2 - 168*l - 322. Let n(x) = 15*i(x) - 3*k(x). Determine m, given that n(m) = 0.
-161, -2
Let d(g) be the second derivative of -g**6/15 + 13*g**5/10 + 37*g**4/6 - 109*g**3/3 + 60*g**2 + 187*g. Suppose d(b) = 0. Calculate b.
-4, 1, 15
Let a(m) be the third derivative of -1/4*m**5 + 1/6*m**6 + 20/3*m**3 + 1/42*m**7 - 206*m**2 - 25/12*m**4 + 0 + 0*m. Solve a(z) = 0 for z.
-4, -2, 1
Let m be (1 - 0) + (-156)/221. Let l(r) be the first derivative of 20 + 8/17*r + m*r**2 + 2/51*r**3. Factor l(p).
2*(p + 1)*(p + 4)/17
Let z = 39/373 + 295/746. Let o be (-2)/8*(-5 - 1). Determine v, given that v - o + z*v**2 = 0.
-3, 1
Determine x, given that 43/7*x**2 - 12*x + 36/7 - 5/7*x**3 = 0.
3/5, 2, 6
Let d(p) be the second derivative of -1/6*p**3 + 0 - 1/2*p**2 + 2*p. Let o(k) = -k**2 - 11*k - 11. Let j(l) = 44*d(l) - 4*o(l). Suppose j(z) = 0. What is z?
0
Let v(r) = 11*r**2 + 2*r - 48. Let c(h) = -2*h**2 + 8. Suppose -m + z = 5, -7*z + 2*z + 7 = -2*m. Let n(w) = m*v(w) - 34*c(w). Factor n(q).
2*(q - 4)*(q - 2)
Let b(g) be the second derivative of -g**5/120 + 89*g**4/72 - 215*g**3/4 - 675*g**2/4 + 306*g - 2. Factor b(n).
-(n - 45)**2*(n + 1)/6
Suppose -5*w + 16*w - 319 = 0. Find m such that 71*m + w*m + 3*m**2 - 363 + 56*m - 15*m**2 - 24*m = 0.
11/2
Let n(p) be the second derivative of p**4/72 - 13*p**3/12 + 19*p**2/6 - 59*p + 11. Determine i so that n(i) = 0.
1, 38
Let y(o) be the first derivative of o**5/160 - o**4/96 - 5*o**3/48 - 3*o**2/16 + 9*o - 124. Let v(n) be the first derivative of y(n). Factor v(h).
(h - 3)*(h + 1)**2/8
Let q(d) be the third derivative of d**6/420 - d**5/10 - 18*d**4/7 - 464*d**3/21 - 14*d**2 + 5. Factor q(f).
2*(f - 29)*(f + 4)**2/7
Let v(g) be the third derivative of -g**5/160 - 83*g**4/64 - 41*g**3/8 - 656*g**2. Factor v(m).
-3*(m + 1)*(m + 82)/8
Factor -13*q**3 + 28*q**3 + 611*q - 59*q - 556 + 131*q**2 + 985*q**2 - 7*q**3.
4*(q + 1)*(q + 139)*(2*q - 1)
Let d(k) be the first derivative of 4*k**3/39 - 37*k**2/13 - 38*k/13 + 14722. Find c such that d(c) = 0.
-1/2, 19
Let l(g) = -5*g**3 + 630*g**2 - 555*g - 1190. Let x(d) = -2*d**3 + 209*d**2 - 185*d - 396. Let h(i) = -3*l(i) + 10*x(i). Factor h(y).
-5*(y - 39)*(y - 2)*(y + 1)
Factor 2/9*l**3 - 20/9*l**2 - 4 + 6*l.
2*(l - 6)*(l - 3)*(l - 1)/9
Suppose -1075*m = -1110*m. Factor m*o + 0 + 75/2*o**2 + 3/2*o**5 + 45/2*o**3 - 27/2*o**4.
3*o**2*(o - 5)**2*(o + 1)/2
Suppose -4*d = -2*a - 8, 0 = -4*d + 16. Suppose s = -2 + a. Let -1/7*y**s + 0 - 3/7*y = 0. Calculate y.
-3, 0
Let t(x) be the first derivative of -73/16*x**4 + 107/12*x**3 - 22/5*x**5 + 2*x + 1 - 2/3*x**6 + 31/4*x**2. Let t(n) = 0. Calculate n.
-4, -2, -1/4, 1
Let p be (1 - ((-16)/(-3) + -1))*(-629)/3145. Let a(b) be the first derivative of 2/9*b**2 - 25 + 2/27*b**3 - p*b. Let a(o) = 0. What is o?
-3, 1
Factor -56/5*u**2 + 188/5*u + 144/5.
