t w(p) be the third derivative of -p**6/24 - 35*p**5/24 - 20*p**4/3 + 20*p**3/3 + p**2 + 23*p. Let i(k) be the first derivative of w(k). Factor i(f).
-5*(f + 1)*(3*f + 32)
Suppose 12*r + 2*c - 52 = 10*r, -8 = 2*c. Factor -5*o**5 - r*o**2 + 15*o**3 + 41*o**4 - 21*o**4 - 60*o**2.
-5*o**2*(o - 3)**2*(o + 2)
Let p(x) be the second derivative of -x**6/15 - 51*x**5/10 - 8*x**4 + 100*x**3/3 - 2490*x. Let p(c) = 0. What is c?
-50, -2, 0, 1
Let t be 40/(-16)*-4*(-6)/(-105). What is j in 2/7*j + 0 + 2/7*j**3 - t*j**2 = 0?
0, 1
Let o be 286/11 + 1*-1. Let f = o - 18. Find n such that -f - 4 + 10*n + 3 + 2*n - 4*n**2 = 0.
1, 2
Let m(d) be the first derivative of 5/2*d**3 - 3/8*d**2 - 15/2*d + 72 + 3/16*d**4. Suppose m(i) = 0. What is i?
-10, -1, 1
Let n be (-1)/(-2)*2 + 45. Suppose 146 + 73 = 5*r + q, -q - 89 = -2*r. Factor n*d**4 - r*d**4 - d - 3*d**3 + d + d**5.
d**3*(d - 1)*(d + 3)
Suppose 56*y - 2190 = -17*y. Let u be (10*-5)/(-42 + y). Factor -u*g**4 - 4*g**2 - 2/3*g - 15/2*g**3 + 0.
-g*(g + 1)*(5*g + 2)**2/6
Let a(p) be the second derivative of 49*p**5/80 - 2359*p**4/12 + 1345*p**3/6 - 96*p**2 + 10237*p. Find f, given that a(f) = 0.
2/7, 192
Let q be (-18)/3 + 2/4*-8. Let d be (9/(-21))/(55/q - -4). Factor 6/7*h**2 - 8/7 - d*h**3 + 0*h.
-2*(h - 2)**2*(h + 1)/7
Let c = -2/2135 + 2147/12810. Let v(y) be the third derivative of c*y**4 + 1/30*y**5 + 0*y + 11*y**2 + 0*y**3 + 0. Factor v(j).
2*j*(j + 2)
Suppose 267*n - 282*n - 180 = 0. Let y be -15 - n - (2 - 5). Factor 0 + y*t - 1/2*t**3 + 1/4*t**4 + 0*t**2.
t**3*(t - 2)/4
Suppose c + 0*c = -7*g + 32, -5*c + 10 = 5*g. Suppose -g*t = 5 - 15. Factor 1/2*j**4 - 5*j - j**3 - 13/2*j**t + 0.
j*(j - 5)*(j + 1)*(j + 2)/2
Let g(v) be the third derivative of 1/25*v**6 + 1/525*v**7 + 256/15*v**3 + 0*v + 2/75*v**5 - 16/5*v**4 + 0 - 211*v**2. What is c in g(c) = 0?
-8, 2
Let h(a) = -a**3 + 7*a**2 + 32*a - 8. Let g be h(10). Let 24*j - 5810*j**4 + 44*j**2 + 5766*j**4 - 12*j**3 - g*j**5 + 1 - 1 = 0. What is j?
-3, -1, -2/3, 0, 1
Factor 1/5*h**4 + 5041/5*h + 143/5*h**3 + 5183/5*h**2 + 0.
h*(h + 1)*(h + 71)**2/5
Let j = 66576 - 66576. Factor 0*d**3 + 0*d - 3/2*d**4 + 6*d**2 + j.
-3*d**2*(d - 2)*(d + 2)/2
Factor 3/4*z**2 + 255/2*z + 507/4.
3*(z + 1)*(z + 169)/4
Let n = 3/6002 - -23987/42014. Find v, given that 0 - n*v - 4/7*v**2 + 4/7*v**3 + 4/7*v**4 = 0.
-1, 0, 1
Let l be 30/(-2) + (1200/(-32))/(5/(-6)). Find s such that 0 + l*s - 5/4*s**3 + 115/4*s**2 = 0.
-1, 0, 24
Find y such that -53*y**4 + 42*y + 4*y**5 - 107/2*y**3 + 0 + 158*y**2 = 0.
-2, -1/4, 0, 3/2, 14
Let s(n) be the second derivative of n**4/12 + 7*n**3/2 + 10*n**2 + 407*n - 4. Factor s(m).
(m + 1)*(m + 20)
Let t be 322 - -20*16/(-40). Let g = t - 312. Suppose 0*l + 3/5*l**g + 0 + 3/5*l**3 = 0. What is l?
