-n**4/12 + 4*n**3/9 - n**2/2 + 5282. Determine q so that i(q) = 0.
0, 1, 3
Suppose -82*n + 198 = 3*n - 19*n. Let c = -13/5 - -109/40. Find x, given that 0 - c*x**4 - 1/8*x + 1/8*x**n + 1/8*x**2 = 0.
-1, 0, 1
Let k(h) be the second derivative of -h**7/210 - 4*h**6/25 + 34*h**5/25 - 127*h**4/30 + 67*h**3/10 - 29*h**2/5 + h - 50. Factor k(x).
-(x - 2)*(x - 1)**3*(x + 29)/5
Let 39/2*t**3 + 63/4*t**4 - 63*t**2 - 66*t + 0 - 3/4*t**5 = 0. Calculate t.
-2, -1, 0, 2, 22
Let m(f) = 21*f**5 + 59*f**4 + 15*f**3 - 3*f**2 - 10*f. Let w(g) = -43*g**5 - 122*g**4 - 30*g**3 + 4*g**2 + 20*g. Let t(j) = -13*m(j) - 6*w(j). Factor t(o).
-5*o*(o + 1)**3*(3*o - 2)
Let k = -4/137 + 592/1507. Let p be ((-5)/935)/(2/10) - 4/(-34). Factor -p*j**4 + 2/11*j**3 + 3/11*j**2 - 4/11*j - k.
-(j - 2)**2*(j + 1)**2/11
Suppose 2*k - 1 = 2*u - 5*u, 2*k = -u + 3. Solve 9*z**3 - 77*z**k - 20 - 81*z + 59 - 35*z**2 + z**2 = 0 for z.
-1, 1/3, 13
What is b in -380/3*b**3 + 5/6*b**4 + 0 - 9375*b + 9875/2*b**2 = 0?
0, 2, 75
Solve 2/23*i**4 + 4/23*i**2 + 0 + 0*i - 6/23*i**3 = 0.
0, 1, 2
Let 136 - 6188*o**2 - 6188*o**2 - 11*o - 14*o + 12377*o**2 = 0. Calculate o.
8, 17
Suppose 2*u - 8*u = -4*u. Suppose 4*x - 3*s - 5 = u, 4*s - 5 = -x + 1. Suppose 20*w - 15 - 3*w**2 + 2*w**x - 4*w**2 = 0. Calculate w.
1, 3
Let z(t) = t**3 + 8*t**2 - 13*t - 32. Let s be z(-9). Factor 10*n - 3*n + 6*n**2 - 3*n**3 - n**s + n.
-n*(n - 2)*(n + 1)*(n + 4)
Suppose 2*p + 4*r = 34, -p - 4*r + 20 = 1. Let s be -2 + p + (-32)/8. Solve -s*l - 3*l**2 + l**3 - 6*l**2 + 3 - 4*l**3 - 6 = 0.
-1
Factor 1772 + 330*j**2 + 61410*j**3 - 2212 - 61315*j**3 - 5*j**4 + 20*j.
-5*(j - 22)*(j - 1)*(j + 2)**2
Let c(h) be the first derivative of 33 + 45*h + 1/15*h**3 + 3*h**2. Find u, given that c(u) = 0.
-15
Let y(d) be the third derivative of -d**6/20 - d**5/15 + 11*d**3 + 55*d**2 + 1. Let t(l) be the first derivative of y(l). Solve t(v) = 0.
-4/9, 0
Let p = -1295 + 893. Let m = -1607/4 - p. Factor 1/4*v**2 + 0*v**3 + 0*v - m*v**4 + 0.
-v**2*(v - 1)*(v + 1)/4
Let q = 5096 - 15284/3. Factor 2/3*o**2 + o + 0*o**4 - 2/3 - q*o**3 + 1/3*o**5.
(o - 1)**3*(o + 1)*(o + 2)/3
Let c(a) be the third derivative of -a**7/70 + 157*a**6/40 + 83*a**5/10 - 313*a**4/2 - 948*a**3 + a**2 - 292. Determine w so that c(w) = 0.
-2, 3, 158
Factor -200/9*a + 4/9*a**2 + 1600/9.
4*(a - 40)*(a - 10)/9
Let f = -403838/3 + 134614. Let -1/6*y**2 + 0*y + 0 + f*y**3 - 19/6*y**4 + 2*y**5 = 0. What is y?
0, 1/4, 1/3, 1
Solve -12*z**2 - 93/2*z + 3/2*z**3 - 33 = 0 for z.
-2, -1, 11
Let p = -76965 - -76968. Find y, given that 9/7*y**2 + 16/7 + 1/7*y**p + 24/7*y = 0.
-4, -1
Let u be 13*-11*(-4)/1430. Let -2/15*c**4 - 4/15*c**2 - u*c**3 + 0 + 0*c = 0. What is c?
