*x**2 + 4/3*x = 0?
0, 2/9, 2
Suppose 0 = 26*w + 11*w - 82880. Suppose w*v = 2239*v + 2. Determine d, given that -4*d + 4/7*d**3 - 24/7 + 0*d**v = 0.
-2, -1, 3
Let s be (-4)/(-8)*(2 - 74)/(-3). Let d be (-15)/s + 3 + 3/12. Factor 0 + 3/4*f + 3/8*f**3 - 9/8*f**d.
3*f*(f - 2)*(f - 1)/8
Let y = -102501/4 + 25626. Let -3/2*t**3 + y*t**2 - 3/8*t**5 + 3/4 - 3/2*t**4 + 15/8*t = 0. What is t?
-2, -1, 1
Let p(q) be the second derivative of 0*q**2 + 0 + 0*q**3 - 28*q - 1/4*q**5 - 35/4*q**4. Suppose p(f) = 0. Calculate f.
-21, 0
Let s(k) be the second derivative of k**6/30 + 41*k**5/10 + 13*k**4 - 164*k**3/3 - 320*k**2 + 3465*k. Factor s(f).
(f - 2)*(f + 2)**2*(f + 80)
Let g = 54 + -55. Let u be ((4 - (4 + -3)) + g)*1. Factor 516 + 12*m - 508 + u*m**2 + 2*m**2.
4*(m + 1)*(m + 2)
Suppose 636 = -7*k + 322 + 349. Determine f so that -2/19*f**2 - 2/19*f**k - 14/19*f**3 + 10/19*f**4 + 16/19*f - 8/19 = 0.
-1, 1, 2
Let r be (-277943)/(-5013) - (52 - -1). Factor 82/9*g**2 - 68/9*g + 8/9*g**3 - r.
2*(g - 1)*(g + 11)*(4*g + 1)/9
Let j(d) be the first derivative of -53*d**4/28 - 61*d**3/21 - 4*d**2/7 - 7625. Factor j(o).
-o*(o + 1)*(53*o + 8)/7
Let p(z) = 21*z - 198. Let c be p(18). Factor 49*x + 4*x + c*x**2 - 52*x**3 + 121 + 4*x**4 + 47*x - 1121.
4*(x - 5)**3*(x + 2)
Let q be (-2)/(-6)*(-25 + 30 + (-102)/21). Let w(k) be the second derivative of -8/21*k**3 + 11*k + q*k**4 + 0 + 6/7*k**2. Factor w(b).
4*(b - 3)*(b - 1)/7
Let x(z) be the first derivative of -14641*z**6/6 + 62557*z**5/5 + 12584*z**4 + 14168*z**3/3 + 872*z**2 + 80*z - 156. Factor x(f).
-(f - 5)*(11*f + 2)**4
Factor -648*o - 23*o**2 + 5*o**2 + 0*o**5 - 20*o**4 - 4381*o**3 + o**5 + 4490*o**3.
o*(o - 9)**2*(o - 4)*(o + 2)
Let u(v) = v**2 + 18*v - 59. Let i be u(-21). Let n(f) = 5*f**2 + 5*f - 65. Let c(o) = -5*o**2 - 3*o + 64. Let q(s) = i*n(s) + 5*c(s). Solve q(r) = 0 for r.
-3, 4
Let c be 14 + -13 - (-10 - (-4 + -2)). Let i(s) be the first derivative of 2/21*s**3 + c - 4/7*s**2 + 8/7*s. Suppose i(k) = 0. What is k?
2
Let t = -21932/21 - -3326/3. Let z(i) be the first derivative of -30/7*i**2 + t*i + 6 + 2/21*i**3. Factor z(l).
2*(l - 15)**2/7
Let i(f) be the second derivative of 0*f**2 - 33*f + f**3 + 3/4*f**4 - 1/10*f**6 + 0*f**5 + 0. What is h in i(h) = 0?
-1, 0, 2
Suppose -5*n + 4 = -4*p, 6*p - 11*p = n + 5. Let o = 117 - 57. Find d such that 55*d**2 + 10*d - o*d**2 + 15 + n*d = 0.
-1, 3
Let s(r) be the second derivative of -2*r**2 - 1/140*r**5 - 10*r - 9/14*r**3 - 3/28*r**4 + 0. Let t(n) be the first derivative of s(n). Factor t(z).
-3*(z + 3)**2/7
Let x(q) be the second derivative of 2/9*q**4 - 1/9*q**3 - 2*q**2 - 63*q - 1/30*q**5 + 0. Factor x(h).
-2*(h - 3)*(h - 2)*(h + 1)/3
Let n(b) = b**3 - b**2 + 1. Let i be n(2). Factor -3*f**i + 116*f**4 - 119*f**4 + 0*f**3 + 0*f**3.
