, 1
Let l(m) be the first derivative of -151 + 0*m + 27/2*m**2 - 1/4*m**3. Factor l(k).
-3*k*(k - 36)/4
Factor -1/4*h**2 + 2421/4 + 201*h.
-(h - 807)*(h + 3)/4
Let h be 4*(-3)/18*(2860/55)/(-52). Determine z, given that 4/9*z**2 + 23/9*z - h = 0.
-6, 1/4
Let p(n) = 4*n - 3. Suppose 11*f + 4*f - 30 = 0. Let r be p(f). Find u, given that 11 - 2 - 29*u**2 + 5*u**3 + 9*u**2 + 21 + r*u = 0.
-1, 2, 3
Let p(w) = 39*w**3 - 357*w**2 + 390*w - 108. Let y(h) = 11*h**3 - 102*h**2 + 111*h - 30. Let q(a) = -5*p(a) + 18*y(a). Find m such that q(m) = 0.
0, 1, 16
Let q(l) = l + 5. Let n be q(-3). Let -5*k + 3*k - 3*k**2 - 3*k + 2*k**n = 0. What is k?
-5, 0
Let c be 3/2*8/6. Let l be 1/10 + 49/10 + -3. Factor 2*x**l + 12*x - 1 - 5*x**c - 11.
-3*(x - 2)**2
Let f(i) = 11*i**2 + 133*i - 265. Let q be f(2). Let l be 0 - (10 - 594/q). What is y in l + 29/5*y**2 + 48/5*y - 17/10*y**3 + 1/5*y**5 - 9/10*y**4 = 0?
-2, -1, -1/2, 4
Let p(y) be the second derivative of -4*y**4 - 47*y**3/3 + 2*y**2 + 98*y - 12. Determine h, given that p(h) = 0.
-2, 1/24
Let r(s) be the third derivative of -113*s**6/240 + 223*s**5/120 + s**4/8 + 3*s**2 - 76*s + 3. What is c in r(c) = 0?
-3/113, 0, 2
Let b(t) be the first derivative of t**6/360 - t**5/5 + 6*t**4 + 9*t**3 + t**2/2 + 64. Let n(c) be the third derivative of b(c). Solve n(y) = 0 for y.
12
Let l(w) be the first derivative of 3*w**7/560 - w**6/15 - 13*w**5/80 + 3*w**4/8 - w**3/3 + 4*w**2 + 58. Let a(m) be the third derivative of l(m). Factor a(h).
3*(h - 6)*(h + 1)*(3*h - 1)/2
Let n(b) be the third derivative of b**5/30 + 43*b**4/12 - 44*b**3/3 - 1833*b**2. Let n(h) = 0. Calculate h.
-44, 1
Let n(q) = -q**2 - 11*q + 44. Let w be n(-13). Let f(p) = p**2 - 15*p - 51. Let r be f(w). Factor 2/7*g**r + 10/7*g**2 + 16/7*g + 8/7.
2*(g + 1)*(g + 2)**2/7
Let g(c) = 2*c**5 + 69*c**4 - 233*c**3 + 251*c**2 - 75*c - 7. Let z(o) = -o**4 + o**3 + o**2 + o - 1. Let p(b) = -g(b) + 7*z(b). Factor p(j).
-2*j*(j - 1)**3*(j + 41)
Let v(b) = -b**3 - b**2. Let j(g) be the third derivative of 2*g**7/105 - 3*g**6/20 - 7*g**5/30 + 3*g**4 - 38*g**2. Let q(x) = j(x) - 2*v(x). Factor q(i).
4*i*(i - 3)**2*(i + 2)
Let m(y) = y**5 - y**4 - y**3 + 2*y**2 + 1. Let q(h) be the first derivative of 2*h**6/3 - 7*h**5/5 + 2*h**3 + 3*h - 120. Let t(c) = 3*m(c) - q(c). Factor t(u).
-u**3*(u - 3)*(u - 1)
Let i be (-4)/1 - (-49 - 7683/(-195)). Let i*s**2 + 392/5*s + 5488/15 + 2/15*s**3 = 0. Calculate s.
-14
Suppose -40 = j - 81 + 38. Let o(t) be the second derivative of 0 + 6/11*t**2 - 5/33*t**j - 1/66*t**4 - 30*t. Find k, given that o(k) = 0.
-6, 1
Let a(s) = 267*s**3 + 589*s**2 + 312*s + 16. Let k(i) = -67*i**3 - 147*i**2 - 78*i - 4. Let x(m) = -6*a(m) - 26*k(m). Suppose x(z) = 0. What is z?
