12
Let r be 1*(2 - (-8)/(-10)). Let t be 16 + -6 + (1/(-3))/(3/54). Factor -2/5*f**t + 2/5*f**3 + r*f**2 + 4/5 - 2*f.
-2*(f - 1)**3*(f + 2)/5
Let m be 14*7 - 140/35. Let l = m + -91. Factor -l*o**4 + 16*o + 16*o**2 - 8*o**4 + 6*o**4 - 4*o**3 + o**4.
-4*o*(o - 2)*(o + 1)*(o + 2)
Let t(x) be the second derivative of -x**6/105 - 3*x**5/70 + x**4/42 + x**3/7 + 200*x. Factor t(p).
-2*p*(p - 1)*(p + 1)*(p + 3)/7
Let o(k) be the second derivative of -k**4/42 - 844*k**3/21 - 178084*k**2/7 + 103*k. Factor o(v).
-2*(v + 422)**2/7
Let p be 192/(-64) - -1*1*-3. Let z be 0 - 2/(-6) - 4/p. Let 0 + 3*l**3 + 4*l**2 - 12*l - 1 + 11*l - z = 0. Calculate l.
-1, 2/3
Suppose -576/5*b**3 + 0*b - 572/5*b**4 + 4/5*b**5 + 0*b**2 + 0 = 0. Calculate b.
-1, 0, 144
Let u(x) = -110*x + 11. Let j be u(17). Let k = -3717/2 - j. What is h in 1/2*h**5 + 1/2*h + 1/2 + k*h**4 - h**3 - h**2 = 0?
-1, 1
Determine f so that -f**2 + 7600 - 3810 - 3814 + 11*f = 0.
3, 8
Factor 0 - 25/3*g**5 - 7010*g**4 + 1180484*g**2 - 4414189/3*g**3 - 708964/3*g.
-g*(g + 421)**2*(5*g - 2)**2/3
Let w = -2/118177 - -472718/590885. Solve -8/5*d - 4/5 - w*d**2 = 0.
-1
Let n(l) = 12. Let w(f) = f + 1. Let m(d) = -n(d) - 3*w(d). Let a be m(-10). Find x, given that 5*x**2 - 9 - 5*x**4 - 5*x**5 + 18 + a*x**3 - 10*x - 9 = 0.
-2, -1, 0, 1
Suppose -3*x - 4*r = -0*x - 14, -1336*r = 4*x - 1340*r. Factor 57/8*j - 9/8*j**3 - 3/4*j**x - 9/4.
-3*(j - 2)*(j + 3)*(3*j - 1)/8
Let f(x) be the first derivative of -1/18*x**4 + 233 - 7/9*x**2 + 20/27*x**3 - 4*x. Factor f(r).
-2*(r - 9)*(r - 2)*(r + 1)/9
Let i(l) be the third derivative of -l**5/12 + 4535*l**4/24 - 755*l**3 + 7*l**2 + 6*l - 10. Factor i(b).
-5*(b - 906)*(b - 1)
Let m(j) = -7*j**2 + 47*j + 15. Let t be m(7). Let g be t/(-6)*(-15)/10. Factor -1/2*r - g*r**3 + 0 + 3/4*r**2.
-r*(r - 2)*(r - 1)/4
Suppose -2709 = -48*g - 15*g. Suppose 4*t + 10 = -3*a, -45*a - 5*t = -g*a + 16. Factor -4/3 + 1/3*y**4 + y**a + 4/3*y - 4/3*y**3.
(y - 2)**2*(y - 1)*(y + 1)/3
Let g = -186885 - -186887. Factor 4/3*v**5 + 1288/3*v**g + 28*v**4 - 196*v - 1372/3 + 584/3*v**3.
4*(v - 1)*(v + 1)*(v + 7)**3/3
Let r = -95 - -101. Let o be r/4 - (-75)/30. Determine g, given that -5/3*g**o + 0 - 5*g**3 + 5/3*g**2 + 5/3*g**5 + 10/3*g = 0.
-1, 0, 1, 2
Let 50/9 + 10*h - 14/3*h**2 - 98/9*h**3 = 0. What is h?
-5/7, 1
Suppose -121 = -5*g + 2*r, -8*g - 4*r - 35 = -9*g. Factor 22*p**3 - g*p**3 + 94*p**2 + 760*p - 4 + 4 - 2969*p.
-p*(p - 47)**2
Find f, given that 7/3*f**3 - 33/2*f**2 + 0 + 7/6*f = 0.
0, 1/14, 7
Let z(f) be the first derivative of 85 + 9*f**5 - 30*f + 95/4*f**4 - 5*f**3 - 5/3*f**6 - 85/2*f**2. Solve z(u) = 0.
-1, -1/2, 1, 6
Let y = -1833254/9 - -203696. Factor 8/9 + y*m**2 - 16/9*m - 2/9*m**3.