-2, -1, 0
Let v = -356263 + 4631421/13. Suppose q = -2*q + 12. Factor 4/13*k**2 + v*k**5 + 0*k + 8/13*k**q + 10/13*k**3 + 0.
2*k**2*(k + 1)**2*(k + 2)/13
Suppose 16*t - 8 = 12*t + l, 0 = -l + 4. Let v(o) be the first derivative of 2/27*o**t + 1/9*o**2 - 22 - 4/9*o. Suppose v(b) = 0. What is b?
-2, 1
Let w(b) be the second derivative of 75*b**7/14 + 58*b**6 - 463*b**5/4 - 5015*b**4/2 - 5780*b**3/3 + 1644*b. Suppose w(o) = 0. Calculate o.
-17/3, -2/5, 0, 4
Let g(t) be the first derivative of 2*t**3 - 42 + 7/24*t**4 + 17/2*t**2 + 1/60*t**5 + 0*t. Let v(z) be the second derivative of g(z). Factor v(h).
(h + 3)*(h + 4)
Let u(b) be the third derivative of 8/15*b**3 + 0*b - 34*b**2 + 17/5*b**5 - 31/15*b**4 + 0 - 3/4*b**6. Determine g, given that u(g) = 0.
2/15, 2
Let j(t) = -6*t**2 + 39*t + 27. Let o(s) = s + 1. Let g = -76 + 81. Let f(d) = g*o(d) + j(d). Factor f(x).
-2*(x - 8)*(3*x + 2)
Let a(i) be the third derivative of 5 - 1/210*i**5 + 0*i + 0*i**3 - 2*i**2 + 1/12*i**4. Factor a(l).
-2*l*(l - 7)/7
Let u = 10836 - 10834. Factor u*z - 1/4*z**2 - 4.
-(z - 4)**2/4
Let p = -489 - -493. Factor 20*m**p - 45*m**2 + 3*m**3 - 80*m + 42*m**3 - 98 + 158.
5*(m - 1)*(m + 2)**2*(4*m - 3)
Let b = -7704 - -7706. Let o(c) be the first derivative of 4*c**3 - 14 + 0*c - 1/2*c**4 - 9*c**b. Factor o(h).
-2*h*(h - 3)**2
Let o(h) = h**3 - h**2 - h - 1. Let v(f) = 4*f**3 + 2*f**2 - 16*f - 2. Let m(b) = -6*o(b) + v(b). Solve m(l) = 0 for l.
1, 2
Let i(v) = 3*v**2 - 70*v + 1019. Let f(g) = 39*g**2 - 924*g + 13248. Let o(t) = -4*f(t) + 51*i(t). Factor o(m).
-3*(m - 31)*(m - 11)
Let f be ((-689)/143 - (-12)/(-66)) + 8. Let t(g) be the second derivative of 1/6*g**4 + 0 - 9*g**2 + 16*g + 8/3*g**f. Factor t(m).
2*(m - 1)*(m + 9)
Factor -64/9*v - 2/9*v**2 + 470/3.
-2*(v - 15)*(v + 47)/9
Let s(d) = 36*d**4 - 156*d**3 - 523*d**2 - 251*d + 11. Let b(w) = 20*w**4 - 78*w**3 - 260*w**2 - 126*w + 6. Let i(v) = -11*b(v) + 6*s(v). Solve i(f) = 0 for f.
-15, -4, -1/2, 0
Let h be (-15)/9*((-56)/10 - -2). Let w(p) = -45*p**3 + 50*p**2 + 5. Let g(t) = t**4 - 45*t**3 + 50*t**2 + 6. Let j(m) = h*w(m) - 5*g(m). Solve j(r) = 0 for r.
-10, 0, 1
Let l be -1*(1/2 + (-10)/4). Let a be 1*l + -1*(-3 - -1). Determine f, given that -53*f**2 + a*f**4 + 48*f**3 - 4*f**4 - 12*f**5 + 14*f**4 + 8 - 5*f**2 = 0.
-2, -1/3, 1/2, 1, 2
Let u(w) be the first derivative of -w**5/10 + 3*w**4/2 - 5*w**3 + 7*w**2 - 21*w + 88. Let o(r) be the first derivative of u(r). Solve o(a) = 0.
1, 7
Let 44*v**2 - 2*v**3 + 16683 - 33285 - 32*v - 33*v - 53*v + 16678 = 0. Calculate v.
1, 2, 19
Let u be (-328)/(-2)*(-18)/(-36). Let t = u + -50. Determine a, given that -20*a**2 + 29*a**2 - t - 24*a - 13*a**2 = 0.
-4, -2
Let u(y) be the first derivative of y**4/20 + 2*y**3/15 - 3*y**2/2 - 36*y/5 - 4999. Suppose u(s) = 0. Calculate s.
