Let y(j) = -j**2 + j. Let c(m) = -3 + 1 - 10 + 8*m + 4*m**2. Let t(q) = -c(q) - 2*y(q). Find w, given that t(w) = 0.
-6, 1
Let c(k) be the first derivative of k**5/100 + k**4/40 - k**3/5 - 6*k**2 - 17. Let u(p) be the second derivative of c(p). Factor u(n).
3*(n - 1)*(n + 2)/5
Let b(s) be the third derivative of 4913*s**7/105 - 22253*s**6/60 + 1258*s**5 - 7100*s**4/3 + 8000*s**3/3 + 273*s**2. Factor b(l).
2*(l - 1)*(17*l - 20)**3
Factor -4/9*q + 2/9*q**2 + 2/9.
2*(q - 1)**2/9
Let x = 255/212 - 24/53. Factor 3/4 + 3/4*u - 3/4*u**3 - x*u**2.
-3*(u - 1)*(u + 1)**2/4
Let s = -18635 - -242263/13. Let r = -2/311 + 648/4043. Factor -8/13*a**3 - s*a - r - 12/13*a**2 - 2/13*a**4.
-2*(a + 1)**4/13
Factor 102*z**2 - 257*z**2 + 1275*z - 1086 - 39 + 5*z**3.
5*(z - 15)**2*(z - 1)
Let d be ((-60)/18)/(4/(-6)). Suppose d*z + 15 - 40 = -5*f, 4*f - 5*z + 7 = 0. Factor 3*v**2 - 7*v**f - 13 + 15 + 2*v**4.
2*(v - 1)**2*(v + 1)**2
Let w(v) be the third derivative of -32*v**7/245 - 2*v**6/5 - 3*v**5/7 - 13*v**4/56 - v**3/14 - 32*v**2 + 1. Factor w(p).
-3*(p + 1)*(4*p + 1)**3/7
Factor 20*b**2 - 5*b + 63*b - 63428*b**3 - 84 + 63430*b**3 + 4*b**2.
2*(b - 1)*(b + 6)*(b + 7)
Let u(c) = 4*c**3 + 13*c**2 + 2*c + 7. Let w(q) = -q**3 - 4*q**2 - q - 2. Let s be (-304)/22 + 30/(-165). Let k(y) = s*w(y) - 4*u(y). Find z such that k(z) = 0.
-1, 0, 3
Factor 28/9*q**2 + 2/9*q**3 - 34/9*q - 20/3.
2*(q - 2)*(q + 1)*(q + 15)/9
Let m = 94 - 90. Let n be 29/22 + m/22. Factor n*x**2 + 3/2*x**3 + 0*x + 0.
3*x**2*(x + 1)/2
Factor 3/5*n**4 + 6/5*n**2 - 1/5 + 8/5*n**3 + 0*n.
(n + 1)**3*(3*n - 1)/5
Suppose -17*n = -21*n + 12. Let 0*j**n + 0*j**3 + j**3 = 0. Calculate j.
0
Suppose 3*x - 2*t - 4 = 0, -t - 28 = -2*x - 6*t. Factor 12*i**2 + 8 - 6*i**2 + 16*i - 9*i**3 + 11*i**3 + x*i**2.
2*(i + 1)*(i + 2)**2
Let -2*f**4 + 899*f**3 + 877*f**3 - 1764*f**3 + 18 + 48*f**2 + 52*f = 0. Calculate f.
-1, 9
Let g(i) be the third derivative of i**5/60 + i**4/24 + i**3/3 - 4*i**2. Let j be g(-2). Factor 2/7*k**j + 0*k + 0*k**2 + 2/7*k**3 + 0.
2*k**3*(k + 1)/7
Let g be -2*(-2)/44 - (-18 + 1062/66). Factor 7/3*j**4 + 1/3*j**5 + 0 + 0*j + 16/3*j**3 + 4*j**g.
j**2*(j + 2)**2*(j + 3)/3
Factor 5*j**2 + 22462 + 19532 + 567 + 32412 - 1130*j - 11128.
5*(j - 113)**2
Suppose -11*j - 16 = -60. Let d(p) be the second derivative of 0 - 1/9*p**6 + 0*p**2 - j*p - 1/60*p**5 - 1/9*p**3 + 7/36*p**4. Determine k, given that d(k) = 0.
-1, 0, 2/5, 1/2
Let b(a) = 13*a**4 - 5*a**3 - a**2 + 7*a. Let r(m) = 14*m**4 - 6*m**3 - 2*m**2 + 6*m. Let n be (15/(-10))/((-6)/(-28)). Let i(l) = n*r(l) + 6*b(l). Factor i(o).
-4*o**2*(o - 1)*(5*o + 2)
Let b = -81/136 + -19509/1496. Let w = 1072/77 + b. Determine u so that 2/7*u**2 + 4/7*u + w = 0.