-2*(m - 2)**2*(m - 1)/9
Factor -26*o + 0 + 97/3*o**2 - 7/3*o**3.
-o*(o - 13)*(7*o - 6)/3
Let x(m) = -7*m - 97. Let d be x(-15). Let c(o) = -10*o**3 - 32*o**2 + 16*o + 64. Let k(t) = t**3 + 2*t**2 - t. Let l(y) = d*k(y) + c(y). Solve l(i) = 0 for i.
-8, -2, 2
Let x(j) be the first derivative of 2*j**5/35 + 17*j**4/14 - 68*j**3/7 + 172*j**2/7 - 176*j/7 - 1257. What is d in x(d) = 0?
-22, 1, 2
Let o = -6/124837 + 31958314/873859. Factor -7*u**2 + 32*u - o.
-(7*u - 16)**2/7
Let p be (-1)/(-1 + -3 - 195/(-50)). Suppose -920 = -0*j - p*j. Factor -6*c + 2*c - 2*c**2 - 86 + j.
-2*(c - 1)*(c + 3)
Let k = 101 - 11. Factor -27*n - k - 15*n - 51*n - 3*n**2.
-3*(n + 1)*(n + 30)
Let l be (12 - 15) + (-13)/((-13)/6). Let -6*d**2 + 18*d - 9/2*d**5 + 0 - 63/2*d**l + 24*d**4 = 0. What is d?
-2/3, 0, 1, 2, 3
Let g be (7 + -4 - 5)*-12. Suppose -8*c - g = -20*c. What is x in 15*x**c + 7*x**3 + 6*x + 10*x**3 + 3*x**4 + 0*x - 5*x**3 = 0?
-2, -1, 0
Let p = 10371 + -10369. Let x(o) be the second derivative of 4*o + o**3 - p*o**2 - 1/10*o**5 + 0*o**4 + 0. Let x(b) = 0. What is b?
-2, 1
Suppose 0 = -10*w + 7*w + 6. Let p be (((-1539)/2)/3)/(w/(-4)). Factor -507*l**3 - l**2 - 2*l**5 + 5*l**2 + p*l**3.
-2*l**2*(l - 2)*(l + 1)**2
Find v such that 66/5*v**2 + 12*v - 24/5*v**4 - 72/5 - 3/5*v**5 - 27/5*v**3 = 0.
-6, -2, 1
Let m(j) = j**4 - 42*j**3 + 114*j**2 + 392*j - 1107. Let t(k) = 5*k**4 - 209*k**3 + 570*k**2 + 1958*k - 5535. Let u(f) = -33*m(f) + 6*t(f). Solve u(w) = 0.
-3, 3, 41
Let q = -17 + 21. Suppose -q*j + 7*j - 45 = 0. Solve 10*n**4 - 15*n**3 + 4*n**2 - n**2 - 13*n**2 + j*n**5 = 0 for n.
-1, -2/3, 0, 1
Factor -614/7 - 88*k - 2/7*k**2.
-2*(k + 1)*(k + 307)/7
Let t be (27/180)/((-6)/(-90)). Let c = t + 9/4. Solve -c*z**4 - 3/2*z**2 - 9/2*z**3 - 1/6*z + 0 = 0.
-1/3, 0
Let n(p) = -p**4 - p**3. Let l(y) be the first derivative of 21*y**5/5 - 5*y**4/2 - y**3/3 + 190. Let x(v) = 3*l(v) - 21*n(v). Factor x(k).
3*k**2*(4*k - 1)*(7*k + 1)
Suppose 123*k**2 + 5*k**3 + 104*k**2 - 124*k**2 + 22*k**2 = 0. What is k?
-25, 0
Suppose 4*v + v = -5*l + 5, l = -4*v + 10. Let d(t) = 29*t + 58. Let u be d(l). Factor u + 12/5*s**5 + 0*s**2 + 8/5*s**3 + 0*s + 4*s**4.
4*s**3*(s + 1)*(3*s + 2)/5
Let w(u) be the first derivative of u**4/14 + 20*u**3/7 - 4*u**2/7 - 240*u/7 - 3333. Factor w(i).
2*(i - 2)*(i + 2)*(i + 30)/7
Let r(s) be the third derivative of 144*s**2 + 0*s + 1/105*s**5 - 1/84*s**4 - 2/21*s**3 + 0 + 1/420*s**6. Solve r(z) = 0 for z.
-2, -1, 1
Let u(h) = h**2 - 18*h + 2. Let w be u(18). Suppose c - 63 = -w*c. Factor 5 + 10*i**2 - 9*i**2 - 23 - 4*i**2 - c*i.
-3*(i + 1)*(i + 6)
Suppose 20 = 4*g - 4*a, 4*g = -0*a + 3*a + 17. Let n be (153/(-8))/(-3) + 6/(-16). Factor -4*u - 9*u**g + 7*u**3 + 20 - 9*u**3 + n*u**3 - 11*u**2.
