et x(b) be the second derivative of -6*b**2 - 1/4*b**4 + 13*b + 5/2*b**3 + 0. Factor x(y).
-3*(y - 4)*(y - 1)
Let m(x) = 6*x**3 - 3*x**2 + 2*x - 1. Let c be m(1). Suppose -5*z - 2*z**4 + 2*z + 123*z**2 - 5*z**3 + z**c - 130*z**2 = 0. What is z?
-3, -1, 0
Let m(v) be the first derivative of 9 + 0*v**3 - 1/6*v**2 + 0*v + 1/12*v**4. Find j, given that m(j) = 0.
-1, 0, 1
Let f = 33 - 30. Factor -3*v**3 - 9*v**2 - 3*v + 0*v + f*v**2.
-3*v*(v + 1)**2
Let c(q) be the first derivative of -6/5*q - 7/5*q**2 - 1/10*q**4 - 2/3*q**3 - 20. Suppose c(a) = 0. Calculate a.
-3, -1
Let k(p) be the first derivative of 0*p + 0*p**2 + 1/6*p**6 + 21 + 0*p**3 - 1/2*p**4 + 1/5*p**5. Find q, given that k(q) = 0.
-2, 0, 1
Let k be 48/(-27) - (3 - 100/36). Let u be -2*(-1 - 0/k). Find t, given that -2/7*t**u - 2/7 + 4/7*t = 0.
1
Let g be (-5)/(-15)*(-4)/(-2). Let h = 647/237 + -5/79. Suppose 0*q + g*q**2 - h = 0. What is q?
-2, 2
Let k be 11*-3 - 12/(-4). Let j = k - -33. Solve -10*h**5 - 16*h**3 + 6*h**3 - 20*h**2 - 11*h**4 + 36*h**4 + 17*h - 5 + j*h = 0 for h.
-1, 1/2, 1
Factor 0 - 14/3*r + 2/3*r**2.
2*r*(r - 7)/3
Let q(l) be the first derivative of 0*l**4 + 0*l**5 + 2*l + 4 - 1/60*l**6 + 1/84*l**7 + 0*l**3 + 0*l**2. Let v(r) be the first derivative of q(r). Factor v(o).
o**4*(o - 1)/2
Let g(q) = 8*q**3 - 93*q**2 - 51*q - 2. Let c(r) = r**3 + 3*r**2 - 1. Let p(t) = 2*c(t) - g(t). Factor p(z).
-3*z*(z - 17)*(2*z + 1)
Let v be (-57 - -58)*(-1)/6*-3. Suppose 3/2*z**2 - v*z**3 - z + 0 = 0. What is z?
0, 1, 2
Let t(z) = 7*z**3 + z**2 + 4*z - 3. Let i(h) = 22*h**3 + 6*h**2 + 12*h - 10. Let d(a) = 3*i(a) - 10*t(a). Factor d(k).
-4*k*(k - 1)**2
Let g be (-216)/180*(-10)/4. Factor -4/5*k + 4/5*k**g - 4/5*k**2 + 4/5.
4*(k - 1)**2*(k + 1)/5
Let n(c) be the third derivative of c**6/80 - 3*c**5/40 - c**4/4 + 3*c**3 + 6*c**2 - c. Factor n(w).
3*(w - 3)*(w - 2)*(w + 2)/2
Suppose -8*q = -4*q - 8, 2*q = r. Let d(m) be the second derivative of 0 - 1/36*m**r + 0*m**3 + 0*m**2 - 5*m - 1/60*m**5. Factor d(b).
-b**2*(b + 1)/3
Suppose 10*v - 8*v + 5*f - 31 = 0, f = -v + 8. Let i(t) be the second derivative of 27*t**2 + 9*t**v + 4*t + 0 + 3/2*t**4 + 1/10*t**5. Factor i(w).
2*(w + 3)**3
Let d(h) = 60*h - 1918. Let r be d(32). Suppose 0 + 2/9*k**4 + 2/9*k - 2/9*k**3 - 2/9*k**r = 0. Calculate k.
-1, 0, 1
Let p(v) be the third derivative of -v**6/30 + 2*v**5/3 - 11*v**4/2 + 24*v**3 - 23*v**2 - 17. Factor p(y).
-4*(y - 4)*(y - 3)**2
Determine m so that 36/7*m**5 - 3*m**3 + 0 + 51/7*m**2 - 15/7*m - 51/7*m**4 = 0.
-1, 0, 5/12, 1
Factor 8*y**3 + 273*y - 163*y + 400*y + 216*y**2 - 100 + 14*y**3.
2*(y + 5)**2*(11*y - 2)
Suppose -101 - 13*n**2 + 2*n**2 - 295 - 144*n + 6*n**2 + n**2 = 0. Calculate n.
