the first derivative of -5/4*k**4 + 55/18*k**3 - 26*k - 5/3*k**2 + 16. Let f(n) be the first derivative of c(n). Find t such that f(t) = 0.
2/9, 1
Let p(g) be the first derivative of -g**6/15 - 46*g**5/25 - 41*g**4/5 - 236*g**3/15 - 77*g**2/5 - 38*g/5 - 1084. Factor p(i).
-2*(i + 1)**4*(i + 19)/5
Let z(f) be the first derivative of 2*f + 1/4*f**4 + 1/5*f**5 + 11 - f**3 - 1/2*f**2. Determine i, given that z(i) = 0.
-2, -1, 1
Let r(j) be the third derivative of 0 + 0*j - 5/3*j**3 - 85*j**2 + 7/24*j**4 - 1/60*j**5. Factor r(a).
-(a - 5)*(a - 2)
Let u(b) be the third derivative of b**8/1848 + 2*b**7/231 + 8*b**6/165 + 16*b**5/165 - 1520*b**2. Factor u(r).
2*r**2*(r + 2)*(r + 4)**2/11
Let u(f) = -14*f**3 + 3*f**2 - 3*f - 7. Let h be u(-3). Let t = 409 - h. Factor 0 - 4/7*p**4 + 0*p - 4/7*p**t + 8/7*p**3.
-4*p**2*(p - 1)**2/7
Let o(i) = 2*i**3 - i**2 + 3. Let z(c) be the first derivative of 11 + 2*c + 0*c**3 + 0*c**2 + 1/4*c**4. Let f(p) = 2*o(p) - 3*z(p). Factor f(a).
a**2*(a - 2)
Suppose 0 = -3*b - 42 + 228. Let x = b - 42. Let x*t**2 + 309*t**3 + 3*t - 335*t**3 + 5*t + 7*t**4 = 0. What is t?
-2/7, 0, 2
Suppose -p = 3*p + 976. Let j = 244 + p. Factor j*i + 0 + 0*i**2 - 2/7*i**3.
-2*i**3/7
Let t(j) = 4 - 8*j**2 - 6 - j**3 - 3 - 8*j. Let k be t(-7). Factor i**3 + 4*i**3 + 22*i**k - 17*i**2.
5*i**2*(i + 1)
Let c = -24623/7 - -3501. Let u = 17 + c. Factor -3/7*t**2 + 3/7 + 3/7*t**3 - u*t.
3*(t - 1)**2*(t + 1)/7
Let h(q) be the second derivative of -33 - 52/21*q**3 - 676/7*q**2 - 1/42*q**4 - 2*q. Factor h(t).
-2*(t + 26)**2/7
Let p(y) = -y**3 + 7*y**2 + 4*y - 18. Let z be p(3). Find m, given that -6875 - 5*m**5 - 5*m**3 + 6875 + z*m**2 - 30*m**4 - 35*m**3 + 45*m = 0.
-3, -1, 0, 1
Suppose 90*n = 96*n - 690. Let y = -111 + n. Determine p so that 0 - 1/4*p + 1/4*p**3 - 1/4*p**y + 1/4*p**2 = 0.
-1, 0, 1
Let q(m) = -1248*m - 1246. Let v be q(-1). Let n(y) be the second derivative of -1/80*y**5 + 0*y**4 + 0 + 7/24*y**3 - 3/4*y**v - 13*y. Factor n(u).
-(u - 2)*(u - 1)*(u + 3)/4
Find d such that 562*d**2 + 900*d + 172/3*d**3 + 2/3*d**4 + 0 = 0.
-75, -9, -2, 0
Let k be (-3*((-325)/78 + 4))/(12/72). Factor -1/3*n**4 + 2/3*n**2 + 0 + 0*n + 1/3*n**k.
-n**2*(n - 2)*(n + 1)/3
Let s(m) = -66*m - 196. Let p be s(-3). Let c(z) be the second derivative of 0 + 4/3*z**4 - 2*z - 36*z**p - 1/5*z**5 + 2*z**3. Factor c(y).
-4*(y - 3)**2*(y + 2)
Solve 825*x - x**2 + 852*x - 1623*x = 0.
