 be the second derivative of -5*n**6/12 - n**5 - 2*n**4/3 - 2*n + 524. Find h, given that p(h) = 0.
-4/5, 0
Suppose -3*f - 3*p = -60, -12*p + 107 = 5*f - 14*p. Let v be 37/7 + (-6)/f. Factor -81/2*n**v - 135*n**3 - 69*n**2 - 243/2*n**4 - 3/2 - 33/2*n.
-3*(n + 1)**2*(3*n + 1)**3/2
Let k(s) be the first derivative of s**4/16 + 17*s**3/4 + 73*s**2/4 + 24*s - 256. What is n in k(n) = 0?
-48, -2, -1
Let u = -361 - -382. Factor -6*g + 5*g**3 + 12*g**5 - 4*g**2 + u*g**5 + 3*g**3 - 35*g**5 + 4.
-2*(g - 1)**3*(g + 1)*(g + 2)
Determine u so that 1041/2*u + 207 + 843/2*u**2 + 3/2*u**4 + 219/2*u**3 = 0.
-69, -2, -1
Let t(p) be the second derivative of -3*p**7/49 + 2*p**6/105 + 27*p**5/70 + 2*p**4/7 - 4*p**3/21 - 874*p. Determine x, given that t(x) = 0.
-1, 0, 2/9, 2
Suppose -155*p**3 + 27081*p**4 - 441*p - 1459*p - 27086*p**4 - 1240*p**2 = 0. What is p?
-19, -10, -2, 0
Let u = -134 - -140. Factor -u*b - b**3 + 0*b**3 - 14*b + b**2 + 22*b.
-b*(b - 2)*(b + 1)
Let c(g) be the second derivative of 0 - 58*g - 4/15*g**3 + 1/30*g**4 + 3/5*g**2. Suppose c(u) = 0. Calculate u.
1, 3
Factor 31/3*p**3 - 1/3*p**4 - 320/3*p + 512/3 - 74*p**2.
-(p - 16)**2*(p - 1)*(p + 2)/3
Suppose 0 = 3*i - 2*n - 6 - 2, -n + 7 = 4*i. Let j(y) be the second derivative of 0 + 2*y**3 + 0*y**4 + 0*y**i + 4*y - 1/10*y**6 - 9/20*y**5. Factor j(w).
-3*w*(w - 1)*(w + 2)**2
Let n(z) be the third derivative of z**7/210 - 43*z**6/120 - 749*z**5/60 - 931*z**4/8 - 393*z**2. Factor n(o).
o*(o - 57)*(o + 7)**2
Let q(y) be the first derivative of 27/7*y**2 + 43 - 60/7*y - 4/7*y**3. Suppose q(v) = 0. Calculate v.
2, 5/2
Let t(y) be the third derivative of 0*y - 3364/15*y**3 - 29/15*y**4 - 1/150*y**5 + 0 + 154*y**2. Factor t(r).
-2*(r + 58)**2/5
Factor 157*m + 26711 - 138267 - 575*m - 250*m - m**2.
-(m + 334)**2
Let q = -8162857/9 - -906986. Solve -1/9*d**2 + 2*d - q = 0.
1, 17
Suppose -27/5*k**3 + 0 + 15*k + 3/5*k**4 + 9*k**2 = 0. What is k?
-1, 0, 5
Let q be (-115)/(-60) - 121/(-1452). What is s in 6/5*s**q + 126/5*s + 24 = 0?
-20, -1
Let q = 7727/69705 + 2/7745. Let v(g) be the first derivative of 5/18*g**2 + 32 + 8/27*g**3 + q*g**4 + 1/9*g. Find p such that v(p) = 0.
-1, -1/2
Let j(x) = -10*x**4 - 2*x**3 + 112*x**2 + 300*x - 1012. Let p(o) = 42*o**4 + 7*o**3 - 447*o**2 - 1197*o + 4049. Let v(k) = -17*j(k) - 4*p(k). Factor v(d).
2*(d - 7)*(d - 2)*(d + 6)**2
Let i = 47 - 44. Let v(k) = 40*k**3 - 115*k**2 + 65*k - 10. Let c(m) = -13*m**3 + 38*m**2 - 21*m + 3. Let n(p) = i*v(p) + 10*c(p). Factor n(h).
-5*h*(h - 3)*(2*h - 1)
Let s(g) be the second derivative of g**5/50 + 13*g**4/15 - 73*g**3/5 + 396*g**2/5 + 51*g - 14. Let s(c) = 0. What is c?
-33, 3, 4
Let o(f) be the first derivative of 13/12*f**3 + 0*f + 0*f**2 - 1/16*f**4 - 73. Let o(k) = 0. What is k?