-4*(u - 4)*(14*u + 9)/5
Let c(l) be the third derivative of l**8/1176 - 4*l**7/245 + l**6/14 + 68*l**5/105 - 35*l**4/4 + 300*l**3/7 - 179*l**2 + 1. Find m, given that c(m) = 0.
-4, 3, 5
Suppose 355/4*d**3 + 801*d + 27/8 + 4263/8*d**2 = 0. What is d?
-3, -3/710
Solve 4*m**2 + 3410*m - 6842*m + 3470*m - 5*m**2 + 80 = 0 for m.
-2, 40
Let d(q) = q**3 + 17*q**2 - 21*q - 58. Let m be d(-18). Let z be m/18*(-2 - (-2 - -3)). Let 0 - u**2 + z*u + 0*u**3 + 1/3*u**4 = 0. Calculate u.
-2, 0, 1
Let w(u) be the first derivative of -u**4/12 + 29*u**3/9 + 5*u**2 - 343. Factor w(m).
-m*(m - 30)*(m + 1)/3
Let d(q) = -5*q**3 + 6*q**2 + 3*q + 4. Let i(c) = -4*c**3 + 6*c**2 + 4*c + 3. Suppose -7*z - 18 + 46 = 0. Let o(k) = z*i(k) - 3*d(k). Factor o(j).
-j*(j - 7)*(j + 1)
Let c(x) = -25*x**4 - 275*x**3 - 275*x**2 + 255*x + 250. Let w(i) = -2*i**4 - i**3 - 2*i**2 - i - 1. Let a(y) = c(y) - 10*w(y). Let a(d) = 0. What is d?
-52, -1, 1
Let a(w) be the second derivative of w**7/7560 - w**6/2160 - w**4/6 - 21*w**2 + 3*w - 16. Let i(x) be the third derivative of a(x). Factor i(t).
t*(t - 1)/3
Solve 58*z**2 - 60 + 10*z**2 + 17*z + 3*z + 55*z**3 + 23*z**2 + 44*z**2 = 0.
-2, -1, 6/11
Let z = -345 + 180. Let u be (z/(-6))/(3/6). Factor 45*v - u*v - 28*v**3 + 250 - 2*v**4 - 90*v - 120*v**2.
-2*(v - 1)*(v + 5)**3
Let s(u) be the third derivative of u**7/1890 - 7*u**6/180 + 3*u**5/20 - 5*u**4/27 + 3705*u**2. Let s(k) = 0. What is k?
0, 1, 40
Let z(v) = -8*v - 133. Let p be z(-22). Factor 60*q**2 - p*q**2 + 27*q - 35*q**2 + 3*q**3 - 12.
3*(q - 4)*(q - 1)**2
Let a(r) be the first derivative of 2*r**5/35 - 12*r**4/7 - 2*r**3/21 + 24*r**2/7 + 1911. Suppose a(s) = 0. Calculate s.
-1, 0, 1, 24
Let z(t) be the first derivative of 0*t - 7/2*t**2 - 8/3*t**3 - 1/4*t**4 - 3. Factor z(u).
-u*(u + 1)*(u + 7)
Factor 2*t**2 + 7*t**3 + 24*t**2 + 5*t**3 + t**3 - 15*t**3.
-2*t**2*(t - 13)
Suppose -969/7*m + 0 + 3/7*m**2 = 0. Calculate m.
0, 323
Let i(x) be the third derivative of -x**6/480 - 3*x**5/80 + 37*x**3/3 + 2*x**2. Let b(z) be the first derivative of i(z). Factor b(j).
-3*j*(j + 6)/4
Suppose 3*s + 4*y - 50 = 0, 0*y - 4*y + 36 = 2*s. Let i be 12/(-8) + s/(-4)*-1. Factor -2*h**3 + 4*h**3 + 9*h**2 + 0*h**3 - 7*h**i.
2*h**2*(h + 1)
Suppose -3*b - 11 = -0*b - s, -b - s - 9 = 0. Let w be 476/(-252) - 1*b. Factor w*q + 98/9 + 2/9*q**2.
2*(q + 7)**2/9
Let v(q) = 2*q + 3. Let c be v(-2). Let j be (c + -1)/(1/(-1)). Factor -2*n**2 + j*n**4 + 4*n - 18 + 10 - n**4 - 5*n**3 + 8*n**2.
(n - 2)**3*(n + 1)
Let z(h) be the third derivative of 13*h**6/240 + 67*h**5/240 - 17*h**4/48 - h**3/8 - 145*h**2. Factor z(r).
(r + 3)*(2*r - 1)*(13*r + 1)/4
Let m(z) = 263*z**2 + 130*z + 611. Let w(g) = 83*g**2 + 43*g + 204. Let j(d) = -6*m(d) + 19*w(d). Find v such that j(v) = 0.
