*2 - 396 - 1186*r + 134*r**3.
-2*(r - 198)*(r - 1)*(4*r + 1)
Let y(l) = l**3 + 8*l**2 - 13*l - 9. Let q be y(-9). Let t = q + -24. Factor -4*o - 4*o - 5*o**t - 4*o**3 + 6*o - 11*o**2.
-o*(o + 1)*(9*o + 2)
Suppose 15*s + 101*s - 170 = 31*s. Let g(q) be the first derivative of 2*q + 2/15*q**3 - 24 + 6/5*q**s. Factor g(m).
2*(m + 1)*(m + 5)/5
Let s(k) = k**3 - 29*k**2 + 46*k - 502. Let g be s(28). Let -46/19*o**4 + 238/19*o**g + 192/19*o + 14/19*o**5 - 86/19*o**3 - 72/19 = 0. Calculate o.
-2, -1, 2/7, 3
Let r(z) be the first derivative of 6*z**2 + 1/270*z**5 + 1/54*z**4 + 0*z**3 + 0*z - 7. Let v(m) be the second derivative of r(m). Factor v(q).
2*q*(q + 2)/9
Let b(o) = -o**3 + 50*o**2 - 42*o + 48. Let t be b(49). Let p = t - 391. Determine f, given that -3*f**2 + 0 + 3/5*f**3 + p*f = 0.
0, 5
Let o = 31 + -27. Factor -17*a**o + 10*a**3 - 22*a**4 + 14*a**3 + 37*a**4.
-2*a**3*(a - 12)
Let f = 387 - 384. Let j(i) be the third derivative of -16*i**2 - 1/210*i**5 + 0*i**f + 0*i + 0 - 1/21*i**4. Factor j(p).
-2*p*(p + 4)/7
Suppose 5*f + 28 = -52. Let x be f/36*(-27)/6. Solve -28*y**4 - 68/3*y**3 + 12*y**5 + 16/3 + 32*y + 44*y**x = 0.
-1, -1/3, 2
Suppose -3*j - a = -55, 2*a - a - 37 = -2*j. Let s be j/4*(-1088)/(-160). Factor 42/5 - s*z + 21/5*z**2.
3*(z - 7)*(7*z - 2)/5
Let f be (-15)/250*2*(-10)/12. Let a(t) be the second derivative of 0 + f*t**5 + 0*t**3 + 0*t**2 - 1/3*t**4 + 19*t. Factor a(h).
2*h**2*(h - 2)
Let y(v) = -3*v - 8. Let z(k) = 1. Let b(g) = y(g) + 4*z(g). Let q be b(-2). Factor -4*r - r + 2*r**2 + 0*r**q - r.
2*r*(r - 3)
Let c(n) be the first derivative of -n**6/6 - 17*n**5/5 - 95*n**4/4 - 175*n**3/3 - 1414. Suppose c(a) = 0. What is a?
-7, -5, 0
Factor 104*g**2 - 144*g**2 + 25*g**3 - 26*g**3.
-g**2*(g + 40)
Let f(s) be the first derivative of -s**5/10 - 3*s**4/2 + 15*s**3/2 - s**2 - 30*s + 3870. Factor f(l).
-(l - 2)**2*(l + 1)*(l + 15)/2
Factor 922*n**2 - 19*n**3 - n**5 + 738*n**2 - 1651*n**2 + 11*n**4.
-n**2*(n - 9)*(n - 1)**2
Suppose -3*h + 6 = -h. Let d(z) = -2*z**2 - 27*z + 47. Let w be d(-15). Determine l, given that l**2 + 8*l**2 + 2*l - 3*l**4 - 6 + 0*l**w - 5*l + 3*l**h = 0.
-1, 1, 2
Let f(l) be the second derivative of -17/5*l**3 + 1/50*l**5 + l - 41 - 4/5*l**4 - 26/5*l**2. Factor f(c).
2*(c - 26)*(c + 1)**2/5
Let w = 107 - 35. Let c = w + -48. Factor -6*s**2 - 6*s**2 - 12*s**3 + c*s**3 - 8*s**2 + 4*s**4 + 8*s - 4*s**5.
-4*s*(s - 1)**3*(s + 2)
Let p(v) = v**3 + 7*v**2 + 6*v + 12. Let n = -81 - -75. Let q be p(n). Factor q - 81*x + 2*x**2 + 171*x - 80*x.
2*(x + 2)*(x + 3)
Let d(g) = -g**3 + g**2 + 1. Let r(w) be the first derivative of -3*w - 28/3*w**3 + 2*w**4 - 19 + 10*w**2. Let u(f) = -3*d(f) - r(f). Factor u(n).
