**3 + 0 + 1/3*v**4 + 0*v + 55*v**2. Determine j, given that z(j) = 0.
-2, 0, 1/2
Let z(x) be the second derivative of x**5/12 + 703*x**4/36 + 1115*x**3/18 + 139*x**2/2 + 27*x - 40. Find a such that z(a) = 0.
-139, -1, -3/5
Let f = 6809/2604 - -45/868. Suppose 3*t - 5*z = 0, -2*t + 0*z + 4*z = 0. Suppose t + f*r + 4/3*r**2 = 0. What is r?
-2, 0
Let z(v) be the first derivative of 2/15*v**3 + 2/3*v + 87 - 1/30*v**4 + 3/5*v**2. Factor z(t).
-2*(t - 5)*(t + 1)**2/15
Solve 2974 + q**3 + 43*q - 4*q**3 - 2434 + 51*q**2 - 331*q = 0 for q.
5, 6
Let c(v) = 11*v - 240. Let f be c(22). Suppose 2*t + 6 - 14 = 0. Suppose h**2 - 92*h**t + 90*h**4 + 0 - 2 + 3*h**f = 0. Calculate h.
-1, 1
Let p be 47 + -49 - (0 + 0 - 8). Suppose 2*g = 4*i + 4, p = 3*g - 0*i - 5*i. Factor -2*x + 396*x**3 + 4*x**2 + g*x - 400*x**3.
-4*x**2*(x - 1)
Solve 859162*a**4 + 125*a**2 - 41*a + 125*a**3 - 859177*a**4 - 284*a + 90 = 0 for a.
-2, 1/3, 1, 9
Let l(y) be the first derivative of -y**6/2340 + 11*y**5/780 - 35*y**3/3 + 56. Let n(b) be the third derivative of l(b). Suppose n(t) = 0. What is t?
0, 11
Find z, given that -816 + 1 - 4010*z**2 - 130 - 132*z + 4007*z**2 = 0.
-35, -9
Let g = -359011/70 + 5129. Let m(s) be the second derivative of g*s**5 + 8/21*s**3 - 4/7*s**2 + 12*s + 9/14*s**4 + 0 + 4/105*s**6. Suppose m(d) = 0. What is d?
-2, -1, 1/4
Let t(d) be the third derivative of -d**6/24 - 607*d**5/4 - 13075*d**2. Find b such that t(b) = 0.
-1821, 0
Let f(s) = -s**2 - 8*s + 2. Let o be f(-8). Factor 8 + 8*x**4 - 2*x**o - 37*x**2 + 28*x + 3*x**5 + 77*x**2 + 25*x**3 - 2*x**5.
(x + 1)**2*(x + 2)**3
Let d be ((-4)/(-110))/((-3182)/5160 + 2 + 8/(-6)). Factor 2/11*z**2 + 0 - d*z.
2*z*(z - 4)/11
Let h be 1*6 + (-12)/((-12)/(-3)). Factor -150*j - 1041 - 5 - h*j**2 - 1191 + 362.
-3*(j + 25)**2
Suppose 0 = -2*b - v + 19, -22 = -4*b + 2*b + 2*v. Let h(j) = 25*j**3 + 30*j**2 + 180*j - 1080. Let s(m) = 3*m**3. Let a(w) = b*s(w) - h(w). Factor a(l).
5*(l - 6)**2*(l + 6)
Let v = -1281104 - -11529944/9. Factor 2/9*f**2 - v - 2/3*f.
2*(f - 4)*(f + 1)/9
Suppose -4*w - 58*y + 63*y = 7, -3*y = -3*w - 3. Let -49/2 - 7*l - 1/2*l**w = 0. What is l?
-7
Let x = 211/4584 - 5/1146. Let l(v) be the first derivative of -1/8*v**2 - x*v**3 - 32 + 0*v. Factor l(o).
-o*(o + 2)/8
Suppose 5*r = 3*w + 350, -w - r = 3*w + 482. Let i be w/(-800) - (-2)/20. Factor i*n**4 - n**2 - 1/4 + 7/8*n + 1/4*n**3 - 1/8*n**5.
-(n - 1)**4*(n + 2)/8
Find m such that -21*m**3 - 501*m**2 - 621/7 - 2925/7*m = 0.
-23, -3/7
Let q(m) be the first derivative of -m**8/336 - m**7/8 - 5*m**6/3 - 25*m**5/6 - 16*m**3/3 + m + 21. Let l(f) be the third derivative of q(f). Factor l(s).
-5*s*(s + 1)*(s + 10)**2
Find w, given that -2888/15 - 22/15*w**3 - 2128*w - 558/5*w**2 = 0.
