- 1)*(3*a + 2)**2
Let s(l) be the second derivative of -1/42*l**7 + 0*l**2 + 0 - 2/15*l**6 + 0*l**3 - 1/4*l**5 + 3*l - 1/6*l**4. Find c, given that s(c) = 0.
-2, -1, 0
Let n(b) be the second derivative of -b**6/20 + b**5/8 + 5*b**4/24 - 5*b**3/12 - b**2/2 - b - 19. Suppose n(h) = 0. Calculate h.
-1, -1/3, 1, 2
What is h in -3/2*h**2 + 149/2*h - 49 = 0?
2/3, 49
Let x be (-1)/4 + 585/52. Let o = 4 + -1. Factor 3*j**2 - 38*j**4 + 36*j**o - x*j**2 + 10*j**4.
-4*j**2*(j - 1)*(7*j - 2)
Suppose -4*s - 487*l = -484*l + 3, -2*l = 2*s + 2. Solve 10*y**3 - 8/3*y**2 + s - 8/3*y = 0 for y.
-2/5, 0, 2/3
Let r(n) be the first derivative of n**7/210 - n**5/20 - n**4/12 - n**2/2 + 3. Let g(y) be the second derivative of r(y). Solve g(t) = 0 for t.
-1, 0, 2
Let d(x) = -9*x**2 - 7*x + 9. Let t(o) be the first derivative of 4*o**3/3 + 3*o**2/2 - 4*o - 11. Let z(p) = -6*d(p) - 14*t(p). Factor z(a).
-2*(a - 1)*(a + 1)
Let y = 9 + -4. Let v = y + -2. What is l in -18*l + 19*l + 0*l**3 - l**v + 0*l**3 = 0?
-1, 0, 1
Let s = -3120/7 - -28094/63. Factor 4/9*a**2 - s + 2/9*a**5 + 2/9*a - 2/9*a**4 - 4/9*a**3.
2*(a - 1)**3*(a + 1)**2/9
Let i(x) be the first derivative of 5*x**7/84 + x**6/4 + 2*x**5/5 + x**4/3 - 5*x**3/3 + 4. Let u(l) be the third derivative of i(l). Factor u(b).
2*(b + 1)*(5*b + 2)**2
Factor -3*t - 14 - 4*t - 5*t + 3*t - t**2.
-(t + 2)*(t + 7)
Let a(g) = -g**3 - 15*g**2 + 27*g + 176. Let u be a(-16). Let h = 2554/11 + -232. Factor 2/11*c**3 + h*c + u - 4/11*c**2.
2*c*(c - 1)**2/11
What is n in 8/11*n - 64/11 + 2/11*n**2 = 0?
-8, 4
Suppose 3*l - 3*k = 12, 2*l - 9 = 5*k - 16. Let w(r) be the first derivative of 0*r**2 + 3/20*r**5 + 9/16*r**4 + 0*r + 1/2*r**3 - l. Factor w(m).
3*m**2*(m + 1)*(m + 2)/4
Let f(d) be the first derivative of 5*d**6/6 + 3*d**5 + 5*d**4/2 - 10*d**3/3 - 15*d**2/2 - 5*d - 20. What is l in f(l) = 0?
-1, 1
Let r = 667 - 664. Factor -2/9*b**4 - 4/9*b**r + 4/9*b + 2/9*b**2 + 0.
-2*b*(b - 1)*(b + 1)*(b + 2)/9
Let k(x) be the first derivative of -x**4/4 - 29*x**3/3 - 55*x**2/2 - 27*x - 214. Factor k(i).
-(i + 1)**2*(i + 27)
Let k(y) be the first derivative of -y**4/14 + 10*y**3/21 + 8*y**2/7 - 24*y/7 + 289. Factor k(w).
-2*(w - 6)*(w - 1)*(w + 2)/7
Factor -4*f**2 - 10 - 35 - 132*f + 120 + 61.
-4*(f - 1)*(f + 34)
Let m(b) be the second derivative of 6*b + 1/4*b**4 + 6*b**2 - 2*b**3 - 3. Determine y so that m(y) = 0.
2
Suppose 15*a = 3*a + 2*a. Factor 0*x + 8/7*x**3 + 0 + a*x**2 + 4/7*x**4.
4*x**3*(x + 2)/7
Factor 8*m**2 + 4/5*m**3 - 8 - 4/5*m.
4*(m - 1)*(m + 1)*(m + 10)/5
Let k = 71 + 73. Let z be (k/(-14))/4 + 4. Determine o, given that -z*o + 10/7*o**3 + 2/7*o**2 - 6/7*o**4 + 4/7 = 0.
