Let t(s) be the third derivative of -1/240*s**6 + 0 - 1/120*s**5 + 1/48*s**4 - k*s**2 + 1/12*s**3 + 0*s. Factor t(n).
-(n - 1)*(n + 1)**2/2
Let y = 23413 + -23413. Factor y - 13/2*i**2 - i**4 + 11/2*i**3 + 2*i.
-i*(i - 4)*(i - 1)*(2*i - 1)/2
Factor 115/3*l - 59*l**2 + 3*l**3 - 19/3.
(l - 19)*(3*l - 1)**2/3
Let j(q) = -q**2 - 41*q + 92. Let c be j(-43). Let z(u) be the first derivative of 0*u**3 - 3/4*u**4 + c*u + 9/2*u**2 + 9. Find l such that z(l) = 0.
-1, 2
Suppose -5*f + 3*y = 1 - 24, -4*f - 4*y = -44. Factor 3*j**3 - j**4 - f*j**3 + 6*j**3 + 3*j**2.
-j**2*(j - 3)*(j + 1)
Suppose -21*d = -26*d + 15. Suppose 22*l + 3*l**d - 9*l**2 - 16*l + 0*l**2 = 0. What is l?
0, 1, 2
Let y(r) = 2*r + 68. Let d be y(-34). Factor 0 - 1/4*z**2 + d*z.
-z**2/4
Let f(j) be the first derivative of 1/24*j**6 - 3/20*j**5 + 7/12*j**3 + 0*j**2 - 1/16*j**4 - j + 18. Find d such that f(d) = 0.
-1, 1, 2
Let j be (-4)/(-14) + (1 - 15/(-21)). Find a such that 27*a**j - 54*a**2 - 4*a + 31*a**2 = 0.
0, 1
Suppose 5*j = -5*p + 3*j + 51, 0 = p - 3*j - 17. Suppose 0 = 3*u - p - 1. Factor -n**3 + 5*n**4 - 4*n - 2*n**4 + u*n**3 - 3*n**2 + n.
3*n*(n - 1)*(n + 1)**2
Let f(r) = 15*r + 18. Let a(j) = j**2. Let k(t) = 3*a(t) + f(t). Factor k(g).
3*(g + 2)*(g + 3)
Let w(c) = c**3 + 7*c**2 + 8*c - 7. Let f be w(-5). What is i in -35*i - 14*i**2 - 8 - 2*i**5 + 19*i**2 - 38*i**3 - 55*i**2 - 14*i**4 + f*i = 0?
-2, -1
Let g = 3/5 - -13/5. Let b(l) be the second derivative of l + 1/30*l**4 + g*l**2 + 8/15*l**3 + 0. Suppose b(k) = 0. Calculate k.
-4
Let j(v) be the second derivative of -v**4/96 - v**3/12 - 3*v**2/16 - 114*v. Factor j(o).
-(o + 1)*(o + 3)/8
Factor -96*c**3 - 2690*c**2 - 106879 - 55296*c - 224897 - 766*c**2 - 3*c**4 + 2*c**4.
-(c + 24)**4
Let -2*t**2 + 5/6*t**3 - 2*t + 16/3 = 0. Calculate t.
-8/5, 2
Let l(s) be the third derivative of -s**5/90 - 4*s**4/9 - 5*s**3/3 + 201*s**2 + 2. Factor l(g).
-2*(g + 1)*(g + 15)/3
Solve -5*r**3 + 80*r - 68*r**2 + 51*r**2 - 58*r**2 = 0.
-16, 0, 1
Let h = 421 - 418. Factor 9/7*w + 0 - 48/7*w**4 + 24*w**h - 75/7*w**2.
-3*w*(w - 3)*(4*w - 1)**2/7
Let i(y) = 3*y - 48. Let b be i(17). Let a(l) = -2*l**2 + 10*l - 10. Let k be a(b). Factor -32/13*m**3 + 14/13*m**4 + 0 + 8/13*m**k + 0*m.
2*m**2*(m - 2)*(7*m - 2)/13
Let c = 9 - -16. Let p = c - 21. Let 3*v + 5*v**3 + 10*v**4 + 3*v**2 + 2*v**p + 3*v**2 - 26*v**3 = 0. What is v?
-1/4, 0, 1
Let z = 318 + -303. Suppose -9*s + 6*s = -z. Let 0 + 8/7*x**2 - 6/7*x**s + 4/7*x**3 - 8/7*x**4 + 2/7*x = 0. Calculate x.
-1, -1/3, 0, 1
Let q = -1174 - -3533/3. Let -q*t**4 - 1/3*t**2 - 1/3*t + 3*t**3 + 4/3*t**5 + 0 = 0. What is t?
-1/4, 0, 1
Let i be 34/7 + (10/20*-18 - -5). Let 4/7*b**2 + 4/7 - i*b**3 + 2*b = 0. Calculate b.