-3*f**4*(f + 1)
Let q = 34507/34 - 106711/170. Solve 88/5*l + 1/5*l**2 + q = 0 for l.
-44
Let r be 0/(5*(-4 + -5 - 572/(-65))). Solve 28/5*v + r - 2/15*v**2 = 0.
0, 42
Let f(x) = -4*x**4 - 208*x**3 + 593*x**2 - 596*x + 205. Let u(g) = g**4 + g**3 + 2*g**2 - g - 1. Let l(q) = -f(q) - 5*u(q). Factor l(z).
-(z - 200)*(z - 1)**3
Let z be (15*((-870)/(-1050) + (-15)/35))/21. Factor -24/7 + 16/7*i - z*i**2.
-2*(i - 6)*(i - 2)/7
Let k be (-2)/(-5) + 962844/615. Let t = 6291/4 - k. Solve 3/4*i**2 - t*i + 6 = 0.
1, 8
Let z(l) = -2*l**2 + 15*l - 18. Let w be z(6). Factor -8*f**2 + 4*f**5 + 49*f**3 - 61*f**3 + w*f**5.
4*f**2*(f - 2)*(f + 1)**2
Let p(x) = x**2 + 33*x + 134. Let m be p(-29). Let u be m/27 + (-10)/(-3). Factor 2/9*l**2 - 1/9*l**u + 0*l**3 - 1/9 + 0*l.
-(l - 1)**2*(l + 1)**2/9
Determine r so that -192 - 429 - 115*r**2 - 2030*r**3 + 101*r + 81 - 621*r + 2035*r**3 = 0.
-2, 27
Let v(c) = 6*c**2 - 54*c - 95. Let u be v(12). Factor -u + 11*d - 1/4*d**2.
-(d - 22)**2/4
Let i(r) = 0*r - 11*r - 22 - 30*r**2 + 31*r**2. Let n be i(13). Factor -4 + 9*h**2 + h**2 + 58*h**4 - 62*h**n - 2*h**2.
-4*(h - 1)**2*(h + 1)**2
Factor -23657 + 129625*d + 5*d**2 - 125875*d + 726782.
5*(d + 375)**2
Suppose 0 + 10/11*v**3 + 2/11*v**4 + 6/11*v**2 - 2/11*v**5 + 0*v = 0. What is v?
-1, 0, 3
Let d(l) be the first derivative of 4*l**5/45 - 31*l**4/6 + 734*l**3/9 - 391*l**2/9 - 1058*l/3 - 426. Solve d(q) = 0.
-1, 3/2, 23
Let q(n) be the second derivative of n**6/45 - n**5/2 + 13*n**4/6 + 55*n**3/9 + 7659*n. Factor q(x).
2*x*(x - 11)*(x - 5)*(x + 1)/3
Solve 56/9 - 1/9*w**3 + 22/3*w + w**2 = 0 for w.
-4, -1, 14
Let 404/3*j - 4/3*j**2 - 400/3 = 0. What is j?
1, 100
Let r(c) be the second derivative of c**4/24 - 37*c**3/6 - 120*c**2 + 2950*c. Factor r(u).
(u - 80)*(u + 6)/2
Solve 4/3*u**3 - 2/15*u**4 + 32/3*u + 0 + 182/15*u**2 = 0 for u.
-5, -1, 0, 16
Let u(h) be the first derivative of h**4/66 + 8*h**3/11 + 4*h**2 + 200*h + 24. Let l(b) be the first derivative of u(b). Let l(k) = 0. Calculate k.
-22, -2
Suppose -a + 1973*v - 1971*v + 9 = 0, 3*a - 4*v = 21. Let -3/2*u**2 - 3/2*u**4 + 0 + a*u**3 + 0*u = 0. What is u?
0, 1
Let q = 65596/120461 + 10/10951. Factor l**2 + 0 - q*l + 1/11*l**4 - 6/11*l**3.
l*(l - 3)*(l - 2)*(l - 1)/11
Let h(v) be the third derivative of -v**5/300 + 39*v**4/4 - 22815*v**3/2 - 2300*v**2. Factor h(k).
-(k - 585)**2/5
Let c(a) = -42*a**3 - 299*a**2 + 392*a - 31. Let r(s) = 460*s**3 + 3290*s**2 - 4315*s + 340. Let j(o) = -45*c(o) - 4*r(o). Let j(g) = 0. Calculate g.
-7, 1/10, 1
Let a = -57 - -61. Suppose 0*y = -a*b - 3*y - 4, 4*y + 16 = 0. Determine c so that 13*c**5 + 4*c**5 - b*c**5 - 10*c**2 + 15*c**3 + 40*c**4 = 0.