-3, 4
Let m = 437 + -435. Let h(b) = -1. Let k(r) = 20*r**2 + 172*r - 74. Let p(n) = m*h(n) - k(n). Determine y so that p(y) = 0.
-9, 2/5
Let b be -1*((-2)/1)/(6/9). Suppose 4*d + 3 = 3*r, -2*r = b*d - 6 - 13. Find c such that -10*c**2 - c**4 - 13*c**4 + 0*c**2 + 4*c**5 - c + 3*c + 18*c**d = 0.
0, 1/2, 1
Let c(a) = 89*a**3 - 3171*a**2 + 2293*a + 744. Let y(g) = -22*g**3 + 793*g**2 - 574*g - 187. Let k(u) = -2*c(u) - 9*y(u). Factor k(w).
5*(w - 39)*(w - 1)*(4*w + 1)
Let v(m) be the third derivative of -m**8/1344 - m**7/105 - m**6/160 + 7*m**5/30 + m**4/24 - 2*m**3 - m**2 - 74. Find t such that v(t) = 0.
-6, -4, -1, 1, 2
Let s be 10/6*(-3 + -9*2). Let l = 37 + s. Suppose 5*x**4 + l*x**2 + 3*x**5 - x**5 + 16*x**3 + x**4 - 10*x**3 = 0. Calculate x.
-1, 0
Let y(b) be the first derivative of b**4/126 + b**3/21 - 4*b**2/21 + 137*b + 11. Let n(z) be the first derivative of y(z). What is q in n(q) = 0?
-4, 1
Let v be (-6)/(-32)*8 + (-765)/(-2). Factor -v - 380 - 63*t - 3*t**2 + 764.
-3*t*(t + 21)
Let i be ((-1)/4 - 45528/(-224))*-7. Let r = 1421 + i. Factor 18/7*q**2 + r - 16/7*q**3 - 2/7*q.
-2*q*(q - 1)*(8*q - 1)/7
Suppose -2*r = -3*i - 0*r + 26, -2*i - 2*r + 4 = 0. Factor 7*t**3 - 3*t**4 + 2*t**4 - 10*t**2 + t**2 - i*t**2 + 9*t.
-t*(t - 3)**2*(t - 1)
Suppose 0 = -5*z + 6*z + 1. Let h(t) = 2*t + 8. Let f be h(z). Factor -12*w - 7*w**3 + 18*w**2 - 8*w**3 + 0*w**4 + f*w**2 + 3*w**4.
3*w*(w - 2)**2*(w - 1)
Let s(j) = -j**2 + 1428*j - 169934. Let o(v) = -v**2 + 2856*v - 339869. Let h(g) = 2*o(g) - 5*s(g). Find n, given that h(n) = 0.
238
Factor -815*o + 1067*o + 3446*o + 29*o**3 + 275*o**2 - 27*o**3 - 103*o**2.
2*o*(o + 43)**2
Let c(d) be the first derivative of 1/3*d**3 + 5776*d + 232 + 76*d**2. Let c(v) = 0. What is v?
-76
Let f(u) be the second derivative of 1/165*u**6 - u + 9/110*u**5 + 5/33*u**4 + 78 - 12/11*u**3 - 56/11*u**2. Suppose f(z) = 0. Calculate z.
-7, -2, 2
Let -23*u**5 + 125*u**4 - 209*u**4 + 24*u**5 + 574*u - 192*u + 189*u**2 - 383*u**3 - 105*u**4 = 0. What is u?
-2, -1, 0, 1, 191
Suppose -533*q + 537*q - 20 = 0. Let s(x) be the second derivative of 8/3*x**3 + 29*x + x**4 + 0 - 2/5*x**q - 2/15*x**6 - 8*x**2. Factor s(m).
-4*(m - 1)**2*(m + 2)**2
Let l be (96/10)/((-788)/260 - -3). Let t = l - -625/2. Let -t*v**2 + 0 - v = 0. What is v?
-2, 0
Let k be 780/50 - (-4)/10. Let q be 6/(2 + -1) + (k - 19). Let 1 - 10*f + 2*f**2 + 2*f**q + 2*f + f**2 - f**4 + 3 = 0. What is f?
-2, 1, 2
Let v(t) be the first derivative of 167/8*t**4 - t + 165 - 11/2*t**5 + 61/4*t**2 - 57/2*t**3. Factor v(b).
-(b - 1)**3*(55*b - 2)/2
Let q be 26 - 22 - (-130)/(-126) - 4. Let x = q - -8/7. Solve 0 + 0*l - x*l**5 - 4/3*l**4 - 64/9*l**2 - 16/3*l**3 = 0.
-4, 0
Let p(c) be the third derivative of -c**8/16