e of l(u). Find k, given that g(k) = 0.
-2, 0, 1
Let b = 164460 + -164454. Factor -14/5*a**3 + 36/5*a**2 - b*a + 8/5.
-2*(a - 1)**2*(7*a - 4)/5
Let z be (-10492)/(-2838) + (-4)/11. Let x = -3/22 + 119/66. Solve x*a**2 - 5/3*a - z = 0 for a.
-1, 2
Factor 805 + 1/2*y**2 - 237/2*y.
(y - 230)*(y - 7)/2
Suppose 7*b = -4*f + 11*b + 1396, 0 = 5*f + 4*b - 1709. Let u = 349 - f. Factor 0*p**2 + 0 + 0*p + 8/5*p**3 + 2/5*p**u.
2*p**3*(p + 4)/5
Let v(s) be the third derivative of 5*s**6/36 + 67*s**5/9 + 131*s**4/9 + 104*s**3/9 - 2*s**2 + 1410. Factor v(l).
2*(l + 26)*(5*l + 2)**2/3
Let c be 6/21*(-1722)/(-328). Suppose -1/2*q - c*q**4 + 3/2*q**2 - 7/8*q**5 + 0 + 11/8*q**3 = 0. What is q?
-2, -1, 0, 2/7, 1
Let b = 180 - 179. Let n be (b - -39)*4/24. Suppose -n*g - 50/3 - 2/3*g**2 = 0. What is g?
-5
Let o(y) be the second derivative of y**4/30 - 7*y**3/3 - 36*y**2/5 + 2643*y. Factor o(f).
2*(f - 36)*(f + 1)/5
Suppose -130 = -4*i + 86. Factor 32*q**3 - 60*q**2 - i*q - 14 - 7*q**3 + 44 - q.
5*(q - 3)*(q + 1)*(5*q - 2)
Let x(q) be the second derivative of 0 - 1/2*q**2 - 4*q - 1/6*q**4 - 4/3*q**3 + 1/15*q**5. Let m(n) be the first derivative of x(n). Factor m(t).
4*(t - 2)*(t + 1)
Let o(j) be the first derivative of j**4/6 + 59*j**3/18 + 41*j**2/12 - 7*j/3 + 1365. Factor o(t).
(t + 1)*(t + 14)*(4*t - 1)/6
Let c = -3/436 + 1093/436. Let s(l) be the second derivative of 0 - 3*l**2 - c*l**3 - l**4 - 5*l - 3/20*l**5. Suppose s(n) = 0. Calculate n.
-2, -1
Let f = -419 + 429. Factor -f - 20 + 727*r**2 - 700*r**2 - 129*r.
3*(r - 5)*(9*r + 2)
Suppose 9*f - 248 = 103. Find q such that f*q**3 - 426*q**2 - 4*q**4 - 390*q + 45*q**3 + 30*q**2 - 94*q = 0.
-1, 0, 11
Let i = -13279 + 27396. Let m = -239909/17 + i. Factor 66/17*o**2 + 32/17 - m*o - 20/17*o**3 + 2/17*o**4.
2*(o - 4)**2*(o - 1)**2/17
Let u = -33 + 37. Suppose -2*t + 4*f + 13 = t, -u*t = 2*f - 10. Factor -47*i**t - 5*i - 2*i**4 + 4*i + 47*i**3 + 2*i**2 + i**5.
i*(i - 1)**3*(i + 1)
Determine g, given that -836352*g - 792*g**2 - 294395904 - 1/4*g**3 = 0.
-1056
Let v be (-1)/(-1) + (-4)/(-1). Suppose -4*l = -38*l + 680. Find a, given that -v*a**2 - l - 8*a**3 + 20 + a**2 = 0.
-1/2, 0
Find w, given that -74/3*w**3 + 272/3*w**2 + 0 - 88*w + 2/3*w**4 = 0.
0, 2, 33
Let i(u) be the third derivative of u**7/42 + 3*u**6/4 - 13*u**5/12 - 205*u**4/4 - 180*u**3 + u**2 + 255*u - 1. Find n such that i(n) = 0.
-18, -3, -1, 4
Let g(m) be the second derivative of -29*m**7/70 - 28*m**6/25 + 621*m**5/100 - 13*m**4/2 + 4*m**3/5 + m - 899. What is c in g(c) = 0?
-4, 0, 2/29, 1
Let u(f) be the second derivative of 37/40*f**5 + 15/2*f**4 + 0*f**2 + 27/4*f**3 + 1/30*f**6 - 15*f + 0. Solve u(i) = 0.