-1, -2/35
Let c(a) be the first derivative of -a**6/90 - 2*a**5/5 + 44*a**3/3 + 55. Let h(i) be the third derivative of c(i). Factor h(r).
-4*r*(r + 12)
Let i(q) be the first derivative of -1/20*q**5 + 3/8*q**4 - 148 - 27/2*q**2 + 9/4*q**3 - 81*q. What is t in i(t) = 0?
-3, 6
Determine v, given that 3/2*v**3 + 609/2*v - 1617/2 - 75/2*v**2 = 0.
7, 11
Solve 2790*f**2 - 5703*f**2 + 2742*f**2 + 24 + 78 - 2901*f = 0 for f.
-17, 2/57
Let w(y) be the first derivative of y**5/120 + 11*y**4/48 + 2*y**3 + 54*y**2 + 2*y + 3. Let s(a) be the second derivative of w(a). Find p, given that s(p) = 0.
-8, -3
Let q(u) be the third derivative of 1/36*u**4 + 0 - 1/360*u**5 - 76*u**2 - 1/12*u**3 + 0*u. Factor q(a).
-(a - 3)*(a - 1)/6
Factor -2/5*a**3 + 2/5*a - 54/5 + 54/5*a**2.
-2*(a - 27)*(a - 1)*(a + 1)/5
Let t(f) be the second derivative of f**7/14 - 11*f**6/10 + 99*f**5/20 - 37*f**4/4 + 7*f**3 - 1700*f - 3. Determine g, given that t(g) = 0.
0, 1, 2, 7
Find r such that -3*r**2 - 44/5 - 48/5*r - 1/5*r**3 = 0.
-11, -2
Let j(t) = 8*t**4 + 15*t**3 + 59*t**2 + 123*t + 65. Let q(s) = 0 - s + s - s**4 + s**2 - s + 1. Let y(p) = -5*j(p) - 35*q(p). Find u such that y(u) = 0.
-9, -2
Let h(q) be the first derivative of -2*q**6/3 + 38*q**5 + 49*q**4/2 - 32*q**3 - 2124. Let h(l) = 0. Calculate l.
-1, 0, 1/2, 48
Let m(v) = -147*v**2 - 69*v - 42. Let x(p) = -36*p**2 - 17*p - 10. Let l(k) = 5*m(k) - 21*x(k). Factor l(o).
3*o*(7*o + 4)
Let a(v) be the third derivative of -82*v**2 + 7/12*v**4 + 49/2*v**3 + 1/180*v**5 + 0*v + 0. Factor a(o).
(o + 21)**2/3
Let g(c) be the third derivative of c**5/12 - 205*c**4/24 - 235*c**3 - c**2 + 5*c + 52. Factor g(h).
5*(h - 47)*(h + 6)
Let u(z) be the first derivative of 1/7*z**4 + 24/7*z**2 - 20/7*z**3 + 277 + 16*z. Factor u(s).
4*(s - 14)*(s - 2)*(s + 1)/7
Suppose 29 + 190 = 3*p. Suppose 0 = 2*b - p + 63. Factor 9*d**2 + 4*d**3 + 64*d - b*d**2 + 24*d**2 + 48.
4*(d + 2)**2*(d + 3)
Factor -2/5*q**4 + 8/5*q**2 - 16/5*q + 4/5*q**3 + 0.
-2*q*(q - 2)**2*(q + 2)/5
Suppose -292*o + 3710 = -282*o. Let i = o + -369. Determine w, given that -i*w**3 + 16/3*w**2 - 8/3*w + 0 = 0.
0, 2/3, 2
Let h be 7896/21420 - (-20)/(-85). Factor -8/15*c**4 + 2/3*c**3 - 4/15*c**2 + 0*c + 0 + h*c**5.
2*c**2*(c - 2)*(c - 1)**2/15
Let c = -898 + 893. Let b(h) = -2*h**3 - h**2 - h. Let r(i) = i**3 - 21*i**2 + 48*i - 24. Let v(y) = c*r(y) - 5*b(y). Factor v(l).
5*(l - 1)**2*(l + 24)
Let h = -30049/10 + 3005. Let s(u) be the second derivative of 0*u**2 + 1/3*u**4 + 0 - h*u**5 + 0*u**3 - 6*u + 1/120*u**6. Suppose s(r) = 0. Calculate r.
0, 4
Let u be (-6 + 112/21)*3 - -6. Let k(x) be the second derivative of 1/30*x**u + 0 + 8/15*x**3 + 16/5*x**2 - 16*x. Factor k(h).
2*(h + 4)**2/5
Solve -111*j**2 - 5*j**2 + 7975845 - 6*j**2 + 127*j**2 - 12630*j = 0.