-33, -3
Factor -2*q**2 + 7*q**2 + 10*q**3 + 5623*q**4 - 5628*q**4 - 10*q.
-5*q*(q - 2)*(q - 1)*(q + 1)
Let z(f) be the third derivative of -5*f**2 - 1/180*f**4 + 0*f + 1/900*f**6 - 2/45*f**3 + 0 + 1/225*f**5. Factor z(b).
2*(b - 1)*(b + 1)*(b + 2)/15
Let f be (-1 + -2)/(6/(-8)). Let x(k) be the first derivative of 0*k - 2/9*k**3 + 0*k**2 - 2/5*k**5 - 1/9*k**6 + 5 - 1/2*k**f. Determine b so that x(b) = 0.
-1, 0
Let o(m) = -72*m**3 + 73*m**3 + 1 + 3*m**2 - 5*m**2 + 3*m**2. Let c(v) = 7*v**3 + 4*v**2 - 9*v - 2. Let l(w) = -c(w) + 4*o(w). Factor l(y).
-3*(y - 2)*(y + 1)**2
Determine x so that -1/3*x + 1/3*x**2 + 0 + 2/3*x**3 = 0.
-1, 0, 1/2
Let h(x) be the first derivative of 3*x**3 + 21*x**2/2 - 5*x + 22. Let d(w) = 4*w**2 + 10*w - 2. Let r(a) = 5*d(a) - 2*h(a). Suppose r(y) = 0. Calculate y.
-4, 0
Let m(r) = 2*r + 1. Let z be m(1). Let v(p) be the second derivative of 1/3*p**2 - 4/9*p**z + 5*p + 0 + 2/9*p**4. Let v(l) = 0. What is l?
1/2
Suppose -3386*a**4 + 3*a**5 + a**3 - 7*a**3 + 3389*a**4 = 0. Calculate a.
-2, 0, 1
Factor 20/3 - 4/3*l - 5/3*l**2 + 1/3*l**3.
(l - 5)*(l - 2)*(l + 2)/3
Factor 64/5 + 2/5*n**4 - 12/5*n**2 + 64/5*n - 2*n**3.
2*(n - 4)**2*(n + 1)*(n + 2)/5
Let i(d) = d + 5. Let v be i(0). Suppose 4*a = -5*w + v + 1, 7 = 5*w + 3*a. Determine o so that -9/5*o**w - 1/5 + o + 7/5*o**3 - 2/5*o**4 = 0.
1/2, 1
Let p = -3/119 - -253/595. Factor 0*s + p*s**2 + 0.
2*s**2/5
Suppose -n + 3*a - a + 38 = 0, -4*a = 4. Suppose 5*u + 13*u = n. Determine f so that 0*f + 0*f**u + 0 + 0*f**4 + 1/3*f**3 - 1/3*f**5 = 0.
-1, 0, 1
Let s(c) be the first derivative of -c**4/4 + c**3/3 + 2*c**2 - 4*c - 271. Find t, given that s(t) = 0.
-2, 1, 2
Let x(j) be the second derivative of 5*j + 0*j**5 - 1/210*j**6 + 0*j**2 + 0*j**3 + 0 + 1/84*j**4. Factor x(n).
-n**2*(n - 1)*(n + 1)/7
Let j be (-2 - -5) + 0 + (-8)/(-4). Suppose j*k = 7 + 8. What is w in 3/4*w**2 + 0 + 1/4*w**4 + 3/4*w**k + 1/4*w = 0?
-1, 0
Let b(w) be the third derivative of w**7/5460 - w**6/780 + w**4/39 - 3*w**3/2 + 8*w**2. Let f(h) be the first derivative of b(h). Let f(m) = 0. Calculate m.
-1, 2
Let n(k) be the second derivative of -k**10/15120 - k**9/7560 + k**8/3360 + k**7/1260 - k**4/3 - 18*k. Let v(d) be the third derivative of n(d). Factor v(l).
-2*l**2*(l - 1)*(l + 1)**2
Let a be 3 - (3 - -7 - 0). Let g be (3/7)/((-1)/a). Factor -g*r - r + 5*r - r**2.
-r*(r - 1)
Find f, given that -3/2*f**2 - 864 + 72*f = 0.
24
Let i(m) = 4*m - 18. Let f be 2 + (7 - 5) + (1 - 0). Let n be i(f). Determine d, given that 3/7*d**n + 6/7 + 9/7*d = 0.
-2, -1
Suppose 5*d - 68 = -23. Let s(h) = 2*h. Let y be s(2). Factor -3*q**4 + d*q**2 + q**2 - 3 - y*q**2.
