*2 - 560*t + 69. Let u(w) = 256*w**3 + 88*w**2 - 112*w + 14. Let n(i) = 2*f(i) - 11*u(i). Find z, given that n(z) = 0.
-1, 2/9, 2/7
Factor -24/5*b**4 + 12*b**3 - 56/5*b**2 + 2/5*b**5 + 0 + 18/5*b.
2*b*(b - 9)*(b - 1)**3/5
Let i = -57 - -60. Suppose 0 = -5*w + 5*u + 60, 54 = i*w + w + 2*u. Factor -6 - w*m + 6*m**2 + 6*m**2 - 5*m - 3*m.
3*(m - 2)*(4*m + 1)
Let v be (-11845)/(-28325) - (-13)/((-1144)/(-16)). Find d, given that 54/5*d + 0 + 57/5*d**2 - v*d**5 - 51/5*d**3 - 57/5*d**4 = 0.
-18, -1, 0, 1
Let f(s) be the second derivative of -3/50*s**5 + 27*s + 0*s**2 - 5/6*s**3 + 4/75*s**6 - 2/3*s**4 - 1/210*s**7 + 2. Factor f(w).
-w*(w - 5)**2*(w + 1)**2/5
Suppose 2*i + 94 = 4*h, 0*h - 3*h + 66 = -3*i. Suppose -h*v**2 - 28 + 8*v**2 + 15*v**2 - 18*v = 0. What is v?
-7, -2
Let m(y) be the third derivative of -2/5*y**6 + 0 - 10*y**3 - 1/10*y**7 - 11/2*y**4 + 0*y + 87/20*y**5 - 33*y**2. Solve m(q) = 0.
-5, -2/7, 1, 2
Let r(k) be the second derivative of k**6/8 + 171*k**5/80 + 9*k**4/2 + 5*k**3/2 - 56*k + 1. Suppose r(m) = 0. Calculate m.
-10, -1, -2/5, 0
Let s(r) = 8*r**3 + 79*r**2 - r + 4. Let j be s(0). Factor j - 22/9*g + 2/9*g**2.
2*(g - 9)*(g - 2)/9
Let c(g) = 10*g**2 + 915*g + 7420. Let q(x) = 41*x**2 + 3669*x + 29679. Let z(w) = 21*c(w) - 5*q(w). Factor z(d).
5*(d + 9)*(d + 165)
Let f be (609/435)/((-105)/(-100)). Let w(q) be the third derivative of 1/30*q**6 + 2/15*q**5 - 27*q**2 - 1/6*q**4 + 0 - f*q**3 + 0*q. Factor w(t).
4*(t - 1)*(t + 1)*(t + 2)
Suppose 48 = -9*q + 3*q. Let w(p) = 44*p**3 + 58*p**2 + 6*p. Let x(f) = 29*f**3 + 38*f**2 + 4*f. Let c(y) = q*x(y) + 5*w(y). Factor c(r).
-2*r*(r + 1)*(6*r + 1)
Let s = -2272 + 2272. Let d(q) be the first derivative of s*q**3 - 1 + 0*q**2 + 0*q + 1/22*q**4 + 2/55*q**5. Factor d(g).
2*g**3*(g + 1)/11
Suppose 69 = 8*d + 45. Let j be (-2)/(-7) + (-668)/(-14). What is z in 32*z + 484*z**2 - 140*z**5 - j + 54*z**d + 67*z**3 - 436*z**4 - 13*z**3 = 0?
-3, -1, -2/5, 2/7, 1
Suppose -3 = -n - y - 0, 2*n - 3*y - 6 = 0. Let f(i) = -2*i**2 + 68*i + 395. Let l be f(39). Solve 19*d + 3*d**n - d - 8*d**3 - 8*d + l*d**2 = 0 for d.
-1, 0, 2
Solve 17190*x**2 + 3216 + 11655*x**3 - 1381 - 1355 + 4847*x - 2450*x**4 + 1553*x = 0.
-4/7, -1/10, 6
Let g(y) be the second derivative of y**5/80 - 19*y**4/48 - 25*y**3/12 + 21*y**2 - 4521*y. Factor g(i).
(i - 21)*(i - 2)*(i + 4)/4
Let h = -317029/20 - -79321/5. Factor 12*j**3 + h*j + 30*j**2 + 3/2.
3*(j + 2)*(4*j + 1)**2/4
Let i(w) be the first derivative of -w**4/18 - 2*w**3 - 17*w**2/3 + 67*w + 62. Let d(a) be the first derivative of i(a). Let d(x) = 0. Calculate x.
-17, -1
Let g = -40 + 40. Suppose -14*k + 17 + 39 = g. Factor 3*s**3 + 5*s**4 - 10*s - 5 + s**k + 7*s**3 - s**4.