-9, -1/2, 0
Suppose -275*u = -51*u - 9856. Let t(d) be the second derivative of 1/12*d**7 + 0 + 0*d**2 + 0*d**3 + 1/12*d**4 + 11/40*d**5 - u*d + 4/15*d**6. Factor t(h).
h**2*(h + 1)**2*(7*h + 2)/2
Let q(j) be the second derivative of -j**6/5 - 184*j**5/5 - 2501*j**4 - 67240*j**3 + 68921*j**2 - 682*j + 2. Factor q(f).
-2*(f + 41)**3*(3*f - 1)
Let l = -61704/11 + 5610. Let o be (-6)/8 - 82/(-88). Solve l*i - o*i**2 + 8/11 = 0.
-1, 4
Factor 4/3 - 65/6*q**2 - 11/6*q**3 - 41/3*q.
-(q + 2)*(q + 4)*(11*q - 1)/6
Let h(a) = a**2 + 41*a - 24. Let i = 32 - 30. Suppose -i*z + 77 = -33. Let f(n) = 10*n**2 + 370*n - 215. Let w(r) = z*h(r) - 6*f(r). Let w(c) = 0. What is c?
1, 6
Suppose 1/5*s**4 + 0 + 16/5*s**2 + 0*s - 2*s**3 = 0. What is s?
0, 2, 8
Solve 1027*z**3 - 5*z + 220*z**2 + 1027*z**3 - 4103*z**3 + 1028*z**3 - 220 + 1026*z**3 = 0.
-44, -1, 1
Let n(a) = -a**3 - a**2. Suppose -10*k + 12 + 28 = 0. Let s(g) = 11*g**3 + 46*g**2 + 55*g + 20. Let d(y) = k*n(y) - s(y). Find f, given that d(f) = 0.
-4/3, -1
Factor 59*v + 148*v**2 - v**4 - 213471*v**3 - 3*v**4 + 213511*v**3 + 45*v.
-4*v*(v - 13)*(v + 1)*(v + 2)
Let i(t) = 30*t**3 - 28*t**2 - 490*t + 520. Let h(x) = -11*x**3 + 9*x**2 + 164*x - 174. Let z(g) = -8*h(g) - 3*i(g). Factor z(o).
-2*(o - 12)*(o - 1)*(o + 7)
Solve 57/5*x**4 - 216/5*x - 44*x**2 + 2*x**3 + 11/5*x**5 - 32/5 = 0.
-4, -2, -1, -2/11, 2
Factor 100/11*c - 2/11*c**2 + 1488/11.
-2*(c - 62)*(c + 12)/11
Let c be -17 + (-4)/(-5) + 6156/380. Suppose -6/7*f**4 + 0*f**3 + 8/7*f**2 + c - 2/7*f**5 + 0*f = 0. Calculate f.
-2, 0, 1
Let v(z) = -z**3 - 26*z**2 - 24*z + 27. Let y be v(-25). Let -326*u**2 - y*u**3 - 57 - 39 - 104*u + 294*u**2 = 0. What is u?
-12, -2
Let y = -6469 - -77635/12. Let n(r) be the third derivative of 0*r + 0 - 1/60*r**5 - 3*r**2 - 49/6*r**3 + y*r**4. Find x such that n(x) = 0.
7
Let i(m) = 4*m**2 - 9*m - 9. Let l be i(-1). Let h be 2 + -8 + l + 3 + 3. Find z, given that -2*z**5 + 1/2 - z**2 - 2*z + 1/2*z**4 + h*z**3 = 0.
-1, 1/4, 1
Let c(a) be the first derivative of 175/3*a**3 + 60*a**2 - 180*a - 37 - 125/4*a**4. Factor c(q).
-5*(q + 1)*(5*q - 6)**2
Suppose -347 = -18*x + 49. Solve -20*d**3 - 16 - 15*d**4 + 46*d**4 + x*d + 4 - 2*d**5 - 19*d**4 = 0.
-1, 1, 2, 3
Let z(m) be the first derivative of m**5/50 - 2*m**4/15 - m**3/15 + 4*m**2/5 + 68*m - 33. Let f(s) be the first derivative of z(s). Factor f(w).
2*(w - 4)*(w - 1)*(w + 1)/5
Let x(j) = -8*j**2 - 368*j - 440. Let s(c) = c**2 + c - 24. Let l(z) = -12*s(z) - x(z). Factor l(r).
-4*(r - 91)*(r + 2)
Let j(q) = 16*q**3 - 225*q**2 + 2404*q + 2634. Let i(n) = 3*n**3 - 45*n**2 + 481*n + 527. Let m(o) = -33*i(o) + 6*j(o). Let m(g) = 0. What is g?
-1, 23
Suppose -380*b + 700 = 348*b - 756. Factor 0*k + 0 - 9*k**4 - 300/7*k**b - 360/7*k**3 - 3/7*k**5.
-3*k**2*(k + 1)*(k + 10)**2/7
Factor -27*n**3 - 183 + 89 - 140*n**2 + 94 + 22*n**3.