-5*n*(n - 4)*(n - 1)
Let a(f) be the third derivative of -f**8/112 - 12*f**7/7 - 1229*f**6/10 - 36621*f**5/10 - 187083*f**4/8 - 59319*f**3 + 6340*f**2. Solve a(i) = 0 for i.
-39, -2, -1
Let r be 13405/35 + (-8 - -1). Let z be r/(-705)*15/(-6). Factor -z*y - 8/3 + 4/3*y**2.
4*(y - 2)*(y + 1)/3
Let h(a) = -5*a**2 + 6*a - 8. Let w(m) = -12*m**2 + 13*m - 16. Let q(r) = 7*h(r) - 3*w(r). Let l be q(-5). Factor 2/11*c**3 - 4/11*c - 2/11*c**l + 0.
2*c*(c - 2)*(c + 1)/11
Suppose 63*x = 49*x - 1666. Let a = 245/2 + x. Determine r, given that a*r - 1 - 3/2*r**2 = 0.
1/3, 2
Let n(x) = x**3 - 197*x**2 + 1556*x + 23660. Let v(z) = -10*z**3 + 2160*z**2 - 17115*z - 260260. Let f(b) = 45*n(b) + 4*v(b). Suppose f(g) = 0. Calculate g.
-7, 26
Suppose 0 = -w - 3, 2*a - 11 - 14 = 3*w. Suppose -a*n = -19 - 13. Factor -2*v**4 + 6*v**n - 2*v**4.
2*v**4
Let l(x) = -2*x**2 + 20*x + 24. Let n be l(11). Let m be (n + 16)*1/3 - 3. Factor 5/2*z + 1/2*z**2 - m.
(z - 1)*(z + 6)/2
Let x(c) = 2*c**2 - 1. Let p(s) = 3 - 13*s + 2070*s**2 - 10*s - 7 - 2061*s**2. Let h(q) = -p(q) + 4*x(q). What is k in h(k) = 0?
0, 23
Let z be 20*(1*10 - 23188/2387). Let -z*c - 38/7 - 2/7*c**2 = 0. Calculate c.
-19, -1
Let l(z) be the third derivative of 4*z**2 - 1/30*z**5 - 5/18*z**4 + 0 + 5*z - 8/9*z**3. Suppose l(t) = 0. What is t?
-2, -4/3
Let z(m) be the third derivative of -1 - 4/9*m**3 + 25*m**2 + 0*m - 1/45*m**5 - 1/6*m**4. Factor z(i).
-4*(i + 1)*(i + 2)/3
Let l(j) be the first derivative of -j**4/8 + 43*j**3/6 + j**2/4 - 43*j/2 + 1972. Determine t, given that l(t) = 0.
-1, 1, 43
Let w(l) be the second derivative of -l**6/15 + 41*l**5/8 - 431*l**4/24 - 493*l**3/12 + 147*l**2/4 + 11*l - 121. Solve w(x) = 0 for x.
-1, 1/4, 3, 49
Suppose 16 = 23*j - 19*j + 4*w, -4*w = 0. Let i be (j/(-26) + 18/117)/(-1). Factor -1/3*h**2 - 2/3*h**3 + 2/3*h + 1/3*h**4 + i.
h*(h - 2)*(h - 1)*(h + 1)/3
Let k(j) be the first derivative of 34/3*j**3 + 0*j**2 + 1 - 1/315*j**5 + 0*j - 1/3780*j**6 + 0*j**4. Let r(o) be the third derivative of k(o). Factor r(u).
-2*u*(u + 4)/21
Let v(z) = 3*z**3 - 29*z**2 + 27*z + 1. Let q be v(1). Factor 3 - 3/2*r**3 + 6*r**q - 15/2*r.
-3*(r - 2)*(r - 1)**2/2
Suppose -8/3 - 14/9*a**2 - 2/9*a**3 - 32/9*a = 0. What is a?
-3, -2
Let v be ((-9656)/36210)/((-8)/6). Factor 2/5*h**2 + 1/5*h - v.
(h + 1)*(2*h - 1)/5
Let r(f) be the third derivative of -f**6/600 + 9*f**5/100 - 103*f**4/60 + 52*f**3/5 - 2601*f**2. Factor r(w).
-(w - 13)*(w - 12)*(w - 2)/5
Let h(b) = -b**3 - b**2 + b - 1. Let l be (27 + -29)*(-2)/4. Let i(y) = 17*y**2 - 16*y + 1. Let r(j) = l*i(j) + h(j). Factor r(s).
-s*(s - 15)*(s - 1)
Let f(m) be the third derivative of m**6/10 - 8*m**5/15 - m**4/6 + 20*m**3/3 + 66*m**2 + 7*m. Find t such that f(t) = 0.
-1, 5/3, 2
Solve 58*p + 231/4 + 1/4*p**2 = 0.
