)/11
Let j(c) be the third derivative of -c**6/120 + c**5/30 - c**4/24 + 1845*c**2. Factor j(y).
-y*(y - 1)**2
Let t(y) be the first derivative of 2*y**3/15 - 13*y**2/5 + 1855. Factor t(m).
2*m*(m - 13)/5
Factor -16/9 - 1/9*k**4 + 4/9*k + 1/9*k**3 + 4/3*k**2.
-(k - 4)*(k - 1)*(k + 2)**2/9
Let d(k) be the third derivative of k**8/168 + 341*k**7/210 - 403*k**6/40 + 1561*k**5/60 - 869*k**4/24 + 29*k**3 - 5*k**2 - 100*k. Factor d(p).
(p - 1)**3*(p + 174)*(2*p - 1)
Suppose -261*t + 1111 - 10*t**2 - 2215 + 8*t**2 - 23*t = 0. What is t?
-138, -4
Let w(q) be the first derivative of -q**4/30 + q**3/15 + 2*q**2/5 + 3*q - 39. Let u(k) be the first derivative of w(k). Factor u(n).
-2*(n - 2)*(n + 1)/5
Let c(t) = 762*t - 9901. Let a be c(13). Suppose 3 + 3/2*o**3 + 3*o**4 - 6*o**2 - 3/4*o - 3/4*o**a = 0. What is o?
-1, 1, 4
Let i(h) be the first derivative of -h**4/12 + 50*h**3/9 - 94*h**2/3 + 184*h/3 + 407. Solve i(t) = 0.
2, 46
Let h(u) be the second derivative of u**6/30 - 24*u**5/5 - 5*u + 5. Determine j so that h(j) = 0.
0, 96
Suppose -2*w = -6, -5*k = -0*k - w - 2. Let o be (2/k)/(1/9). Solve -2 - 6*f + 10 + 8*f - o*f**2 - 5*f**3 - 14*f = 0.
-2, 2/5
Suppose 5*q = 4*z, -q + 3*q + 2*z = 5*z. Let d(a) be the third derivative of 0 + 0*a**4 - 1/30*a**6 + 19*a**2 + 0*a + q*a**3 + 0*a**5. Solve d(u) = 0.
0
Suppose 32/7*d - 1/7*d**3 + 5/7*d**2 + 36/7 = 0. What is d?
-2, 9
Suppose -4*s - 199 = 3*m - 23, 0 = 3*s - 3. Let j be 6/4*-1 - m/40. Factor -3/8*b**2 - 1/4*b + 1/8*b**4 + j + 0*b**3.
b*(b - 2)*(b + 1)**2/8
Let j be -2 + (-3)/5 + (-23)/(-5). Factor 1 - z**j + 18*z - 43 - 14 - 25.
-(z - 9)**2
Let y(b) = b**2 + 7*b + 3. Let q be y(-7). Factor -7*l**2 + l**4 - 13*l**3 - 4*l + 0*l**q + 11*l**3.
l*(l - 4)*(l + 1)**2
Let i = -9081 + 9086. Let u(x) be the first derivative of 0*x - 29 - 1/4*x**6 - 3/10*x**i + 0*x**2 + 3/4*x**4 + 0*x**3. Factor u(o).
-3*o**3*(o - 1)*(o + 2)/2
Let f = 282082 + -282078. Determine y so that -2/5*y + 3/5*y**f + 8/5*y**3 + 0 + 3/5*y**2 = 0.
-2, -1, 0, 1/3
Let n(x) be the third derivative of -2*x**7/105 - 17*x**6/10 + x**5/15 + 17*x**4/2 - 632*x**2 - x + 1. Find m such that n(m) = 0.
-51, -1, 0, 1
Let p be (33 + (-11064)/336)*28. Factor -1/9*k**2 + p - 1/3*k.
-(k - 3)*(k + 6)/9
Let r(n) = -n + 10. Let m be r(7). Let z(o) = o**3 - 27*o**2 + o + 666. Let x be z(26). Solve 3*i**2 + 7 + i**2 - m - x + 8*i = 0.
-3, 1
Let t = 135926 + -679629/5. Factor -t - 8*f**3 - 16/5*f**4 - 2*f - 33/5*f**2.
-(f + 1)**2*(4*f + 1)**2/5
Let j be ((-4)/18)/(10/(-3) - (-18)/27). Let i(h) be the first derivative of j*h**3 - 1/2*h**2 - 34 + 0*h. Factor i(c).
c*(c - 4)/4
Let s(i) be the second derivative of -19*i + 4*i**2 - 2*i**3 - 3/5*i**5 - 8/3*i**4 + 1. Let s(l) = 0. What is l?