-1, -1/3, 2
Let q = -4075 + 4075. Factor 1/4*r**3 - r + 0 + q*r**2.
r*(r - 2)*(r + 2)/4
Let n(s) = s**3 - s**2 - 1. Let t be 8*(-4)/((-32)/6). Let l = t + -7. Let x(i) = 9*i**3 - 9*i**2 + 3*i - 15. Let z(r) = l*x(r) + 12*n(r). Solve z(v) = 0 for v.
-1, 1
Let n(q) = -q**2 + 7*q - 10. Let x be ((-1)/(-3) + 0)*9. Let z be n(x). Let -6/5*u - 4/5 - 2/5*u**z = 0. Calculate u.
-2, -1
Let q(p) be the third derivative of 0*p + 0 - p**2 - 1/18*p**4 - 1/540*p**6 - 2/3*p**3 + 1/60*p**5. Let w(g) be the first derivative of q(g). Factor w(r).
-2*(r - 2)*(r - 1)/3
Suppose -4*i + 4*h - 8 = 0, -2*h = 140*i - 145*i + 2. Factor 4*b**2 + i*b**4 - 22/3*b**3 + 0 + 0*b.
2*b**2*(b - 3)*(3*b - 2)/3
Let c(m) = 11*m**4 - 26*m**3 + 3*m**2 + 80*m + 56. Let z(s) = -7*s**4 + 17*s**3 - 2*s**2 - 53*s - 37. Let r(d) = -5*c(d) - 8*z(d). Determine x so that r(x) = 0.
-1, 4
Let n(w) be the first derivative of -w**3/2 + 21*w**2/2 - 147*w/2 + 118. Factor n(a).
-3*(a - 7)**2/2
Let v(b) be the first derivative of 0*b + 2/7*b**4 + 0*b**2 + 4 - 4/21*b**3. Determine l so that v(l) = 0.
0, 1/2
Determine q, given that -230*q**3 + 27*q**4 + 110 + 460*q**2 - 375*q + 3*q**4 + 9*q**5 + 2*q**5 + 9*q**5 - 15*q**5 = 0.
-11, 1, 2
Let s(x) be the first derivative of -x**7/126 - x**6/45 - x**5/60 + x - 4. Let a(k) be the first derivative of s(k). Let a(m) = 0. Calculate m.
-1, 0
Factor -210713 - 15*m**3 - 31*m**2 + 210821 + 60*m + 4*m**2.
-3*(m - 2)*(m + 2)*(5*m + 9)
Let c be (-44)/(-3) - (-10)/(-15). Let d(m) = m**3 - 14*m**2 + m - 6. Let r be d(c). Solve 2*j**2 + 6 - r + 0 = 0.
-1, 1
Let g(c) = -12*c - 31. Let v be g(-8). Find q, given that -45*q**4 - 190*q**3 + 190*q - v*q**2 + 40 + 35*q**2 + 35*q**2 = 0.
-4, -1, -2/9, 1
Let c(f) = -f**5 - 2*f**3 - 6*f**2 + f + 2. Let g(y) = -4*y**5 - y**4 - 6*y**3 - 19*y**2 + 3*y + 6. Let r(u) = 7*c(u) - 2*g(u). Factor r(w).
(w - 1)**2*(w + 1)**2*(w + 2)
Let h(w) = 2*w**3 + w - 1. Let z(u) = -11*u**3 - 25*u**2 - 6*u + 6. Let t(l) = 6*h(l) + z(l). Find v, given that t(v) = 0.
0, 25
Let z be ((-9)/21)/(24/(-168)). Let x(k) be the second derivative of -z*k + 3/2*k**2 + 2/3*k**3 + 0 + 1/12*k**4. Find p, given that x(p) = 0.
-3, -1
Let a(v) be the first derivative of 10*v**3/3 - 15*v**2/2 - 10*v + 66. Factor a(o).
5*(o - 2)*(2*o + 1)
Suppose 2*m + 0*m = 4. Suppose w + m*w - 24 = -3*i, -3*i - w + 28 = 0. Factor 1 + 18*g**2 - 3*g**2 + i*g - 5 - g**2.
2*(g + 1)*(7*g - 2)
Let y(c) be the second derivative of 3*c**6/50 - 7*c**5/10 + 29*c**4/60 + 68*c**3/15 + 14*c**2/5 + 2*c. Suppose y(p) = 0. What is p?
-1, -2/9, 2, 7
Let f = 333383/283390 + 1/16670. Suppose 80/17*b + f*b**3 + 66/17*b**2 + 32/17 + 2/17*b**4 = 0. What is b?
-4, -1
Let c(r) be the third derivative of -r**5/100 + r**4/20 + 3*r**3/2 + 114*r**2. Suppose c(i) = 0. Calculate i.