5*(s - 1)*(s + 1)**3
Let r be ((-5187)/(-8645))/(36/(-50))*(-3)/((-90)/(-4)). Solve -2/9*x**2 + r*x**3 - 1/9*x + 2/9 = 0.
-1, 1, 2
Let -23/5*v**3 + 0 - 171/10*v**2 - 1/10*v**4 - 63/5*v = 0. What is v?
-42, -3, -1, 0
Let i(x) = 2*x**2 - x. Let t(s) = 12*s**4 - 39*s**3 - 303*s**2 - 252*s + 84. Let m(l) = 12*i(l) + t(l). Factor m(z).
3*(z - 7)*(z + 2)**2*(4*z - 1)
Let a(r) = -r**2 + 424*r - 510. Let k(y) = -5*y**2 + 2092*y - 2551. Let o(i) = -16*a(i) + 3*k(i). Find h such that o(h) = 0.
1, 507
Factor -2/5*l**4 - 28/3*l**3 + 192/5*l - 256/5*l**2 + 0.
-2*l*(l + 12)**2*(3*l - 2)/15
Let l(w) be the second derivative of -w**5/70 + 5*w**4/42 + 22*w**3/21 - 8*w**2 + 4873*w. Factor l(t).
-2*(t - 7)*(t - 2)*(t + 4)/7
Let f = 598 - 620. Let i be (-125)/f - ((-600)/88 - -7). Factor 3/2*l**2 + i*l + 3.
(l + 3)*(3*l + 2)/2
Let i = -28 + 31. Let m be ((-5)/(-10) - -4) + i/(-2). Find n such that -17*n**m - 5*n**2 + 5*n + 12*n**3 - 2 + 7 = 0.
-1, 1
Let c be (-3 + (-332)/(-108))/((-18)/(-3) - (-8520)/(-1440)). Let x = 202/7 - 1804/63. Factor c*b + 2/3 + x*b**2.
2*(b + 1)*(b + 3)/9
Let q(w) = w**2 - 8. Let k(y) = -11*y**2 - 290*y + 343. Let f(d) = k(d) + 6*q(d). Factor f(z).
-5*(z - 1)*(z + 59)
Suppose t - 47 = -4*f, t - 4*f - 57 = -3*f. Suppose 10 + 89*p**2 - 94*p**2 + t + 60*p = 0. What is p?
-1, 13
Suppose 0 = -0*v - 5*v - 40. Let y be 2*12/v + 9. Solve -4*t**2 + y - 4*t + t**2 + 4*t - 3*t = 0.
-2, 1
Let f(r) = r**2 - 2*r + 5. Let w(h) = 2*h**2 - 220*h - 578. Let x(v) = 5*f(v) - w(v). Solve x(m) = 0 for m.
-67, -3
Suppose -10 = v - 2*b - 2*b, 5*b = 2*v + 8. Factor -v*g**2 - 45*g**2 - 52*g + 6*g**3 - 88 - 2*g**3 + 91*g**2.
4*(g - 2)*(g + 1)*(g + 11)
Suppose 510*a + 2*v = 506*a + 36, 0 = -3*a + 3*v - 36. Factor 6/7 + 27/7*s**a - 3*s + 3/7*s**4 - 15/7*s**3.
3*(s - 2)*(s - 1)**3/7
Let n(r) = -r + 3. Suppose -3 - 6 = -9*d. Let o be n(d). Factor -6 + 10 + 5*m**o + 0 + 20*m + 16.
5*(m + 2)**2
Let u(h) be the third derivative of h**8/1344 - 13*h**7/504 + h**6/3 - 3*h**5/2 - 43*h**4/8 + 89*h**2. Let j(a) be the second derivative of u(a). Factor j(b).
5*(b - 6)**2*(b - 1)
Let k be (-43)/(-86)*1*211*4. Let n = k - 2108/5. Factor -n - 2/5*b**2 + 4/5*b.
-2*(b - 1)**2/5
Let q(x) be the third derivative of 16*x**7/525 + 74*x**6/75 + 1993*x**5/150 + 481*x**4/5 + 2028*x**3/5 + x**2 - 6*x - 132. Factor q(b).
2*(b + 6)**2*(4*b + 13)**2/5
Let m(o) be the first derivative of o**5/15 + 14*o**4/3 + 6*o**3 - 28*o**2/3 - 55*o/3 - 2963. Factor m(b).
(b - 1)*(b + 1)**2*(b + 55)/3
Factor -2*j**2 + 3*j**2 + j**2 + 601 + 703 - 160 - 576*j.
2*(j - 286)*(j - 2)
Let s = 30 + -24. Suppose -132 = -s*j - 0*j. Let -j*t + 12*t**2 - 13*t - 6 + 14*t = 0. Calculate t.
-1/4, 2
Let p(f) be the second derivative of -241*f + 0 + 1/84*f**4 + 62/21*f**3 + 1922/7*f**2. Let p(i) = 0. What is i?