1263
Let x(o) be the first derivative of -15*o**2 + 73 + 5/3*o**3 - 35*o. Factor x(w).
5*(w - 7)*(w + 1)
Suppose 120 - 1330 = -5*j. Factor 152*t + 648 + 270*t + j*t**2 + 370*t.
2*(11*t + 18)**2
Let l(v) = v + 16. Let q be l(-6). Suppose -p + 63 = -45. Suppose 4*y**4 - 16*y**3 - 14*y**3 - 16*y**3 - p*y + 108*y**2 + q*y**3 = 0. Calculate y.
0, 3
Let v(c) be the first derivative of -90*c**5/11 + 9165*c**4/22 + 4912*c**3/33 + 164*c**2/11 + 1442. What is x in v(x) = 0?
-2/15, 0, 41
Let t(v) = -v**2 + 53*v - 275. Let c be t(47). Suppose -5*a + 12 = -c*j + 11*j, -a + 6 = -j. Factor -32/5*k - 8/5*k**3 - 24/5*k**2 - 1/5*k**a - 16/5.
-(k + 2)**4/5
Solve y**3 + 99007/3*y + 1088/3*y**2 + 65522/3 = 0.
-181, -2/3
Let x(j) = 6*j**2 + 88*j + 392. Let a(m) = 2*m**2 + 29*m + 131. Let w = -43 + 19. Let k be w/216 - 28/(-9). Let t(l) = k*x(l) - 8*a(l). Solve t(c) = 0.
-8
Let m(o) = -2*o**2 + 29*o - 11. Let y be m(14). Let i(n) = -n + 6. Let q be i(y). Solve 2*r**2 + 20*r - 2*r - 97 + 16 - q*r**2 = 0.
9
Suppose 135*v - 959 = 3901. Let p(i) be the third derivative of 0*i + 1/100*i**5 + 3/10*i**3 - 1/10*i**4 - v*i**2 + 0. Factor p(c).
3*(c - 3)*(c - 1)/5
Suppose 8*w - 13*w = -2*c + 3, 0 = -4*c - 5*w + 21. Let r be (-180)/135 - ((-6)/(-3) - c). Factor 4/3 - p**2 + r*p - 5/6*p**3 - 1/6*p**4.
-(p - 1)*(p + 2)**3/6
Factor 3*i**3 - 62*i + 159*i + 119*i - 66*i**2 - 216 + 12*i.
3*(i - 18)*(i - 2)**2
Let r(y) = -18*y**3 - 656*y**2 - 2523*y - 2486. Let p(g) = -100*g**3 - 3608*g**2 - 13876*g - 13672. Let s(m) = 5*p(m) - 28*r(m). Solve s(u) = 0.
-78, -2
Let d(q) be the third derivative of -5*q**8/96 - 47*q**7/84 + 7*q**6/16 + 47*q**5/24 - 35*q**4/24 + q**2 + 4*q - 208. Determine i so that d(i) = 0.
-7, -1, 0, 2/7, 1
Let v(a) = 19*a + 857. Let b be v(-45). Suppose 0 + 7/3*n - 1/3*n**b = 0. Calculate n.
0, 7
Let y(g) = g**2 + g + 1. Let m be 30/(-195) - (-1)/13*-11. Let s(r) = 2*r**2 - 2*r + 3. Let a(h) = m*s(h) + 3*y(h). What is k in a(k) = 0?
-5, 0
Let c(b) be the first derivative of b**6/432 + b**5/72 - 5*b**4/18 + 113*b**3/3 + 95. Let y(t) be the third derivative of c(t). Factor y(s).
5*(s - 2)*(s + 4)/6
Let d(p) be the first derivative of p**7/3360 - p**6/288 - p**5/80 + 71*p**3/3 + 92. Let m(r) be the third derivative of d(r). Let m(y) = 0. Calculate y.
-1, 0, 6
Let t = 11 - 41. Let k be t/(-20) + 22/4. Factor 15*j**3 - 15*j + k*j**4 - j**4 - 5*j**2 - 3*j**4 + 2*j**4.
5*j*(j - 1)*(j + 1)*(j + 3)
Let d(c) be the second derivative of -c**6/15 + c**5/25 + 17*c**4/10 + 4*c**3/3 - 68*c**2/5 - 9481*c. Find r, given that d(r) = 0.
-2, 1, 17/5
Let n(t) = 3*t**2 - 58*t + 57. Let q(b) = -3*b**2 + 57*b - 57. Let p = 522 + -525. Let m(a) = p*n(a) - 2*q(a). Solve m(u) = 0 for u.
1, 19
Solve -20*r + 35 - 912*r +