-231, -1
Let x be (2 + -7)*1 + 109. Suppose x*r = 111*r. Find v, given that -6/7*v**4 + 0 + 12/7*v**3 - 6/7*v**2 + r*v = 0.
0, 1
Let l(h) = 8*h**2 + 188*h + 124. Let p(d) = -d**2 - 27*d - 17. Let i(u) = -3*l(u) - 20*p(u). Factor i(j).
-4*(j + 2)*(j + 4)
Let s(u) be the third derivative of 0*u + 33*u**2 + 0*u**5 - 1/315*u**7 + 0 - 1/18*u**4 + 1/90*u**6 + 1/9*u**3. Find o such that s(o) = 0.
-1, 1
Factor 2/5*v**4 + 55296/5*v**2 + 1769472/5*v + 576/5*v**3 + 0.
2*v*(v + 96)**3/5
Let h(i) be the first derivative of 0*i**3 + 129/10*i**5 + 0*i**2 + 41/4*i**6 + 0*i - 140 + 3/4*i**4. Factor h(s).
3*s**3*(s + 1)*(41*s + 2)/2
Let j(q) be the first derivative of q**6/51 + 16*q**5/85 + 25*q**4/34 + 76*q**3/51 + 28*q**2/17 + 16*q/17 + 1060. Factor j(a).
2*(a + 1)**2*(a + 2)**3/17
Factor 2/7*n**3 + 23328/7 + 22896/7*n - 430/7*n**2.
2*(n - 108)**2*(n + 1)/7
Let t be (-274)/(-90) + (-8552)/192420. Find x, given that -1/2 - 1/4*x + 1/2*x**2 + 1/4*x**t = 0.
-2, -1, 1
Let f(u) be the second derivative of 3*u**5/20 + 41*u**4/2 + 745*u**3/2 + 2700*u**2 + 10845*u. Let f(q) = 0. Calculate q.
-72, -5
Factor -8*o**5 + 8*o**5 - 30*o**4 + 63*o**3 + 224*o + 2*o**5 - 312*o**2 + 40*o**3 + 49*o**3.
2*o*(o - 7)*(o - 4)*(o - 2)**2
Suppose -3*n - 7 = 5*g, -7*g + 2*n = -4*g + 8. Let j be g/(-3)*(-29)/(-174). What is o in 0*o**2 - 1/9*o**5 + j*o**4 + 0*o + 0 + 2/9*o**3 = 0?
-1, 0, 2
Let y = -323 + 870. Let r = -2185/4 + y. Solve -5/4*a + 1/4*a**3 - 1/4*a**4 + 1/2 + r*a**2 = 0.
-2, 1
Let a(m) = -2*m**3 + 7*m**2 + 2637*m - 5284. Let p be a(2). Let z be 0 + (26/7 - 2). What is b in -3/7*b**4 - z*b**3 + 12/7*b + 12/7 - 9/7*b**p = 0?
-2, -1, 1
Let u be (-5 - -1)*(19 - (-1386)/(-72))*2. Find r, given that -32*r**u + 31/2*r**4 + 0*r + 0 - r**5 - 56*r**3 = 0.
-1/2, 0, 8
Let h be (-9)/(-4)*4/(-6)*(-2085)/6255. Let c(f) be the second derivative of 3/20*f**5 - h*f**3 - 7*f + 0 + 0*f**2 + 1/10*f**6 - 1/4*f**4. Factor c(a).
3*a*(a - 1)*(a + 1)**2
Factor -1928/3*t**2 + 1924/3*t + 4/3.
-4*(t - 1)*(482*t + 1)/3
Let y(s) be the second derivative of -20*s - 1/4*s**3 - 2 - 1/40*s**5 + 1/4*s**2 + 1/8*s**4. Determine u, given that y(u) = 0.
1
Let v(a) be the second derivative of -a**6/10 + 36*a**5/5 + 25*a**4/2 - 24*a**3 - 147*a**2/2 - 2*a - 842. Factor v(x).
-3*(x - 49)*(x - 1)*(x + 1)**2
Let v(g) be the third derivative of g**5/210 - 109*g**4/21 + 145*g**3/7 - 154*g**2 - 10. Factor v(q).
2*(q - 435)*(q - 1)/7
Let j(z) be the first derivative of z**3/27 - 52*z**2/9 - 35*z/3 - 1549. Factor j(p).
(p - 105)*(p + 1)/9
Let k(i) be the third derivative of -i**6/1620 + i**5/20 + 7*i**4/27 + 25*i**3/2 + 3*i**2 + 11. Let t(p) be the first derivative of k(p). Factor t(j).
-2*(j - 28)*(j + 1)/9
Suppose 6*x - 42 = -h, 14*h + 5*x = 11*h + 35. Factor 0*z + 0*z**2 + 0 