-2, -1, 1/3
Suppose -5*o = -1 - 9. Let h(z) be the first derivative of -z**3 - 17 + 131*z**2 - 119*z**o - 23*z - 25*z. Factor h(s).
-3*(s - 4)**2
Find j such that 67*j**2 - 3*j - 10*j**2 - 17*j**2 - 37*j**2 - 468 = 0.
-12, 13
Suppose -13*j - 51 = 1. Let z be j - (-10)/135*60. Factor 2/9*n**3 + 10/9*n - z - 8/9*n**2.
2*(n - 2)*(n - 1)**2/9
Let j(i) be the first derivative of i**3/3 + 4*i**2 - 21*i + 30. Let k(h) = 2*h**2 + 17*h - 42. Let g(q) = 9*j(q) - 4*k(q). Factor g(y).
(y - 3)*(y + 7)
Suppose -585*d**2 + 330*d**2 + 4*d**3 - 45*d - 9*d**3 + 205*d + 325*d**2 = 0. Calculate d.
-2, 0, 16
Suppose b = g - 1, 5*g - 3*b = -14 + 21. Factor -87*i**2 - 5*i - 99*i**g + 1 - 3*i**3 + 193*i**2.
-(i - 1)**2*(3*i - 1)
Let m(k) be the second derivative of k**8/13440 - k**7/2520 - k**6/480 + 64*k**4/3 + 307*k. Let j(u) be the third derivative of m(u). Find h such that j(h) = 0.
-1, 0, 3
Let w(f) be the first derivative of f**6/2 + 6*f**5/5 - 45*f**4/4 - 40*f**3 + 6*f**2 + 144*f - 1099. Solve w(b) = 0 for b.
-3, -2, 1, 4
Let j(v) be the second derivative of v**7/126 + 53*v**6/45 - 217*v**5/30 + 164*v**4/9 - 439*v**3/18 + 55*v**2/3 - 3263*v. What is r in j(r) = 0?
-110, 1
Let t(v) = -23*v**3 - 706*v**2 - 1547*v - 399. Let o(k) = -34*k**3 - 1056*k**2 - 2320*k - 600. Let s(q) = 5*o(q) - 8*t(q). Factor s(z).
2*(z + 2)*(z + 24)*(7*z + 2)
Let x = 30 + -26. Find w such that -7*w**2 + 305*w**3 - 42*w + 12*w + 12*w**2 - 280*w**x = 0.
-2/7, 0, 3/8, 1
Let t(b) be the first derivative of b**6/120 - 13*b**5/120 + b**4/6 + 2*b**3/3 + 11*b - 32. Let j(s) be the third derivative of t(s). Let j(f) = 0. Calculate f.
1/3, 4
Suppose -f + 1144 = -5*g, g = f - 1514 + 362. Let 2*n**2 + 110*n + 58*n + 3801 + 4409 - n**2 - f = 0. Calculate n.
-84
Suppose -653*x + 657*x + 200 = 0. Let q be -3 - (x/40 - 2). Factor 0 + 0*t**2 + q*t**3 - 1/4*t.
t*(t - 1)*(t + 1)/4
Let u(k) be the first derivative of 58 + 0*k - 8/9*k**3 + 5/12*k**4 - 1/15*k**5 + 2/3*k**2. Suppose u(z) = 0. What is z?
0, 1, 2
Let m(u) be the third derivative of -2*u**7/105 - 13*u**6/60 - 4*u**5/15 + 4*u**4 + 1145*u**2. Factor m(x).
-2*x*(x + 4)**2*(2*x - 3)
Let k(v) be the second derivative of 39*v + 2/27*v**6 + 0 + 2*v**2 + 1/189*v**7 + 19/45*v**5 + 34/27*v**4 + 19/9*v**3. Suppose k(z) = 0. What is z?
-3, -2, -1
Let w(t) be the third derivative of t**8/84 - 4*t**7/21 - t**6/5 + 112*t**5/15 + 197*t**4/6 + 60*t**3 - 600*t**2. Let w(x) = 0. What is x?
-2, -1, 5, 9
Find u, given that 306*u**5 - 607*u**5 - 6020*u**2 - 1330 - 4665*u - 690*u**4 + 296*u**5 - 3370*u**3 = 0.
-133, -2, -1
Let s(p) be the second derivative of -p**6/72 + p**5/24 + 5*p**4/4 + p**3/6 + 42*p**2 + 22*p + 2. Let a(t) be the second derivative of s(t). Factor a(l).
-5*(l - 3)*(l + 2)
Let q(k) = -8*k**2 - 44*k - 48. Let s(b) = -6*b**2 - 44*b - 48. Let r(t) = -5*q(t) + 6*s(t). Find m such that r(m) = 0.