0, 54
Let v(g) = -g**4 - 2*g**3 + g - 1. Let q(z) = 25*z**3 - 10*z**3 - 2 - 4*z**3 - 20*z**2 + 3*z**4 + 2*z. Let n(d) = q(d) - 2*v(d). Factor n(y).
5*y**2*(y - 1)*(y + 4)
Let p(o) be the first derivative of -2*o**3/3 - 1612*o**2 + 4010. What is n in p(n) = 0?
-1612, 0
Let t be -6 + (-111)/(-18) - (-1)/18. Factor 0*d**2 + 0 + 0*d - t*d**3.
-2*d**3/9
Let i(g) be the third derivative of g**5/480 + 37*g**4/12 + 197*g**3/16 + 23*g**2 - 23*g. Factor i(r).
(r + 1)*(r + 591)/8
What is f in -8*f**3 + 4*f**3 + 1594*f**2 + 268*f + 1665*f**2 - 3515*f**2 + 520 = 0?
-65, -1, 2
Let l(r) be the first derivative of 2/105*r**5 + 0*r + 1/21*r**2 - 1/42*r**4 - 60 - 2/63*r**3. Solve l(o) = 0.
-1, 0, 1
Let i(a) = a**3 + 29*a**2 + 32*a + 104. Let s be i(-28). Let l be ((-5)/((-60)/(-9)))/(-11 - s). Solve -1/2*o + 0 - l*o**2 = 0.
-2, 0
Suppose 4*q = -1822 + 1754. Let u(k) = -2*k**3 - 33*k**2 + 12*k - 83. Let j be u(q). Let o + 0 + 5/2*o**2 + 1/2*o**4 + j*o**3 = 0. Calculate o.
-2, -1, 0
Factor -7234*r + 3 + 2337841*r**2 + 1 + 13350*r.
(1529*r + 2)**2
Let t(k) be the first derivative of 2*k**6/15 - 76*k**5/25 + 11*k**4 + 484*k**3/5 + 5465. Solve t(a) = 0.
-3, 0, 11
Let f(a) = -9*a**2 - 46*a + 15. Let y(u) = u**3 - 3*u**2 + 4*u - 3. Let m be y(3). Let h(k) = 36*k**2 + 186*k - 60. Let p(r) = m*f(r) + 2*h(r). Factor p(c).
-3*(c + 5)*(3*c - 1)
Let l(f) be the second derivative of f**6/45 + 19*f**5/15 + 107*f**4/18 + 70*f**3/9 - 1953*f. Factor l(j).
2*j*(j + 1)*(j + 2)*(j + 35)/3
Suppose -5*x = 195 - 1270. Suppose 0*z**4 + 227*z + 72 - 59*z + 2*z**4 - 10*z**2 + x*z**3 + 132*z**2 - 187*z**3 = 0. What is z?
-6, -1
Factor -165/4*j**3 + 81/4*j**2 - 3/4*j**5 + 87/4*j**4 + 0*j + 0.
-3*j**2*(j - 27)*(j - 1)**2/4
Let v = 65 + -65. Suppose -5*k = -2*t - v*t + 4, -29 = -3*t - 4*k. Find z, given that -9*z**3 - 20*z**2 - 3*z**3 + t*z**3 - 12*z - 13*z - 10 = 0.
-2, -1
Let p be -17*(-210)/357*(-8)/(-15). Factor 2/3*z**2 + 4*z + p.
2*(z + 2)*(z + 4)/3
Suppose -25*l = -22*l - 714. Let 132*p**3 + 14*p**5 - l*p**2 + 109*p**2 + 41*p**2 + 16*p - 74*p**4 = 0. What is p?
0, 2/7, 1, 2
Let m = -467 + 469. Let u be ((-6)/(-9))/(m - (-48)/(-27)). What is a in 0*a + 2/11*a**2 + 0 - 2/11*a**u = 0?
0, 1
Let a be ((-9)/(-25))/((-3)/135 + (-612)/(-2754)). Factor -a*w**3 + 8/5*w**2 + 11/5*w - 2.
-(w - 1)**2*(9*w + 10)/5
Let d be 15*9/27 + -2. Suppose t**3 - d*t + 271 - 267 + 3*t - 3*t**2 = 0. What is t?