-38, -1/11
Suppose -4*z + 14 = 5*v, -6*v - 5*z = -10*v + 3. Factor 7*h**4 - 4*h**4 - 7*h**2 + h**v + 3*h**3 + 0*h**3.
3*h**2*(h - 1)*(h + 2)
Suppose 268 = 2*k - 3*l - 359, -4*l - 630 = -2*k. Let i = k - 307. Factor 1/4*z + 0 + 1/4*z**i.
z*(z + 1)/4
Let p be (75/(-396))/(2/(-9)) - (-9885)/36245. Find j such that j - 1/8*j**4 - p - j**3 + 5/4*j**2 = 0.
-9, -1, 1
Suppose -44*o + 279 = 323. Let p(k) = k**2 - 4*k. Let v(x) be the second derivative of x**3/6 - x. Let h(s) = o*p(s) - 5*v(s). Find f such that h(f) = 0.
-1, 0
Let g = 19/5560 + 10949/50040. Find u, given that g*u**3 + 4/3*u**2 + 0 + 0*u = 0.
-6, 0
Suppose 0 - 11/5*h**2 + 1/5*h**3 + 0*h = 0. What is h?
0, 11
Let -6/5*c**2 + 273/5*c - 264/5 - 3/5*c**3 = 0. What is c?
-11, 1, 8
Let n = -32 - -24. Let i = 4 - n. Factor -b**3 + b**3 + b**3 - 12*b**2 - 4*b**3 - i*b.
-3*b*(b + 2)**2
Let n(j) be the third derivative of -48*j - 1/21*j**4 - 1/42*j**5 - 1/420*j**6 + 0*j**3 + 0 - 2*j**2. Factor n(o).
-2*o*(o + 1)*(o + 4)/7
Suppose 1023*z = 1021*z. Let i(q) be the third derivative of 0*q + 1/60*q**6 + 0*q**3 + z*q**5 + 0 - 16*q**2 + 0*q**4 - 1/105*q**7. Find u, given that i(u) = 0.
0, 1
Solve -6440*g - 967*g**2 - 40*g**3 - 1/2*g**4 - 11025/2 = 0.
-35, -9, -1
Let r(h) = -h**3 + 4*h**2 - 7. Let v be r(3). Let z be 3 - (-1 + v - 46). Factor -21*c - z*c**2 + 3*c**4 - 15*c - 21*c**3 - 6*c**4.
-3*c*(c + 2)**2*(c + 3)
Let j be (-28)/(-33) + (4/(-6))/(-1113 - -1114). Factor -26/11*p**2 + 102/11*p + j*p**3 - 126/11.
2*(p - 7)*(p - 3)**2/11
Let i(t) be the second derivative of -t**4/12 - t**3/6 - t**2/2 - 14*t. Let p(n) = 4 + 4*n - 19 - 28*n - 15*n**2. Let b(l) = 18*i(l) - p(l). Factor b(y).
-3*(y - 1)**2
Let i(p) be the first derivative of -p**5 - 45*p**4/4 + 70*p**3 + 610*p**2 + 1320*p - 4423. Factor i(j).
-5*(j - 6)*(j + 2)**2*(j + 11)
Let h(s) be the first derivative of -s**5/40 - 113*s**4/32 + s**3/24 + 113*s**2/16 + 586. Factor h(i).
-i*(i - 1)*(i + 1)*(i + 113)/8
Let i(j) = 21*j + 108. Let y be i(-5). Determine g so that 7*g**y - 8*g**2 + 12*g**4 - 4*g**5 - 4 + 3*g**3 + 12*g + 0*g**3 - 18*g**3 = 0.
-1, 1
Suppose -3/2*z**2 - 87*z - 795/2 = 0. What is z?
-53, -5
Let p = 2315 - 4064. Let a = -5246/3 - p. Determine h, given that -8/3*h - a*h**4 + 2*h**2 + 1 + 0*h**3 = 0.
-3, 1
Suppose 224 - 2*o**3 + 280/3*o**2 - 1192/3*o = 0. Calculate o.
2/3, 4, 42
Suppose -570 - 32*m**2 + 5*m**3 + 16*m + 36*m + 16*m + 132*m**2 - 3*m = 0. What is m?
-19, -3, 2
Suppose -5*t = 2*u - 20, -u + 0*t - 3 = -4*t. Suppose -26 = -2*o + 5*r, -u*o + 4 = -3*r - 23. Factor 3 + x**2 + o + 4*x + 3 + 2*x.
(x + 3)**2
Let l be -1 - (3/(-8))/((-3)/(-68)). Let y(u) be the first derivative of 0*u**3 + 1 - 5/4*u**4 - 10*u + l*u**2. Let y(v) = 0. What is v?