-1, 12
Find s, given that 37044*s + 2884*s**2 + 500/7*s**3 + 4/7*s**4 + 0 = 0.
-49, -27, 0
Let b(m) be the second derivative of 2 + 9/16*m**2 - 1/32*m**4 + 1/8*m**3 + 61*m. Factor b(j).
-3*(j - 3)*(j + 1)/8
Let c(b) be the second derivative of -5*b**9/168 + b**8/35 + b**7/105 - 28*b**3/3 + 25*b. Let q(n) be the second derivative of c(n). Find o such that q(o) = 0.
-2/15, 0, 2/3
Let c(y) = 4*y**3 + 16*y**2 - 4*y. Let a = 547 + -546. Let j(k) = k**3 + k**2 - k + 1. Let l = 4 - 12. Let u(v) = a*c(v) + l*j(v). Factor u(h).
-4*(h - 2)*(h - 1)*(h + 1)
Suppose 5*u - 856 - 1019 = 0. Factor 1521*q**2 + u - 70*q - 130 - 1516*q**2.
5*(q - 7)**2
Let u = 800649 - 800647. Find o such that 11250/11 + 300/11*o + 2/11*o**u = 0.
-75
Let y(a) be the third derivative of -a**7/210 + 19*a**6/120 + 5*a**5/12 - 103*a**4/24 + 10*a**3 + 2661*a**2. Factor y(h).
-(h - 20)*(h - 1)**2*(h + 3)
Let m be (-20860)/(-196) + (-2 - -1) + -1. Let p = m + -103. Factor 4/7*o + 8/7*o**3 - 2/7*o**4 - p*o**2 + 0.
-2*o*(o - 2)*(o - 1)**2/7
Let y be ((-3)/(-4))/((-1872)/128 + 15). Let y*w**5 - 7*w**2 - w**3 + 45*w - 25*w - 22*w + w**5 + 7*w**4 = 0. Calculate w.
-2, -1, -1/3, 0, 1
Let i = 580 - 553. Solve -51*c + 488 - c**3 - 261 - i*c**2 - 252 = 0 for c.
-25, -1
Let l(s) be the first derivative of -2*s**3 + s - 3/4*s**2 - 3 - 7/8*s**4. What is q in l(q) = 0?
-1, 2/7
Let k = 3896744/3247295 - -2/649459. Factor 0 + k*a**2 + 72/5*a.
6*a*(a + 12)/5
Suppose 0 = s + 34 + 38. Let l be (s/84)/(9/(-42)). Factor -45*o**4 + 38*o**3 - 30*o**2 + 2*o + 4 + 63*o**l - 32*o**4.
-2*(o - 1)**3*(7*o + 2)
Let j(d) be the second derivative of 5*d**4/12 - 295*d**3/3 + 580*d**2 - 1265*d. Suppose j(w) = 0. Calculate w.
2, 116
Suppose 5*z - 2*h - 145 = 0, -129 = -5*z - 2*h - 4. Suppose 5*w - z = -3*q, 5*w - q - 25 + 14 = 0. Factor -4/3*v**w + 0 + 2/9*v + 10/9*v**2.
-2*v*(v - 1)*(6*v + 1)/9
Let j(r) be the third derivative of -r**5/90 + 41*r**4/36 + 94*r**3/3 + 2032*r**2 + r. Solve j(i) = 0 for i.
-6, 47
What is a in 64/7*a + 4374/7*a**4 - 4248/7*a**3 - 96/7 + 1472/7*a**2 - 1566/7*a**5 = 0?
-6/29, 2/3, 1
Let c(y) be the second derivative of -y**5/20 - 29*y**4/8 + 93*y**2/2 + 13*y + 2. Let v(o) be the first derivative of c(o). Factor v(r).
-3*r*(r + 29)
Let l(u) = 9*u**2 + 95*u - 122. Let v(d) = 155*d**2 + 1615*d - 2085. Let t(a) = -35*l(a) + 2*v(a). Determine k, given that t(k) = 0.
-20, 1
Solve -24 - 10/7*g**2 - 8/7*g**3 + 136/7*g = 0 for g.
-21/4, 2
Let b be (1379 - 1371 - 84/(-10)) + (-2)/(-5). Suppose -129/5*i**3 - 9/5*i**4 + 0 + b*i - 36/5*i**2 = 0. Calculate i.
-14, -1, 0, 2/3
Suppose -p = 4*d - 4*p + 712, 0 = -3*d + 5*p - 534. Let t = d + 178. Factor 22/3*h**2 +