-1, 0
Let j(q) be the third derivative of -2/165*q**5 - q + 7/12*q**4 - 5*q**2 - 19/33*q**3 + 0. What is s in j(s) = 0?
1/4, 19
Let f(u) be the first derivative of -u**6/21 + 4*u**5/7 - 9*u**4/14 - 818. What is o in f(o) = 0?
0, 1, 9
Solve 1206/5*u + 156/5*u**2 - 2/5*u**3 - 272 = 0.
-8, 1, 85
Suppose 3*y - 57 = 3*p - 9, -y + 24 = p. Let n = y - -34. Determine x so that -30*x**4 - 15*x**5 + 3*x**3 + n*x**4 - 6*x**2 - 6*x**3 = 0.
-2/5, 0, 1
Let h = -200 + 205. Suppose 0 = 2*p - 2*g - 18, -p - 56 = h*g - 41. Determine k, given that -26/7*k**3 + 32/7*k - 8/7 + 26/7*k**4 - 18/7*k**2 - 6/7*k**p = 0.
-1, 1/3, 1, 2
Let x be (8 + -5)/(9/717). Factor -215 + 3*w**2 + w**2 - 20*w + x.
4*(w - 3)*(w - 2)
Factor 608*m + 1/2*m**3 + 73/2*m**2 - 2166.
(m - 3)*(m + 38)**2/2
Let u(c) be the second derivative of c**5/5 - 8*c**3/3 + 19*c. Factor u(o).
4*o*(o - 2)*(o + 2)
What is h in -279/8*h**2 - 91/8*h**3 - 281/8*h + 1/8*h**4 - 47/4 = 0?
-1, 94
Suppose -4544 = -6*m - 1490. Suppose -2*n - m = -519. Determine i so that -7/2*i**2 + 1/2 + i**3 - 7/4*i**n + 3*i**4 + 3/4*i = 0.
-1, -2/7, 1
Let x = 40013/6 - 6668. Let v(d) be the third derivative of 0*d + 0 - d**2 - x*d**4 + 0*d**3 - 1/12*d**5. Let v(l) = 0. What is l?
-4, 0
Let g be 18/33 + (-24717)/3388 - (-1 - 11 - -5). Suppose -5 - g*m**2 + 9/4*m = 0. What is m?
4, 5
Let h(d) = -25*d**3 - 15150*d**2 - 6110*d. Let b(g) = 25*g**3 + 15172*g**2 + 6108*g. Let a(u) = 5*b(u) + 4*h(u). Factor a(s).
5*s*(s + 610)*(5*s + 2)
Let p be 48/(-112)*(-3)/(3/7). Suppose -12 = p*o, -3*h - 3 + 13 = -o. Determine l so that -1/2*l**4 - 3/2*l + 3/2*l**3 + 1 - 1/2*l**h = 0.
-1, 1, 2
Let z(p) be the third derivative of p**7/42 - 49*p**6/24 - 55*p**5/6 + 85*p**4 - 74*p**2 - 26. Factor z(d).
5*d*(d - 51)*(d - 2)*(d + 4)
Factor -24*k + 220 + 1/5*k**2.
(k - 110)*(k - 10)/5
Let k(g) = 85*g**2 - 1155*g + 1670. Let a(h) = -5*h**2 + 68*h - 99. Let u(m) = 50*a(m) + 3*k(m). Factor u(x).
5*(x - 12)*(x - 1)
Let i be (1/(-2))/(1/(-10)). Suppose -i*x + x + 57 = -5*r, 2*r = -2*x + 6. Factor -2*z**4 + 3*z**2 + 2*z - x*z**2 - 2*z**3 + 7*z**2.
-2*z*(z - 1)*(z + 1)**2
Let f(h) be the first derivative of -13*h + 1/180*h**5 + 1/2*h**3 + 1/12*h**4 - 33 + 3/2*h**2. Let q(x) be the first derivative of f(x). Factor q(i).
(i + 3)**3/9
Let i be 24/10 + (-44)/110. Let u(k) = -3*k + 9. Let w be u(i). Factor 0*v - 6 - w*v**2 - v - 4*v - 4*v.
-3*(v + 1)*(v + 2)
Let y(c) be the third derivative of -4*c**7/945 - 11*c**6/108 + 41*c**5/135 + 103*c**4/108 - 10*c**3/9 - 53*c**2 - 2*c - 1. Solve y(l) = 0.
-15, -1, 1/4, 2
Let p(d) be the second derivative of -16/15*d**3 - 3/50*d**5 - 3*d - 4 + 13/15*d**4 + 0*d**2. Solve p(y) = 0.