-2, -1, 0, 1/3
What is g in 34404*g - 4752 - 31622*g**2 + 10142*g**2 + 147*g**4 + 13881*g**3 - 44700*g**2 = 0?
-99, 2/7, 4
Let j(l) be the third derivative of -l**7/105 + 83*l**6/30 - 1566*l**5/5 + 16038*l**4 - 209952*l**3 + 2*l**2 + 842. Factor j(v).
-2*(v - 54)**3*(v - 4)
Let y = -95652/119 + 5634/7. Let o(k) = -2*k**2 - 25*k - 10. Let t be o(-12). Factor -y*f - 2/17*f**t + 20/17.
-2*(f - 1)*(f + 10)/17
Let o be (-8)/(-4) + 22/(-2). Let u be (-6)/o + 8/6. Find y such that u + 2 - 3*y**2 - 4 = 0.
0
Let b(n) be the third derivative of 0*n - 44/45*n**5 - 1 + 4/45*n**6 + 63*n**2 - 2/3*n**3 - 47/36*n**4. Determine m so that b(m) = 0.
-1/4, 6
Suppose -10/3*c**2 + 1534/3*c - 204 = 0. Calculate c.
2/5, 153
Let l(w) = 2*w**3 + 16*w**2 + 11*w - 19. Suppose -4*s = 4, -23 = 8*m - 5*m + 2*s. Let r be l(m). Find b, given that 3*b**3 + 21/5*b - 33/5*b**r - 3/5 = 0.
1/5, 1
Let q = -38/3 + 14. Let h = -68239/3 - -22747. What is y in -h*y**2 + q*y**3 - 4/3*y + 0 + 2/3*y**4 = 0?
-2, -1, 0, 1
Let u(a) = -5*a**2 + 7964*a - 7968. Let r(y) = 8*y**2 - 7964*y + 7968. Let z(j) = 3*r(j) + 4*u(j). What is t in z(t) = 0?
-1992, 1
Suppose 3*b - 8 = 7, 117*x + 3*b - 15 = 125*x. Solve -2/5*c**4 + 16/5 + 36/5*c + 22/5*c**2 + x*c**3 = 0.
-2, -1, 4
Find g, given that -75*g**2 - 20*g - 4/3 = 0.
-2/15
Factor -528/5 + 526/5*r + 2/5*r**2.
2*(r - 1)*(r + 264)/5
Let b(o) be the first derivative of 1/12*o**3 + 11/8*o**2 + 32 + 0*o. Factor b(u).
u*(u + 11)/4
Let u be -7 + 33/6*(-27 + 29). Let b(l) be the second derivative of 1/60*l**u + 1/60*l**3 + 0*l**2 + 5*l + 1/200*l**5 + 6. Factor b(g).
g*(g + 1)**2/10
Let d(n) be the first derivative of n**4/48 - 3*n**3/8 + 9*n**2/4 - 105*n + 129. Let g(o) be the first derivative of d(o). Let g(w) = 0. What is w?
3, 6
Let o(c) be the first derivative of c**6/24 - 301*c**5/20 + 11549*c**4/8 - 33749*c**3/6 + 66901*c**2/8 - 22201*c/4 - 1117. Factor o(i).
(i - 149)**2*(i - 1)**3/4
Suppose -k - 318 = -264. Let y be (-3 - k/20)*(-400)/50. Solve -y - 46/5*f**3 + 10*f**2 + 2*f**4 - 2/5*f = 0 for f.
-2/5, 1, 3
Let p(k) = -6*k**2 + 117*k - 61. Let x(u) = 6*u**2 - 117*u + 60. Suppose -15*i = 11*i - 78. Let q(s) = i*p(s) + 4*x(s). Suppose q(g) = 0. Calculate g.
1/2, 19
Let n(g) be the first derivative of -g**4/2 + 2740*g**3/3 + g**2 - 2740*g - 5700. Determine k, given that n(k) = 0.
-1, 1, 1370
Let a = -15 - -27. Let b be a/28 - (-25)/7. Factor -b*d**5 + 0*d**3 + 4*d**4 + 7*d**3 - 7*d**3.
-4*d**4*(d - 1)
Let j(n) be the third derivative of -7/8*n**4 + 0*n + 24*n**2 + 1/3*n**3 - 343/480*n**6 + 0 + 49/40*n**5. Factor j(z).
-(7*z - 2)**3/4
Let u(x) be the first derivative of -8/3*x**2 + 4/3*x + 5/6*x**6 + 29/12*x**4 + x**3 - 23 - 41/15*x**5. Suppose u(h) = 0. What is h?
-2/3, 2/5, 1
Let i = -11151388/117 - -95290. Let l = 276/13 + i. S