-1, 2/3, 1
Let r = 1851/3422 + -70/1711. Factor -3/2*p**3 + 0*p**4 + r*p**5 + p**2 + 0 + 0*p.
p**2*(p - 1)**2*(p + 2)/2
Let i be (1 + -7)*(-57)/1881. Determine f so that i*f**2 - 2/11 + 2/11*f - 2/11*f**3 = 0.
-1, 1
Let o be 1888/80 - 4/(-10). Factor 53*i + 5*i**3 - 25*i - o*i - i**4 - 6*i**2 - 2*i**2.
-i*(i - 2)**2*(i - 1)
Let p(c) be the first derivative of c**3 - 21*c**2/2 + 36*c + 6. Factor p(g).
3*(g - 4)*(g - 3)
Let v(m) be the third derivative of m**9/2520 - m**8/2240 + m**7/6720 - 17*m**4/12 + 30*m**2. Let n(x) be the second derivative of v(x). Factor n(z).
3*z**2*(4*z - 1)**2/8
Let i be (-8)/(-32) - ((-14)/8 - 1). Find h such that h**2 + i*h**2 + 11*h**2 - 10 - 5*h = 0.
-2/3, 1
Let b be -4 - -2*6/4. Let o be (b - 0)*5*-1. Let -7*z**3 + 0*z**o - 8*z**4 - 5*z**5 - 8*z**2 - 5*z**3 + 3*z**5 - 2*z = 0. Calculate z.
-1, 0
Let s = 12624/44233 - -2/6319. Factor -4/7 - 2/7*r + s*r**2.
2*(r - 2)*(r + 1)/7
Let r(h) be the first derivative of -h**6/15 - 2*h**5/5 - 3*h**4/5 + 4*h**3/15 + 7*h**2/5 + 6*h/5 + 114. Let r(x) = 0. What is x?
-3, -1, 1
Let k(c) = 20*c**2 - 243*c - 43. Let j(o) = 2*o**2 - o + 1. Let l(u) = -5*j(u) + k(u). Factor l(s).
2*(s - 24)*(5*s + 1)
Let n(p) be the second derivative of p**7/840 + p**6/120 + p**5/40 + p**4/24 - 4*p**3/3 - 15*p. Let g(x) be the second derivative of n(x). Factor g(s).
(s + 1)**3
Factor 4/5*m**3 + 0 + 0*m + 32/5*m**2 - 28/5*m**4.
-4*m**2*(m + 1)*(7*m - 8)/5
Let b be 5/(-10)*0/(-11). Let l(i) be the third derivative of -3*i**2 + 1/30*i**5 + b + 0*i**4 + 0*i - 1/210*i**7 - 1/120*i**6 + 0*i**3. Solve l(r) = 0 for r.
-2, 0, 1
Let n(t) be the third derivative of -t**6/30 + 8*t**5/15 - 10*t**4/3 + 32*t**3/3 - 12*t**2 - 2*t. Factor n(b).
-4*(b - 4)*(b - 2)**2
Let z(q) = 6 - 16 + 9. Let d(g) = -5*g**2 - 35*g - 28. Let w(r) = d(r) + 2*z(r). Let w(k) = 0. What is k?
-6, -1
Suppose -118 = -5*y - 4*x, 2*y - y - 5*x = 12. Let z = 70/3 - y. Factor -22/3*d - 25/6*d**3 + 35/3*d**2 + z.
-(d - 2)*(5*d - 2)**2/6
Let o = 43 - 34. Find y, given that 319 - o*y - 5*y**2 - 289 - 16*y = 0.
-6, 1
Suppose -3*w - 94 = -5*k + 36, 3*k = -2*w + 59. Suppose -17 + k = 3*g. Find u, given that g*u**5 + 68/7*u**3 + 32/7*u**2 + 52/7*u**4 - 4/7 - 2/7*u = 0.
-1, 2/7
Let l(r) = 8*r**2 - 27*r - 18. Suppose 0 = -2*i + 13 - 1. Let q(a) = -3*a**2 + 9*a + 6. Let u(y) = i*l(y) + 17*q(y). Determine o so that u(o) = 0.
-2, -1
Let u be 6/(-69) + (-624)/(-299). Let j(o) be the first derivative of 16/7*o + 5 + 4/21*o**3 - 8/7*o**u. Suppose j(i) = 0. What is i?
2
Determine l, given that -11/2*l**2 + 45/4*l**4 - 69/4*l**3 + 17*l - 6 = 0.
-1, 2/3, 6/5
Suppose 10*t - 3*t - 28 = 0. Let v(n) = n**2 + 7*n + 3. Let l be v(-7). Suppose 0*d**4 - d**3 + 3*d**t + 6*d**l - 2*d**3 = 0. What is d?
-1, 0
Suppose 3*l - 17 + 11 = 0. Suppose 7*j**2 + 4*j**3 + 2*j - 11*j**l - 2*j**3 + 0*j**3 = 0. What is j?