-62
Solve -48/7 - 10/7*y + 2/7*y**2 = 0 for y.
-3, 8
Factor -8/9*r + 2/9*r**2 - 154/9.
2*(r - 11)*(r + 7)/9
Let g = -1162 + 4657/4. Let q(i) be the first derivative of -g*i + 11 - 3/4*i**2 + 1/4*i**3. Factor q(y).
3*(y - 3)*(y + 1)/4
Suppose 42*x = 23*x - 55*x + 412 + 180. Determine g so that -x*g**2 - 2*g + 0 + 25/2*g**4 - 5/2*g**3 = 0.
-2/5, 0, 1
Suppose 0*d + 3 = x - 3*d, -5*x = -4*d + 18. Let f be 8/12 + x/(-3). Find q, given that -q**3 - 4/3 - 1/3*q**2 + f*q = 0.
-2, 2/3, 1
Let b(c) be the second derivative of 1/63*c**7 - 1/10*c**5 + 0*c**2 + 0*c**3 + 1/9*c**4 + 0*c**6 - 29*c + 0. Suppose b(u) = 0. What is u?
-2, 0, 1
Let x(y) be the first derivative of y**4 + 20*y**3 - 36*y**2 - 128*y - 1591. What is m in x(m) = 0?
-16, -1, 2
Let v be 1/(-11) - (-35 - 64168/(-2002)). Let p = 5 - 3. Factor -24/7 - v*t - 4/7*t**p.
-4*(t + 2)*(t + 3)/7
Factor 38/11*r - 40/11 + 2/11*r**2.
2*(r - 1)*(r + 20)/11
Let z(k) = -842*k + 96833. Let s be z(115). Determine x so that -1/2*x**s - 6 - 3/2*x**2 + 8*x = 0.
-6, 1, 2
Let q = -30/1417 - -49655/2834. Factor q*l**2 + 1/2*l**3 + 289/2 + 323/2*l.
(l + 1)*(l + 17)**2/2
Let 1/2*j**5 + 0 - 313/2*j**3 + 155/2*j**4 + 0*j + 157/2*j**2 = 0. What is j?
-157, 0, 1
Let 784/5 + 2/5*o**3 + 314*o + 788/5*o**2 = 0. What is o?
-392, -1
Factor 176*a**2 - 537*a**2 + 508*a - 510 + 179*a**2 + 184*a**2.
2*(a - 1)*(a + 255)
Let p = 33/1559 - -5477/35857. Factor 4/23*i**3 - p*i + 0 - 6/23*i**2.
2*i*(i - 2)*(2*i + 1)/23
Determine r so that -2*r**3 + 1/2*r**4 - 45/2*r**2 + 0 + 0*r = 0.
-5, 0, 9
Let x be -1*(-8)/(-2)*(41789/(-870) + 48). Let k(u) be the third derivative of 0 + 0*u**3 + 0*u - 1/3*u**4 - 1/60*u**6 - x*u**5 - 12*u**2. Solve k(i) = 0 for i.
-2, 0
Factor -186/5*p - 68/5*p**2 - 2/5*p**3 + 0.
-2*p*(p + 3)*(p + 31)/5
Suppose 3*o - 20 + 0 = -5. Let s(u) be the first derivative of -1/16*u**6 + 1/8*u**3 + 0*u - 9/32*u**4 + 0*u**2 - 11 + 9/40*u**o. Factor s(k).
-3*k**2*(k - 1)**3/8
Let h(a) be the second derivative of 1/30*a**6 - 1/12*a**4 + 7*a - 1/42*a**7 + 1/20*a**5 + 0*a**2 + 0*a**3 + 0. Determine o, given that h(o) = 0.
-1, 0, 1
Let c(w) be the second derivative of -w**4/60 + 9*w**3/10 - 36*w**2/5 + 6*w. Determine k, given that c(k) = 0.
3, 24
Let i(p) be the third derivative of -p**5/40 + 11*p**4/16 + 45*p**3 - 2927*p**2. Find t, given that i(t) = 0.
-9, 20
Suppose 0 = 5*c + 5*h + 110, 42 = 3*c - 5*c - h. Let f be 12/30 + c/(-325). Suppose 0*s + f*s**3 + 2/13*s**4 + 4/13*s**2 + 0 = 0. Calculate s.
-2, -1, 0
Solve 1/8*u**2 + 41472 - 144*u = 0 for u.
576
Let d(m) = 1209*m + 175. Let u be d(-2). Let z = u + 2245. Solve 75/4*w**3 + 15/2*w**z + 3/4*w + 0 = 0.
-1/5, 0
Factor 11611*j - 1253*j - 206045 - 5*j**4 + 34302*j - 220*j**3 - 390*j**2.
-5*(j - 7)**2*(j + 29)**2