-5*n**2*(n + 28)
Let s(i) be the third derivative of -3/11*i**4 + 0*i**3 - 4/55*i**5 - 35 + 0*i - 2*i**2 - 1/220*i**6. Factor s(y).
-6*y*(y + 2)*(y + 6)/11
Let v = -37 + 32. Let m be (2 - (-12)/v)*(-12)/24. Factor -2/5*c**3 + 0 + 3/5*c**2 - m*c.
-c*(c - 1)*(2*c - 1)/5
Let h(p) be the first derivative of -6*p**6 - 24*p**5 - 22*p**4 + 32*p**3/3 + 14*p**2 - 8*p + 2559. Suppose h(r) = 0. Calculate r.
-2, -1, 1/3
Let y(a) be the third derivative of 11*a**6/24 + 173*a**5/12 - 10*a**4 + 3*a**2 - 265. Suppose y(p) = 0. Calculate p.
-16, 0, 3/11
Let q(m) = -m**5 + m**4 + m**3 + m**2. Let k(z) = 2*z**5 - 6*z**4 + 7*z**3 - 5*z**2. Let i(d) = 2*k(d) + 2*q(d). Factor i(x).
2*x**2*(x - 2)**2*(x - 1)
Let z be ((-58)/1)/((-24)/36). Let r = z - 85. Solve 8*g**r - 293*g + 0*g**3 - 32 + 309*g - 4*g**3 = 0 for g.
-2, 2
Let q(d) = 7028*d + 7030. Let h be q(-1). Factor -3/5*i**h + 6 - 9/5*i.
-3*(i - 2)*(i + 5)/5
Let f(q) be the second derivative of q**5/60 - q**4/3 + 2*q**3 + 31*q**2/2 + 4*q - 3. Let m(b) be the first derivative of f(b). Solve m(r) = 0 for r.
2, 6
Let f(o) be the second derivative of -29/40*o**5 - 3/14*o**7 + 13/20*o**6 + 1 + 0*o**2 + 3/8*o**4 - 17*o - 1/12*o**3. Determine p so that f(p) = 0.
0, 1/3, 1/2, 1
Factor -4 - 23/3*y - 7/6*y**2.
-(y + 6)*(7*y + 4)/6
Let q be 13 - ((-801)/(-135) - -7). Let y(r) be the first derivative of 0*r**2 + 0*r**4 + 0*r - 5 + 0*r**3 + 2/25*r**5 - q*r**6. Suppose y(j) = 0. Calculate j.
0, 1
Let d be ((-3315)/(-300) - 11) + (-4520)/(-5600). Factor d*h**4 + 26/7*h**3 + 32/7*h**2 + 0 + 8/7*h.
2*h*(h + 2)**2*(3*h + 1)/7
Suppose 14*c - 8 = -3 - 5. Let b(o) be the second derivative of 2/15*o**3 + 1/30*o**4 - 8*o + c - 1/5*o**5 + 0*o**2. Let b(k) = 0. What is k?
-2/5, 0, 1/2
Suppose -w + 8*w = 21. Let 4*i**4 - 5*i - 4*i**w + 4*i**2 + 18*i**3 + 3*i + 4*i**4 = 0. Calculate i.
-1, 0, 1/4
Suppose 434/5*y**2 - 9/5*y**3 - 40 + 804/5*y = 0. Calculate y.
-2, 2/9, 50
Let v(u) be the third derivative of -1/45*u**7 + 5/9*u**3 - 1/504*u**8 - 42*u**2 + 0 + 1/45*u**5 - 1/18*u**6 + 0*u + 11/36*u**4. Solve v(k) = 0.
-5, -1, 1
Let p(w) = w**3 + 70*w**2 + 136*w. Let g be p(-68). Find q such that 1/7*q**2 + g + 0*q = 0.
0
Factor 33856 - 184*s + 1/4*s**2.
(s - 368)**2/4
Let m be 16/6*(-1665)/(-1480). Suppose 0 - 11/4*v**2 + 3/2*v + v**m = 0. What is v?
0, 3/4, 2
Let y be -3 - (-1879)/5 - 7/(-35). Factor -4 + 185*l**2 - y*l**2 + 191*l**2 + l**4 - 5*l + 5*l**3.
(l - 1)*(l + 1)**2*(l + 4)
Let y = 1530988 - 1530983. Factor 1/3*s**y - 1/3*s**4 - s**3 + 2/3*s + 1/3*s**2 + 0.
s*(s - 2)*(s - 1)*(s + 1)**2/3
Suppose -d = 4*r, d + 2*d - 22 = -r. Suppose d*m = 7*m + 20. Determine l, given that 8*l**3 + 10*l + 8*l**2 - 2*l - 2*l**4 - m*l**2 - 2 = 0.
1
Let w = -7999 - 