0, 1
What is h in h**5 - 23*h**2 + 62*h**2 - 12*h - 29*h**2 - 6*h**3 + h**5 - 32*h**2 + 6*h**4 = 0?
-3, -1, 0, 2
Let y(h) be the first derivative of 2*h**5/115 + 21*h**4/46 + 110*h**3/23 + 25*h**2 + 1500*h/23 + 414. Suppose y(v) = 0. Calculate v.
-6, -5
Suppose -3*b + 16*b = 7*b. Let c be 2 + -3 + ((-4)/(-4) - b). Factor 1/4*k - 1/4*k**2 + c.
-k*(k - 1)/4
Let 2/7*i**4 + 0*i + 648/7*i**2 - 72/7*i**3 + 0 = 0. What is i?
0, 18
Determine s so that -9 + 14*s**2 - 5*s**2 + 3 + s**3 + 13*s - 17*s**2 = 0.
1, 6
Factor 3/7*c**4 - 30/7*c**2 + 9/7*c**3 + 0 - 72/7*c.
3*c*(c - 3)*(c + 2)*(c + 4)/7
Let s(l) be the third derivative of 1/300*l**5 + 0 + 1/120*l**4 + 0*l + 14*l**2 - 1/15*l**3. Factor s(h).
(h - 1)*(h + 2)/5
Let w(a) = -a**3 - 43*a**2 + 1262*a + 131. Let i be w(-63). Let -4/3*b**i - 20/3*b**3 + 0*b - 10/3*b**2 - 5*b**4 + 1/3 = 0. Calculate b.
-1, 1/4
Let y(c) be the second derivative of -4374*c**6/35 + 5832*c**5/35 - 648*c**4/7 + 192*c**3/7 - 32*c**2/7 + 26*c - 2. Let y(i) = 0. What is i?
2/9
Let k(z) = z**2 - z - 4. Let h be k(3). Suppose -3*j - p = -7*j + 13, -2*p = -4*j + 14. Factor -22*u**4 + j*u**2 - h*u**3 + 2*u + 19*u**4 + 0*u**3.
-u*(u - 1)*(u + 1)*(3*u + 2)
Factor 0*t + 2/9*t**4 + 0*t**2 + 0 + 2/3*t**3.
2*t**3*(t + 3)/9
Let d(b) = 7*b - 14. Let n be d(2). Let k(u) be the first derivative of n*u**2 + 2/5*u - 2/15*u**3 - 7. Factor k(p).
-2*(p - 1)*(p + 1)/5
Let k = 649 + -649. Factor 0*i + k + 2/3*i**3 + 4/3*i**2.
2*i**2*(i + 2)/3
Let s(c) = 4*c**4 + 18*c**3 - 6*c**2 + 10*c - 10. Let b(z) = -z**3 + z**2 - z + 1. Let j(n) = -10*b(n) - s(n). What is l in j(l) = 0?
-1, 0
Let c(y) = -y**5 + 4*y**4 - y**3 - 2*y. Let a(b) = -2*b**5 + 5*b**4 - b**3 + b**2 - 3*b. Let z(r) = -2*a(r) + 3*c(r). Factor z(x).
x**2*(x - 1)*(x + 1)*(x + 2)
Let p(t) be the second derivative of t**7/42 + t**6/8 + t**5/4 + 5*t**4/24 + 27*t**2/2 - 27*t. Let i(m) be the first derivative of p(m). What is z in i(z) = 0?
-1, 0
Let -280*z**2 - 69*z + 12*z**5 + 127*z**3 - 23*z + 63*z**3 + 70*z**3 - 180*z**3 + 280*z**4 = 0. What is z?
-23, -1, -1/3, 0, 1
Let h(v) = -v**3 + 10*v**2 - 18*v + 12. Let x be h(10). Let a = -166 - x. Determine w, given that -4/9*w**3 + 8/9*w - 2/3 + 10/9*w**a = 0.
-1, 1/2, 3
Solve 13/6*g**2 + 0 + 0*g - 1/6*g**4 + 2*g**3 = 0 for g.
-1, 0, 13
Let i(y) = -10*y**2 - 38*y - 33. Let n(c) = -2*c**2 - 8*c - 6. Let s(v) = -4*i(v) + 22*n(v). Factor s(z).
-4*z*(z + 6)
Let k(x) = -4*x**2 - x + 11. Let v(f) = -5*f**2 - 2*f + 12. Let n(z) = -4*k(z) + 3*v(z). Determine g, given that n(g) = 0.
-2, 4
Let m(i) be the first derivative of i**4/20 - i**2/10 - 138. Solve m(z) = 0 for z.
-1, 0, 1
Let 7/2*h**5 + 27/2 - 81/4*h + 83/4*h**3 - 117/4*h**2 + 79/4*h**4 = 0. Calculate h.
-3, -1, 1/2, 6/7
Let x(z) be the fir