-3, 5
Let t = 379 + -376. Let a(l) be the second derivative of 1/18*l**4 + 0 + 0*l**2 + 8*l + 0*l**5 - 1/45*l**6 - 1/18*l**t + 1/126*l**7. Factor a(h).
h*(h - 1)**3*(h + 1)/3
Let r(x) be the third derivative of -5*x**8/1344 - x**7/84 + 5*x**6/96 + x**5/8 + 53*x**2. Suppose r(y) = 0. What is y?
-3, -1, 0, 2
Let o(y) be the second derivative of 5*y**7/42 - 10*y**6/3 + 117*y**5/4 - 135*y**4/2 - 71*y. Solve o(l) = 0 for l.
0, 2, 9
Let p be ((-8)/90)/(98/(-125)*-5 + -4). Solve 2/9*i**3 + 8/9*i + p*i**2 + 0 = 0 for i.
-4, -1, 0
Let n be (1/((-6)/(-6)))/((-14)/(-4)). Suppose -h - 2*h - 2*h = 0. Let 2/7*m**2 - 2/7*m**4 + n*m + h - 2/7*m**3 = 0. Calculate m.
-1, 0, 1
Let y(u) be the third derivative of u**5/15 + 15*u**4 + 1350*u**3 + 4*u**2 + 2. Factor y(q).
4*(q + 45)**2
Let k(w) = w**2 - 4*w + 4. Let m be k(4). Suppose -m*g = 3*g - 21. Factor 2/7*v + 0 + 2/7*v**g + 4/7*v**2.
2*v*(v + 1)**2/7
Let a = -194172/7 + 27739. Factor a*o**4 - 1/7*o**2 + 0*o + 0*o**3 + 0.
o**2*(o - 1)*(o + 1)/7
Suppose -20*n = 44*n - 13 + 13. Let 0*w + n + 10/3*w**3 - 1/3*w**2 - 25/3*w**4 = 0. Calculate w.
0, 1/5
Let v be 6 + -3 - 1 - 5. Let d(l) = -l**3 - 2*l**2 + l - 4. Let t be d(v). Factor 3*q**t + 12 + 9 - 24.
3*(q - 1)*(q + 1)
Let k(x) be the first derivative of 9*x**4/4 + 10*x**3 - 81*x**2/2 - 30*x - 112. Solve k(n) = 0 for n.
-5, -1/3, 2
Let f(r) = 9*r**3 + 529*r**2 + 16891*r - 17419. Let d(y) = -28*y**3 - 1588*y**2 - 50672*y + 52256. Let h(w) = -5*d(w) - 16*f(w). Factor h(z).
-4*(z - 1)*(z + 66)**2
Let w(u) = u**5 - 11*u**4 - 8*u**3 + 3*u**2. Let k(r) = 10*r**4 + 8*r**3 - 2*r**2. Let s(f) = -3*k(f) - 2*w(f). Find h, given that s(h) = 0.
-2, 0
Let m(z) be the second derivative of z**9/75600 + z**8/11200 - 17*z**4/12 + 8*z. Let r(l) be the third derivative of m(l). Find y, given that r(y) = 0.
-3, 0
Let f(m) be the third derivative of -m**5/15 + 11*m**4/3 - 48*m**3 + 100*m**2. Factor f(a).
-4*(a - 18)*(a - 4)
Let u = 80 + -23. Let f be 15/15 - (2 - u/33). Factor -18/11*l + f*l**2 + 4/11.
2*(l - 2)*(4*l - 1)/11
Let j(f) be the second derivative of 27*f**6/2 + 279*f**5/4 - 265*f**4/3 - 110*f**3 - 40*f**2 - 146*f. What is d in j(d) = 0?
-4, -2/9, 1
Let c(x) = 10*x**5 - 33*x**4 + 40*x**3 - 21*x**2 + x + 3. Let n(m) = 11*m**5 - 34*m**4 + 39*m**3 - 20*m**2 + 4. Let t(z) = 4*c(z) - 3*n(z). Factor t(y).
y*(y - 2)*(y - 1)**2*(7*y - 2)
Let s(w) be the third derivative of -1/210*w**6 - 3*w**2 + 0*w**7 + 0*w**3 + 1/84*w**4 + 1/1176*w**8 + 0*w**5 + 0*w + 0. Factor s(i).
2*i*(i - 1)**2*(i + 1)**2/7
Let c(z) be the third derivative of -7*z**6/30 - 11*z**5/15 - 2*z**4/3 + 3*z**2 + 10*z. Find g, given that c(g) = 0.
-1, -4/7, 0
Let v(d) be the first derivative of -2*d**6/21 + 4*d**5/35 + 2*d**4/7 - 8*d**3/21 - 2*d**2/7 + 4*d/7 -