-2, 1
Let w = -2241 + 2244. Let v(k) be the first derivative of 0*k**5 + 1/45*k**6 + 0*k**w + 0*k - 5 - 1/15*k**4 + 1/15*k**2. Find q such that v(q) = 0.
-1, 0, 1
Suppose 0 = 14*i - 10*i - 24, 0 = -4*k + i + 2. Let p(h) be the second derivative of 0 - 1/3*h**4 - 2*h**k + 4*h + 4/3*h**3. Solve p(q) = 0 for q.
1
Suppose 0 = -14*s - 87*s + 11*s - 67*s. Factor 1/3*w**3 + 1/3*w**4 - 2/3*w**2 + 0 + s*w.
w**2*(w - 1)*(w + 2)/3
Let v = -19/2979 - -12049/20853. Factor 0 - v*k - 12/7*k**2 - 8/7*k**3.
-4*k*(k + 1)*(2*k + 1)/7
Suppose -5*b = -13*b + 32. Let i(z) = z**2. Let r(u) = u**2 + 10*u - 40. Let y(v) = b*i(v) + r(v). Suppose y(g) = 0. What is g?
-4, 2
Let z(n) = -2*n**2 + 6*n + 4. Let r(l) = l**3 + 14*l**2 + 14*l + 16. Let v be r(-13). Let k be z(v). Solve -k*s - 5*s + 29*s**2 - 33*s**2 - 7*s = 0 for s.
-4, 0
Solve 0*v + 44/3*v**3 - 17/3*v**4 + 1/3*v**5 + 0 - 28/3*v**2 = 0 for v.
0, 1, 2, 14
Let m(f) = -f**4 - f**3 + f**2 - 4. Let a(r) = -5*r**4 - 4*r**3 - 50*r**2 + 78*r + 111. Let b(o) = a(o) - 6*m(o). Find h, given that b(h) = 0.
-9, -1, 3, 5
Let x(f) be the second derivative of 7*f**6/75 - 29*f**5/50 - 12*f**4/5 - 12*f**3/5 - 21*f + 148. Find g such that x(g) = 0.
-1, -6/7, 0, 6
Solve 160/3 - 28/3*g**2 + 8/3*g + 4/3*g**3 = 0 for g.
-2, 4, 5
Let b(t) be the second derivative of t**6/10 + 87*t**5/20 + 27*t**4/4 - 29*t**3/2 - 42*t**2 + 1117*t - 2. Factor b(j).
3*(j - 1)*(j + 1)**2*(j + 28)
Suppose -1599*r - 4*r**2 - 272769 + 3880*r + 359*r - 162831 = 0. Calculate r.
330
Let p(k) be the first derivative of -k**6/24 + 3*k**5/10 - k**4/4 - k**3/2 + 5*k**2/8 - 1221. Suppose p(t) = 0. What is t?
-1, 0, 1, 5
Let l = -103 - -105. Factor -3*v + 30*v**3 + 12*v - 12*v**3 + 9*v**5 - 12*v**5 + 24*v**l.
-3*v*(v - 3)*(v + 1)**3
Determine l, given that -8*l**2 - 1/5*l**3 + 83/5*l - 42/5 = 0.
-42, 1
Let z(t) be the first derivative of t**5/3 - 23*t**4/8 + 113*t**3/18 + t**2 - 14022. Determine g so that z(g) = 0.
-1/10, 0, 3, 4
Let a(z) be the second derivative of z**8/1120 + z**7/448 + z**6/960 + 2*z**3/3 - 8*z**2 - 4*z - 15. Let y(v) be the second derivative of a(v). Factor y(m).
3*m**2*(m + 1)*(4*m + 1)/8
Let j(p) = 3*p**3 - 2*p**2 - 2*p + 1. Let b(o) = 8*o**3 - 24*o**2 + 37*o + 63. Let r(m) = b(m) - 3*j(m). Suppose r(h) = 0. Calculate h.
-20, -1, 3
Let n(r) be the third derivative of 1/10*r**5 + 1/60*r**6 - 1/35*r**7 + 0*r**3 - 1/6*r**4 + 0*r + 1/168*r**8 - 82*r**2 + 0. Factor n(x).
2*x*(x - 2)*(x - 1)**2*(x + 1)
Let -238*g - 5*g**3 - 16 - 134*g**2 + 886 - 306*g**2 - 246*g + 59*g = 0. Calculate g.
-87, -2, 1
Let n(l) = -839*l - 7547. Let i be n(-9). Let g(c) be the second derivative of 0 - 10*c**2 - 5*c + 2/3*c**i - 6*c**3. Determine t, given that g(t) = 0.
-1/2, 5
Let -1/6*z**3 + 59/2*z - 88/3*z**2 + 0 = 0. Calculate z.
-177, 0, 1
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