0, 2/3, 8
Let -172*a**2 + 14/3*a**4 + 158/3*a**3 + 112/3 + 232/3*a = 0. Calculate a.
-14, -2/7, 1, 2
Let f(a) = -a - 133. Let d(y) = 33. Let h(n) = 9*d(n) + 2*f(n). Let u be h(14). Factor 8*k + 0*k**u + 3*k**3 - 8*k - 3*k**2.
3*k**2*(k - 1)
Let g(d) be the second derivative of 0*d**2 - 9/10*d**5 - 11/4*d**4 - 3 - 1/10*d**6 - 3*d - 3*d**3. Solve g(o) = 0.
-3, -2, -1, 0
Let b(o) = -7*o**4 - o**3 + o**2 + 4*o. Let j(n) = -30*n**4 - 178*n**3 + 358*n**2 - 162*n. Let w(m) = 4*b(m) - j(m). Factor w(q).
2*q*(q - 1)**2*(q + 89)
Let h(k) be the first derivative of 3*k**5/10 + 7*k**4/6 - 7*k**3/3 - 3*k**2 + 36*k - 74. Let i(w) be the first derivative of h(w). Factor i(f).
2*(f - 1)*(f + 3)*(3*f + 1)
Let s(i) be the second derivative of -i**8/1512 + i**6/540 - 39*i**2/2 + 8*i + 1. Let m(q) be the first derivative of s(q). Factor m(x).
-2*x**3*(x - 1)*(x + 1)/9
Let y(p) = 54*p + 2. Let h be y(0). Let k(s) be the first derivative of -1/4*s**h + 1/8*s**4 + 13 + 1/3*s**3 - s. What is o in k(o) = 0?
-2, -1, 1
Find d, given that -1212/7*d - 6/7*d**2 - 3582/7 = 0.
-199, -3
Suppose 29*i + 10 = 34*i. Factor 90*s**i + 4 - 44*s - 48*s**2 - 246 - 44*s**2.
-2*(s + 11)**2
Let y(s) be the second derivative of s**6/60 + 7*s**5/40 - 29*s**4/8 + 149*s**3/12 - 35*s**2/2 + 78*s - 19. Factor y(b).
(b - 5)*(b - 1)**2*(b + 14)/2
Let y be (((-2)/5)/(-1))/(-17 + 19) - 476/2380. Find f such that y - 10/19*f**4 - 56/19*f**2 - 40/19*f + 106/19*f**3 = 0.
-2/5, 0, 1, 10
Suppose 214*p + 75 = 219*p. Let g be -3 - (p/(-12))/((-10)/(-40)). What is q in 3 + 3/2*q - 3/2*q**g = 0?
-1, 2
Let u be 21/14*-2*-6. Let o(r) = -r**2 + 13*r + 100. Let t be o(u). Factor t*q**2 + 8*q + 8/5.
2*(5*q + 2)**2/5
Let n(t) = 6*t**3 - 60*t**2 + 219*t - 216. Let h(r) = -7*r**3 + 58*r**2 - 216*r + 216. Let o(i) = 3*h(i) + 4*n(i). What is j in o(j) = 0?
2, 18
Let n(l) = -6*l**3 - 153*l**2 - 90*l + 309. Suppose -67 = 13*h - 262. Let f(v) = -v**3 - 22*v**2 - 13*v + 44. Let a(o) = h*f(o) - 2*n(o). Factor a(u).
-3*(u - 1)*(u + 2)*(u + 7)
Let v(b) = -157*b - 626. Let f be v(-4). Let c(k) be the first derivative of -20 + 1/15*k**3 - k + 2/5*k**f. Determine q so that c(q) = 0.
-5, 1
What is z in -1729225/7 + 2630/7*z - 1/7*z**2 = 0?
1315
Factor -36/7 - 90/7*l**2 + 166/7*l + 8/7*l**3.
2*(l - 9)*(l - 2)*(4*l - 1)/7
Let h(k) be the first derivative of 4/3*k**2 - 1/2*k**4 + 0*k - 1/9*k**6 - 8/15*k**5 + 8/9*k**3 - 55. Suppose h(x) = 0. Calculate x.
-2, -1, 0, 1
Determine i so that 0 - 23*i + 266*i**3 - 253/2*i**4 + 67/2*i**2 - 6*i**5 = 0.
-23, -1/3, 0, 1/4, 2
Let u be (-13)/(27495/(-1500)) + 4/(-94). Factor -2/15*t**3 + 0 + u*t**2 - 8/15*t.
-2*t*(t - 4)*(t - 1)/15
Let u(g) be the third derivative of -g**6/10 + 8*g**5/3 + 62*g**4/3 + 128*g**3/3 - 4474*g**2. Let u(h) = 0. Calculate h.
-2, -2/3, 16
Let k(x) be the third derivative of x**7/1680 - x*