4*(u - 5)*(u - 1)*(u + 1)
Let o(i) be the first derivative of i**3/3 + 33*i**2/2 - 3279. Find d such that o(d) = 0.
-33, 0
Let w(g) be the second derivative of 0*g**4 + 0*g**2 + 1/600*g**5 - 5/6*g**3 + 10*g + 0 - 1/1800*g**6. Let j(s) be the second derivative of w(s). Factor j(t).
-t*(t - 1)/5
Let j(l) be the second derivative of -l**5/12 - 175*l**4/18 - 3230*l**3/9 - 5780*l**2/3 + 11*l + 105. Factor j(o).
-5*(o + 2)*(o + 34)**2/3
Let t(m) be the second derivative of m**4/66 - 32*m**3/11 - 236*m. Factor t(i).
2*i*(i - 96)/11
Let y(q) be the third derivative of -64/3*q**3 - 2/35*q**7 + 1/3*q**6 + 134*q**2 - 1/84*q**8 + 4/3*q**5 - 4*q**4 + 0 + 0*q. Suppose y(c) = 0. What is c?
-4, -2, -1, 2
Suppose 12*q = 24*q - 25*q - 11*q. Let o(u) be the first derivative of 0*u**3 + 0*u**2 + q*u - 3/25*u**5 + 6 - 3/4*u**4. Factor o(w).
-3*w**3*(w + 5)/5
Let c(i) be the first derivative of 0*i**2 + 1/20*i**4 + 0*i - 61 - 1/30*i**6 + 2/25*i**5 - 2/15*i**3. Suppose c(a) = 0. Calculate a.
-1, 0, 1, 2
Let x(k) be the second derivative of -3*k**5/20 + 5*k**4/4 + 8*k**3/3 + k + 56. Let p(a) = a**3 + a**2 + a. Let l(f) = 2*p(f) + x(f). Solve l(v) = 0.
-1, 0, 18
Let a = -22 - 12. Let u be 3/5 + a/(-10). Factor 2*i + 2 + 3*i**2 - 264*i**u + 263*i**4 - 2.
-i*(i - 2)*(i + 1)**2
Let n(l) = 4*l**2 + 1279*l + 2584. Let o(b) = -5*b**2 - 2560*b - 5170. Let u(w) = 5*n(w) + 3*o(w). Find v, given that u(v) = 0.
-2, 259
Let c(z) be the second derivative of z**5/30 - 17*z**4/9 + 320*z**3/9 - 512*z**2/3 + 1248*z - 1. Factor c(i).
2*(i - 16)**2*(i - 2)/3
Suppose 0 = -41*b + 49292 + 16800. Let r = 1614 - b. Suppose 32/7*k + 0 - 4/7*k**r = 0. Calculate k.
0, 8
Let b(m) = -m**3 - m**2 - 5*m + 1. Let w(d) = 20*d**5 - 1005*d**4 + 195*d**3 + 1735*d**2 - 335*d - 730. Let x(p) = 20*b(p) - w(p). Find f such that x(f) = 0.
-1, -3/4, 1, 50
Let c = 367055 + -367052. What is t in 0 - 27/8*t + c*t**2 + 3/8*t**3 = 0?
-9, 0, 1
Let t = -84534/4525 - -47661031/2411825. Let q = t - 3/1025. Determine y so that 8/13*y**2 - 54/13*y - q = 0.
-1/4, 7
Factor -9*z + 1778*z**2 - 3564*z**2 + 60*z + 1773*z**2 - 36 + z**4 - 3*z**3.
(z - 3)**2*(z - 1)*(z + 4)
Let f(j) = 10*j**4 - 36*j**3 + 72*j**2 + 186*j + 14. Let m(g) = -2*g**4 + 7*g**3 - 16*g**2 - 37*g - 3. Let n(d) = -3*f(d) - 14*m(d). Find l such that n(l) = 0.
-2, 0, 2, 5
Suppose -361*p**3 - 40*p**2 - 494*p**3 + 857*p**3 = 0. Calculate p.
0, 20
Suppose 65*y = 70*y - 20. Factor -4*k**2 - 33*k**y + 13*k**4 + 6*k**3 + 18*k**4.
-2*k**2*(k - 2)*(k - 1)
Let t(n) = -20*n**4 + 138*n**3 + 1740*n**2 - 3660*n + 1858. Let j(s) = -7*s**4 + 47*s**3 + 581*s**2 - 1220*s + 619. Let q(o) = 14*j(o) - 5*t(o). Factor q(h).
2*(h - 26)*(h - 1)**2*(h + 12)
Let m(b) = -b**2 + 45*b - 75. Let r be m(43). Let u(t) be the first derivative of -3/5*t**5 - r + 