0, 13
Let i(a) be the second derivative of -5*a**6/24 - 191*a**5/4 + 8581*a**4/48 + 2173*a**3/6 + 465*a**2/2 - 2*a - 2166. Let i(c) = 0. What is c?
-155, -2/5, 3
Suppose 7*l + 2512 + 701 = 0. Let m = l + 461. Suppose 8/5*w**m - 6/5*w - 36/5 + 2/5*w**3 = 0. What is w?
-3, 2
Let i(y) = y**3 - 9*y**2 - 10*y + 2. Let z be i(10). Determine w so that -14*w**4 + 16*w**4 - 3*w + 7*w**4 + 5*w**z + 3*w + 2*w - 16*w**3 = 0.
-2/9, 0, 1
Let w(j) be the third derivative of 0 - 170*j**2 - 1/15*j**5 + 20/3*j**3 + 0*j + 43/18*j**4. Suppose w(x) = 0. What is x?
-2/3, 15
Let c be (6 - 164/6)*-12. Factor -1969*s**2 - 4096 - 1971*s**2 + 3936*s**2 - c*s.
-4*(s + 32)**2
Let s(r) = 7*r - 19. Let a be s(4). Let d(m) = -39*m**2 + 39*m + 72. Let g(v) = 20*v**2 - 18*v - 36. Let j(i) = a*g(i) + 5*d(i). What is c in j(c) = 0?
-4/5, 3
Let j(t) be the third derivative of -32/3*t**4 + 0*t + 32*t**3 + 8 + 8/5*t**5 - 2/105*t**7 - 4*t**2 + 0*t**6. Factor j(o).
-4*(o - 2)**3*(o + 6)
Let -b**3 - 140 - 127*b**2 - 121 - 155*b + 29*b + 261 = 0. What is b?
-126, -1, 0
Let j(l) be the second derivative of 0*l**5 + 0*l**3 + 0*l**2 - 1/4*l**4 + l - 10 + 1/10*l**6. Suppose j(r) = 0. Calculate r.
-1, 0, 1
Let l = 171 + -114. Suppose -53*i - l = -72*i. Find s such that -15/4*s - 3/8*s**4 - 9/8 - 9/2*s**2 - 9/4*s**i = 0.
-3, -1
What is f in -32/7*f + 0 + 72/7*f**2 - 12/7*f**4 - 4*f**3 = 0?
-4, 0, 2/3, 1
Let g(s) be the second derivative of 1/5*s**5 + 4/3*s**3 - 11*s + 0*s**2 - s**4 + 2. Factor g(l).
4*l*(l - 2)*(l - 1)
Let y = 216940 + -216932. Factor -y*v + 2/3*v**2 + 2/3*v**3 + 0.
2*v*(v - 3)*(v + 4)/3
Solve -77 + x**2 + 2 - 23 + 3*x - 20*x - 12 = 0.
-5, 22
Suppose 84*r - 74*r - 210 = 0. Suppose r*t - 160 = -97. Let 9/2 + 9*j**3 - 15/2*j - t*j**2 - 3/2*j**5 - 3/2*j**4 = 0. What is j?
-3, -1, 1
Let n(c) be the third derivative of 0*c + 17*c**2 - 1/3*c**4 - 2 - 1/525*c**7 - 13/300*c**6 + 0*c**3 - 16/75*c**5. Find p, given that n(p) = 0.
-10, -2, -1, 0
Let k be 11 - 2 - 1/(12/(-36)). Factor -14 - 4*n**3 - 3*n**2 + 2 + k*n - n**2 + 8*n.
-4*(n - 1)**2*(n + 3)
Suppose -x - 17*s + 14*s = -745, 5*x + s = 3697. Determine l, given that -739 - l**2 + 8*l + x = 0.
0, 8
Find s, given that -114/7*s**2 + 17/7*s**3 - 108/7 + 225/7*s = 0.
12/17, 3
Let c(y) be the second derivative of -3*y**5/40 + 1353*y**4/4 - 610203*y**3 + 550403106*y**2 + 698*y. Determine t so that c(t) = 0.
902
Determine c, given that -2*c**5 + 33*c + 23104*c**2 + 21*c - 86*c**4 + 386 - 596*c**3 - 24364*c**2 + 1504 = 0.
-35, -3, 1
Let z(b) be the third derivative of b**7/5 - 13*b**6/40 - 29*b**5/20 - b**4/4 + 57*b**2 + 3. Solve z(j) = 0.
-1, -1/14, 0, 2
Let b(a) be the second derivative of -5*a**4/12 - 40*a**3/3 + 330*a**2 - 824*a. Factor b(w).