-5, 42
Let z(f) be the first derivative of 213 + 0*f**3 - 1/4*f**4 + 1/2*f**2 + 0*f. Factor z(v).
-v*(v - 1)*(v + 1)
Let l(r) = 3*r**4 - 30*r**3 + 21*r**2 + 6*r - 12. Let i(g) = -2 + g + 1 - 147*g**3 + 73*g**3 + 75*g**3. Let z(d) = 12*i(d) + l(d). Suppose z(f) = 0. What is f?
-1, 1, 2, 4
Let z = -3675/2 - -1896. Let h = z - 465/8. Determine o, given that h*o**4 + 0*o**3 + 0 - 3/8*o**2 + 0*o = 0.
-1, 0, 1
Let a be (-90)/(-40) - ((-66)/(-165) - 79/(-140)). Solve -a*p + 0*p**2 + 3/7*p**3 - 6/7 = 0.
-1, 2
Let j(k) be the second derivative of -192*k**7/35 + 4304*k**6/75 - 838*k**5/5 + 2253*k**4/10 - 783*k**3/5 + 54*k**2 - 1807*k. What is i in j(i) = 0?
2/9, 3/4, 5
Let b(k) = -k**3 - 11*k**2 + 12*k - 14. Let a be b(-12). Let v = a + 16. Suppose 95*g**3 + 35*g**v - 3*g**4 + 36 + 23*g**4 + 9 - 195*g = 0. What is g?
-3, 1/4, 1
Let q(v) be the second derivative of 1/4*v**4 + 0*v**2 + 0 - 13/40*v**6 + 0*v**3 - 3/20*v**5 - 5/56*v**7 - 44*v. Find i such that q(i) = 0.
-2, -1, 0, 2/5
Let l(i) be the first derivative of 3*i**4/2 - 70*i**3/3 - 12*i**2 + 377. What is z in l(z) = 0?
-1/3, 0, 12
Let w(i) be the third derivative of -i**7/70 - 6*i**6 - 7319*i**5/10 - 3570*i**4 - 14161*i**3/2 - 8277*i**2. Suppose w(c) = 0. What is c?
-119, -1
Let c(k) = -k**3 - 15*k**2 + k + 32. Let l be c(-15). Suppose l*w**3 + 16*w + 18*w**3 - 16*w**2 - 31*w**3 = 0. What is w?
0, 2
Suppose -390 - 4856 = -2*z - 2*o, -3*o = z - 2629. Let i = -10425/4 + z. Factor -15/4 - i*t + 5*t**2.
5*(t - 3)*(4*t + 1)/4
Let w(r) = -r + 23. Suppose 5*a = 3*v + 15, -3*v + 25 = -4*a - 8*v. Let d be w(a). Let -5*u**2 - 15*u**2 - 16*u**3 - 12*u**3 + 30 + d*u**3 - 5*u = 0. What is u?
-3, -2, 1
Factor -3*a**5 - 915*a**4 + 8*a**2 - 5*a**3 + 903*a**4 - 7*a**3 - 8*a**2.
-3*a**3*(a + 2)**2
Factor -1/3*l**2 - 23/3*l - 14.
-(l + 2)*(l + 21)/3
Let b be 6*((-24)/135 - (-18)/45). Let a(x) be the first derivative of 4*x - 4/9*x**3 - 13 + b*x**2. Find g such that a(g) = 0.
-1, 3
Let b(r) be the third derivative of -1/480*r**6 + 0 + 1/48*r**5 + 0*r**3 - 1/32*r**4 + 215*r**2 + 0*r - 1/840*r**7. Determine v so that b(v) = 0.
-3, 0, 1
Find w, given that -4/7 + 6/7*w - 6/7*w**3 - 4/7*w**4 + 8/7*w**2 = 0.
-2, -1, 1/2, 1
Let t(c) = 53*c**2 - 144*c - 890. Let g(b) = 26*b**2 - b - 1. Let y(d) = 2*g(d) - t(d). Factor y(j).
-(j - 148)*(j + 6)
Let 29574576/5 + 708/5*t**2 - 250632/5*t - 2/15*t**3 = 0. What is t?
354
Let -3/2*g**5 + 9/2*g**4 - 129*g**2 + 27*g**3 - 135/2 + 333/2*g = 0. Calculate g.
-5, 1, 3
Let p(a) = 5*a**2 + 3. Let b(k) = -5*k**2 - 4. Let s(l) = 3*b(l) + 4*p(l). Factor s(h).
5*h**2
Let m(a) be the third derivative of 0*a - 2/45*a**4 + 0 - 19*a**2 - 15/2*a