-1
Let g = 851489/2574957 + -160/5181. Let s = g - 1/71. Determine k so that s*k**2 + 6/7*k + 4/7 = 0.
-2, -1
Let b(q) be the first derivative of -3*q**4 - 92*q**3/3 - 28*q**2 - 63. Factor b(l).
-4*l*(l + 7)*(3*l + 2)
Suppose 2*r + 4*x = 10, -2*r - 3*x + 1 = -8. Factor 0*h + 5*h - 12*h**r + 7*h**3.
-5*h*(h - 1)*(h + 1)
Let o(n) be the third derivative of n**5/12 + 35*n**4/9 + 10*n**3 - 112*n**2. What is k in o(k) = 0?
-18, -2/3
Suppose -4 + 67 = p. Let u = p - 251/4. Factor -1/4*y**3 + u*y**2 + 0 + 0*y.
-y**2*(y - 1)/4
Let b(g) = -g**2. Let n(s) = -7*s**2 - s. Suppose y + 34 = 10. Let q(i) = y*b(i) + 3*n(i). Find d, given that q(d) = 0.
0, 1
Let p be -28*25/((-2625)/10). Factor -8/3*b**2 + 2/3*b**3 + p*b + 0.
2*b*(b - 2)**2/3
Let q(t) be the first derivative of -7*t**5/90 - t**4/6 - 2*t**3/27 + 5*t + 4. Let d(j) be the first derivative of q(j). Find f such that d(f) = 0.
-1, -2/7, 0
What is n in 3/7*n**2 + 27648/7 + 576/7*n = 0?
-96
Determine p, given that -51*p**2 - 24 - 9 + 3 - 9*p**2 - 11*p + 96*p = 0.
2/3, 3/4
Let b(m) be the second derivative of 0 + 1/4*m**5 - 5/42*m**7 + 10*m**3 + 55/12*m**4 + 10*m**2 - 31*m - 1/2*m**6. Find f such that b(f) = 0.
-2, -1, 2
Let q be (-105)/(-15) - 82/12. Suppose -1/6*f**4 - 1/2*f - q*f**2 + 1/3 + 1/2*f**3 = 0. Calculate f.
-1, 1, 2
Let b(u) = 9*u**3 - 109*u**2 - 112*u - 2. Let j(n) = -2*n**3 + 2*n**2 + n + 1. Let d(s) = b(s) + 2*j(s). What is c in d(c) = 0?
-1, 0, 22
Let k = 33 - 9. Let j = k - 24. Solve -1/2*m**2 + 0*m - 8*m**4 - 4*m**3 + j = 0.
-1/4, 0
Let q(r) = r**3 - 14*r**2 + 17*r + 27. Let k be q(13). Factor -89*d**3 + k*d**3 + 2*d**2 + 6*d**2 - 2*d + 4*d**4.
2*d*(d - 1)**2*(2*d - 1)
Suppose 3*x + 3*n - 18 = 0, -x + n = -n. Let p(j) be the second derivative of -7*j + 1/66*j**x + 0*j**3 - 1/110*j**5 + 0 + 0*j**2. Factor p(c).
-2*c**2*(c - 1)/11
Factor -17*n**3 + 3*n**4 + 10*n**3 + 10*n**3 - 1 - 3*n**5 - 3*n**2 + 1.
-3*n**2*(n - 1)**2*(n + 1)
Let n(v) be the first derivative of -2/5*v**3 - 3 + 1/30*v**4 - 4*v + 9/5*v**2. Let w(a) be the first derivative of n(a). Factor w(b).
2*(b - 3)**2/5
Let f(h) = -7*h**4 + 52*h**3 - 382*h**2 - 33. Let t(u) = 4*u**4 - 26*u**3 + 192*u**2 + 18. Let c(l) = 6*f(l) + 11*t(l). Factor c(v).
2*v**2*(v - 5)*(v + 18)
Factor -55/8*v**2 - 1/8*v**3 + 0 + 0*v.
-v**2*(v + 55)/8
Suppose u + 146 - 146 = 0. Let m be 2/15 + (u/(-4))/(-2). Factor -2/3*c - m*c**2 - 8/15.
-2*(c + 1)*(c + 4)/15
Let f = -93 - -189/2. Let a(w) be the first derivative of f*w**4 - w**3 - 3*w**2 - 4 + 0*w + 3/5*w**5. Factor a(m).
3*m*(m - 1)*(m + 1)*(m + 2)
Suppose 2*u - 2 = 125*d - 127*d, 0 = 2*d - 2*u - 6. Solve 96 + 2/3*t**d + 16*t = 0 for t.
-12
Let g(b) = -6*b**3 - 6*b**2 + 31*b - 35. Let r(o) = -o**3 - o + 1. Let q(l) = g(l) - 5*r(l). Let q(w) = 0. Calculate w.