-5*(w - 6)*(w + 22)
Let x(s) be the third derivative of 4/3*s**3 - 5/36*s**4 + 152*s**2 + 0 + 1/180*s**5 + 0*s. Factor x(f).
(f - 6)*(f - 4)/3
Suppose 94 = 14*m - 60. Let p be 18/24 - m/132. Find f, given that 4/3*f**3 - 5/3*f + 4/3*f**4 - 2/3*f**2 + 1/3*f**5 - p = 0.
-2, -1, 1
Let b be (-39)/(-12) - 1/4. Suppose -b*w = 12, 5*n - w - 84 = -0*w. Suppose -2*x**5 - 117*x**3 - 2*x**5 - 4*x + 16*x**4 + 93*x**3 + n*x**2 = 0. What is x?
0, 1
Suppose -26 = 4*i + 4*j - 42, -i = 4*j - 4. Let o(t) be the first derivative of -i*t**2 + 1/9*t**3 + 10 + 48*t. Find c such that o(c) = 0.
12
Let y(g) = -20*g**3 + 142*g**2 - 14*g. Let d be y(7). Determine n so that -2/9*n**5 + d*n + 0*n**2 + 2/9*n**4 + 4/9*n**3 + 0 = 0.
-1, 0, 2
Let o(t) be the third derivative of 0*t + 0*t**3 + 2/75*t**6 + 0*t**4 - 2/175*t**7 + 0*t**5 + 0 + 1/840*t**8 - 106*t**2. Factor o(j).
2*j**3*(j - 4)*(j - 2)/5
Let i(d) be the third derivative of -d**6/540 - d**5/5 - 27*d**4/4 + 3907*d**2. Solve i(n) = 0.
-27, 0
Let f(n) = n**2 + 2*n. Let r(m) = -5*m**3 + 17*m**2 + 174*m - 600. Let u(v) = -2*f(v) + r(v). Solve u(t) = 0 for t.
-6, 4, 5
Let b(u) be the third derivative of 169*u**7/210 - 13*u**6/4 + 277*u**5/60 - 5*u**4/2 + 2*u**3/3 + 24*u**2 - 78*u. Suppose b(y) = 0. What is y?
2/13, 1
Suppose -4*v + 0*v = -2*g - 18, 3*g = 4*v - 17. Suppose -5*r = -4*l - 6 + 23, r = -v*l + 14. Factor -25*b**3 + 45*b**l - 18*b**2 + 96 - 17*b**3.
3*(b - 4)**2*(b + 2)
Let j(s) be the second derivative of 74*s**2 - 3*s - 1/3*s**4 - 24*s**3 + 23. Factor j(l).
-4*(l - 1)*(l + 37)
Let q be (-3 - -5) + 115/5. Factor 5*u**3 - 15*u - 7*u - 2*u**3 - 6*u**2 + q*u.
3*u*(u - 1)**2
Factor 1085*n**2 + 5*n**4 + 259219 - 550*n**3 - 259219 - 540*n.
5*n*(n - 108)*(n - 1)**2
Factor 15*r - 48/7*r**2 - 54/7 - 3/7*r**3.
-3*(r - 1)**2*(r + 18)/7
Let o(d) = 27*d**2 - 34*d + 146. Let t(s) = -16*s**2 + 17*s - 74. Let f(b) = -3*o(b) - 5*t(b). Let c be f(10). Solve -3/4*l + 3/8*l**c + 3/8 = 0 for l.
1
Let d(h) be the second derivative of -2*h**6/5 + 98*h**5/5 + 240*h**4 + 1628*h**3/3 + 390*h**2 - 2821*h. Let d(x) = 0. Calculate x.
-5, -1, -1/3, 39
Let n(m) be the first derivative of 12*m - 3*m**3 + 3/8*m**4 + 3/10*m**5 - 3*m**2 + 98. What is x in n(x) = 0?
-2, 1, 2
Let l(r) be the second derivative of 1/20*r**5 + 1/30*r**6 - 1/4*r**4 - 1/6*r**3 + 0 + 91*r + r**2. Factor l(i).
(i - 1)**2*(i + 1)*(i + 2)
Let c(f) be the first derivative of 5*f**6/6 - 86*f**5 + 425*f**4/4 + 3257. Factor c(m).
5*m**3*(m - 85)*(m - 1)
Let s(f) be the first derivative of f**5/15 + 2*f**4 + 83*f**3/9 + 10*f**2 - 1168. Factor s(g).
g*(g + 1)*(g + 3)*(g + 20)/3
Let h(l) be the second derivative of -l**4/66 - 28*l**3/33 + 2*l - 985. Factor h(v).
-2*v*(v + 28)/11
Suppose 648/5 + 32/5*i**3 + 738/5*i + 272/5*i**2 = 0. Calc