-1, 2
Let w be (-1)/(84/30)*(-20)/2575. Let m = 1436/2163 + w. Find d, given that 0 + m*d - 2/3*d**3 + 0*d**2 = 0.
-1, 0, 1
Suppose 0*c = 5*c + 360. Let b = 74 + c. Find k such that -11*k**2 - 6 - k**b - 3*k**3 - 23*k + 8*k = 0.
-2, -1
Let h be ((-13)/650)/((-26)/195). Let m(k) be the second derivative of -2*k**2 + 0 - 1/12*k**4 - h*k**5 + 4/3*k**3 - 4*k. Factor m(y).
-(y - 1)*(y + 2)*(3*y - 2)
Let m(o) = 5*o**2 + 2*o + 28. Let j be m(-14). Solve -980 - 5*v**2 + 65*v + j = 0.
0, 13
Suppose -3*v = -2*m + 23, -5*m - 17 = -5*v - 62. Find b, given that 4*b**5 + 10*b**2 + 27*b**4 - 39*b**m + 6*b**2 = 0.
-1, 0, 2
Let w = 769 - 766. Let 18 + 43*r**4 - 42*r**4 + 25*r - 5*r**w + 0*r**3 - 3*r**2 - 4*r**3 = 0. What is r?
-1, 2, 9
Let t(y) be the first derivative of -y**5/5 + 7*y**4/3 - 22*y**3/3 + 10*y**2 - 10*y - 26. Let w(j) be the first derivative of t(j). Solve w(v) = 0 for v.
1, 5
Let f be (-67 - (-4851)/98)*(-2025)/28. Let -135/8*l**2 - f + 2025/8*l + 3/8*l**3 = 0. What is l?
15
Find p such that 1/8*p**4 - 529/2 + 23/2*p**3 - 23/2*p + 2115/8*p**2 = 0.
-46, -1, 1
Let k(r) be the first derivative of 16*r**6/27 + 208*r**5/15 + 643*r**4/6 + 8150*r**3/27 + 1177*r**2/3 + 242*r + 3476. Determine i so that k(i) = 0.
-33/4, -1
Let x(u) be the second derivative of 4/3*u**3 + 0*u**2 + 11/3*u**4 + 0 - 2*u. Factor x(q).
4*q*(11*q + 2)
Suppose 2 + 6 = 4*t. Suppose 3*f + 799 = -3*o + 3100, -t*o = 4*f - 1524. Let -o - 4*s**3 + 51*s**2 - 15*s**2 + 672 - 60*s = 0. What is s?
-1, 5
What is f in 96/7*f**3 + 270/7*f**2 + 264/7*f + 3/7*f**4 + 87/7 = 0?
-29, -1
Let u(z) = 13*z**2 - 2*z + 9. Let x be u(5). Determine y, given that 36*y - x - y**2 + 9*y - 7*y - 2*y = 0.
18
Let b(q) be the third derivative of q**7/70 + 37*q**6/20 + 423*q**5/5 + 5363*q**4/4 - 12493*q**3/2 - 7414*q**2. Factor b(t).
3*(t - 1)*(t + 13)*(t + 31)**2
Let c(o) = -o**2 - o + 2. Let j(y) = -15*y**2 - 33*y + 18. Let u = -602 - -584. Let p(n) = u*c(n) + j(n). Factor p(s).
3*(s - 6)*(s + 1)
Factor -3 + 12371*v**3 + 39*v**2 - 12368*v**3 + 3.
3*v**2*(v + 13)
Let q(j) = -j**2 + 18*j - 8. Let u = 32 + -15. Let g be q(u). Solve -4*r**2 + g*r**3 + 12*r**3 - r**5 - 30*r**3 + 2*r**4 + 11*r**3 - r + 2 = 0 for r.
-1, 1, 2
Suppose -3*b - 1702 = -2*o, -b - 3*o - 2805 = 4*b. Let c = -562 - b. Suppose -q + 5/2*q**4 + 1/2*q**c + 0 + 4*q**3 = 0. Calculate q.
-1, 0, 2/5
Let u = -213 + 224. Suppose 0 = -2*r + u - 5. Factor 1/5*p**r - 1/