-3*(q - 1)**2*(q + 1)**2
Let j(g) be the second derivative of 24*g + g**3 + 0*g**2 + 1/10*g**6 - 1/2*g**5 + 1/12*g**4 + 0. Factor j(k).
k*(k - 3)*(k - 1)*(3*k + 2)
Suppose 2*w = 0, -r - 4*r + 2*w + 10 = 0. Factor -60*d**3 - 21*d**3 - 5*d**4 - 360*d**r + 2160 + d**3.
-5*(d - 2)*(d + 6)**3
Let j(p) be the first derivative of p**4/4 + 2*p**3 - 15*p**2/2 + 8*p + 20. Let y(r) be the first derivative of j(r). Factor y(f).
3*(f - 1)*(f + 5)
Factor 29/5 + 6*f + 1/5*f**2.
(f + 1)*(f + 29)/5
Let t = -36383/7 - -5198. Suppose -48/7*k - 36/7 - t*k**3 - 3*k**2 = 0. Calculate k.
-3, -2
Let s = 1827 - 1825. Suppose 5/4*j**2 - s*j - 1 = 0. Calculate j.
-2/5, 2
Let p(t) be the third derivative of t**8/30240 - t**7/3780 + 7*t**4/6 - 2*t**2. Let a(s) be the second derivative of p(s). Factor a(f).
2*f**2*(f - 3)/9
Let d = 65 + -65. Let f(x) be the first derivative of -3/16*x**4 - 3/4*x**3 + 3*x + d*x**2 + 13. Solve f(v) = 0 for v.
-2, 1
Find q, given that 165*q**3 + 91*q**3 + q**4 + 22272*q + 30276 + 4792*q**2 + 6*q**4 - 3*q**4 = 0.
-29, -3
Let a be ((-18)/(-15))/((-93)/(-310)). Factor a*u**3 + 2/3*u**5 + 0 - 8/3*u**4 - 8/3*u**2 + 2/3*u.
2*u*(u - 1)**4/3
Find c, given that -27/4 - 27/4*c + 3/4*c**3 + 3/4*c**2 = 0.
-3, -1, 3
Suppose 9*x + 161 = 53. Let h(m) = -4*m - 46. Let u be h(x). Solve 0*p + 3/2*p**3 + 1/2*p**4 + p**u + 0 = 0.
-2, -1, 0
Factor -32/9*b + 2/9*b**2 + 128/9.
2*(b - 8)**2/9
Let p = 825/118 - -30/59. Suppose 0 + 3/2*l**2 + 0*l + p*l**3 = 0. What is l?
-1/5, 0
Let k(x) = x**5 + x**4 + x**3 + x**2 + 1. Let i(b) = -5*b**5 + 5*b**4 + 29*b**3 + 31*b**2 + 12*b - 4. Let h(m) = i(m) + 4*k(m). Factor h(l).
-l*(l - 12)*(l + 1)**3
Let o = -31 + 37. Solve -4*r + 15 + r**2 + o*r - 13 + r = 0.
-2, -1
Let q be 180/120*8/90. Factor -q*h**2 - 2/5 - 8/15*h.
-2*(h + 1)*(h + 3)/15
Let m(d) be the second derivative of d**6/135 + 19*d**5/90 + 25*d**4/27 + 32*d**3/27 + d - 35. Find z, given that m(z) = 0.
-16, -2, -1, 0
Let x(o) = -20*o**2 + 13*o + 9. Let r(i) = 102*i**2 - 66*i - 47. Let z(n) = -4*r(n) - 22*x(n). Solve z(c) = 0.
-5/16, 1
Let o(a) = -82*a - 80. Let m be o(-1). Let l = 9/34 - -4/17. Solve -f**3 + 3/2*f**m + 2*f - 2 - l*f**4 = 0.
-2, 1
Find b such that -31 + 38*b + 51 + 25*b**2 + 7*b = 0.
-1, -4/5
Let w(m) be the third derivative of -66049*m**5/60 - 257*m**4/12 - m**3/6 + 621*m**2. Factor w(u).
-(257*u + 1)**2
Let 4 - 116/3*p - 40/3*p**2 = 0. Calculate p.
-3, 1/10
Let w(b) = -3*b**3 + 48*b**2 + 160*b - 190. Let n(i) = 8*i**3 - 142*i**2 - 480*i + 572. Let k(s) = -5*n(s) - 14*w(s). Determine t so that k(t) = 0.
-10, 1
Let q = -1653 + 19837/12. Let o(v) be the third derivative of 0*v - 1/60*v**6 + q*v**4 + 0*v**5 + 0*v**3 + 0 + 8*v**2. Factor o(g).
-2*g*(g - 1)*(g + 1)
Let a be 3/((-66)/106) + 6 + -1. Let i(w) be the first derivative of 0*w**2 - 4/11*w**3 - 6/55*w**5 - 4/11*w**4 + a*w - 7. Factor i(m).
-2*(m + 1)**3*(3*m - 1)/11
Let j(w