-10, 2
Let f(w) be the second derivative of w**7/147 + 4*w**6/105 - 4*w**5/35 - 32*w**4/21 - 16*w**3/3 - 64*w**2/7 - 163*w - 1. Factor f(m).
2*(m - 4)*(m + 2)**4/7
Let g(j) be the third derivative of j**5/180 - j**4/9 - 227*j**2. Factor g(r).
r*(r - 8)/3
Suppose -12 = 5*q - 2*l, -2*q + 72*l + 24 = 76*l. Let o(j) = 3*j**3 + j. Let i be o(1). Factor q + 0*b**2 + 0*b - 2/5*b**3 + 2/5*b**i.
2*b**3*(b - 1)/5
Let u(o) be the first derivative of -o**4/24 + 5*o**3/9 - 8*o**2/3 + 16*o/3 + 12. Factor u(p).
-(p - 4)**2*(p - 2)/6
Let j(l) be the second derivative of l**4/54 - 10*l**3/27 + 16*l**2/9 + l - 190. Factor j(m).
2*(m - 8)*(m - 2)/9
Suppose 3*n + 4*q + 7 = -0, 0 = 2*n + q - 2. Suppose 6 = n*z - 0*z. Find k such that -9 + 2 - 4*k**z - 1 - 13*k + k = 0.
-2, -1
Let x(u) = u**2 + 9*u + 17. Let i be x(-9). Factor -i*f**2 + 21*f + 12*f**2 + 30 + 8*f**2.
3*(f + 2)*(f + 5)
Suppose 4*t - 6 = 2. Suppose -t*p - 14 = q + 4*q, 3*p = -5*q - 11. Suppose 4*m**2 - 2*m**3 - 7 + 4*m**p + 7 = 0. Calculate m.
-2, 0
Let x(a) be the third derivative of a**6/120 - 37*a**5/30 + 145*a**4/24 - 12*a**3 - 2*a**2 - 47. Factor x(y).
(y - 72)*(y - 1)**2
Let l(y) be the first derivative of -y**5/100 + y**4/40 + 11*y**2/2 - 28. Let c(p) be the second derivative of l(p). Find b such that c(b) = 0.
0, 1
Let x(l) be the second derivative of -7/90*l**6 - 1/126*l**7 + 8/3*l**2 - 56*l - 2/9*l**4 - 4/15*l**5 + 8/9*l**3 + 0. Suppose x(h) = 0. Calculate h.
-2, 1
Let n = -419 + 419. Let y(l) be the second derivative of 0*l**2 + 1/3*l**3 + 9*l + 1/10*l**5 + n + 1/3*l**4. Suppose y(j) = 0. Calculate j.
-1, 0
Suppose -5*d + 42*d - 110 = 38. Solve -1/4*i**2 + 1/2*i + 1/4*i**5 - 3/4*i**3 + 0 + 1/4*i**d = 0 for i.
-2, -1, 0, 1
Let q = 58 + -55. Let c(i) be the third derivative of 0*i**q + 0 - 1/480*i**6 + 0*i**4 + 0*i + 3*i**2 - 1/840*i**7 + 0*i**5. Factor c(k).
-k**3*(k + 1)/4
Factor -7/3*h + 22/3*h**2 - 8*h**3 + 10/3*h**4 + 0 - 1/3*h**5.
-h*(h - 7)*(h - 1)**3/3
Let f(a) be the third derivative of -a**8/784 + a**7/490 + a**6/280 - a**5/140 + 30*a**2. Solve f(l) = 0.
-1, 0, 1
Let o(v) = -3*v**4 - 38*v**3 - 14*v**2 + 7*v + 7. Let k(i) = 2*i**3 - i**2 - i - 1. Let y(c) = -7*k(c) - o(c). Factor y(b).
3*b**2*(b + 1)*(b + 7)
Let z = 62 + -82. Let y be (-6)/(-18)*-3 - z/14. Factor -9/7*a + y*a**2 + 6/7.
3*(a - 2)*(a - 1)/7
Let r(m) be the second derivative of -m**5/110 + m**3/11 - 2*m**2/11 + 16*m. Suppose r(h) = 0. What is h?
-2, 1
Determine v, given that -48*v**2 - 31*v**2 - 16*v + 52*v**4 + 33*v**2 - 26*v**2 - 40*v**2 - 44*v**3 = 0.
-1, -2/13, 0, 2
Let p be 147/1 + (1 - (-10)/(-2)). Let v = 291/2 - p. Factor i - v*i**2 + 0.
-i*(5*i - 2)/2
Let k(h) be the first derivative of -h**4/10 + 16*h**3/15 - 7*h**2/5 + 283. Suppose k(x) = 0. Calculate x.
0, 1, 7
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