- 10*k + 6*k**2. Let w(m) be the first derivative of z(m). Let w(t) = 0. Calculate t.
-2, 0
Suppose -1/2*s**3 + 0 + 0*s - s**2 = 0. Calculate s.
-2, 0
Let l(r) be the second derivative of 1/10*r**6 - 1/2*r**4 - 9/20*r**5 - 12*r**2 + 39*r + 0 + 6*r**3. Find m such that l(m) = 0.
-2, 1, 2
Suppose 52 = -11*m + 173. Let c(z) be the third derivative of 1/120*z**5 + 0*z + 1/16*z**4 + 0 + 1/6*z**3 - m*z**2. Suppose c(i) = 0. What is i?
-2, -1
Suppose 5*f = 3*f + 136. Factor -50*k**2 + 6*k + 9 - 17 + f*k**2 + 4*k**3.
2*(k + 1)*(k + 4)*(2*k - 1)
Suppose 27 + 33 = 20*u. Let y = -4/7 - -27/35. Suppose 0*l - 1/5 + 0*l**u + 2/5*l**2 - y*l**4 = 0. What is l?
-1, 1
Let l = 663 + -659. Let h(g) be the second derivative of 1/6*g**3 + 0 + 0*g**2 + 0*g**5 - 1/42*g**7 + 3*g - 1/15*g**6 + 1/6*g**l. Factor h(i).
-i*(i - 1)*(i + 1)**3
Factor -21/4*h**2 + 1/4*h**3 - 45/4*h - 23/4.
(h - 23)*(h + 1)**2/4
Suppose -s = -4*v - 14, 4 = -5*s + 4*s - 5*v. Solve -30*c**4 + 21*c**5 - 33*c**4 - 6*c + 45*c**3 + s*c**4 - 3*c**2 = 0.
-2/7, 0, 1
Let l = -1980 + 1983. Let m(p) be the first derivative of 4*p**2 + 0*p + 4/3*p**l - 10. Factor m(y).
4*y*(y + 2)
Let i(x) be the first derivative of x**4/28 - 2*x**3/7 + 4*x**2/7 - 8. Factor i(c).
c*(c - 4)*(c - 2)/7
Let k(i) be the third derivative of -i**6/72 + i**5/4 - 25*i**4/24 + 5*i**3/3 - 5*i**2. Let h(n) be the first derivative of k(n). Factor h(o).
-5*(o - 5)*(o - 1)
Let c(m) = 3*m**4 + 18*m**3 - 76*m**2 + 148*m - 92. Let g(a) = -4*a**4 - 18*a**3 + 74*a**2 - 147*a + 91. Let h(o) = -5*c(o) - 4*g(o). Solve h(f) = 0 for f.
2, 12
Let i(s) be the second derivative of -s**4/3 + 4*s**3/3 + 16*s**2 - 5*s + 2. Factor i(p).
-4*(p - 4)*(p + 2)
Let c(p) = -9*p**2 + 51*p - 6. Let d be c(14). Let w be 6/(-45) + d/(-1170). Factor -6/13*l**3 - w*l**2 + 0 + 2/13*l**5 - 4/13*l + 2/13*l**4.
2*l*(l - 2)*(l + 1)**3/13
Let h be 3 + ((-16)/4 - -1). Let f be (-1 - -3 - h - 2) + 3. Suppose 8/3*g + 6*g**4 - 4/3*g**2 + 2/3 - 8*g**f = 0. What is g?
-1/3, 1
Let o(c) be the second derivative of 0 + 0*c**2 + 1/36*c**4 - 1/3*c**3 + 1/60*c**5 + 21*c. Factor o(l).
l*(l - 2)*(l + 3)/3
Let y(b) = -b**3 + 4*b**2 - 2*b. Let t be y(3). Suppose -t*z - 4*d = -16, -9*d + 4*d + 5 = 0. Factor 3*k - 6*k**3 + 3/2*k**2 - 9/2*k**z + 0.
-3*k*(k + 1)**2*(3*k - 2)/2
Let z(s) = 43*s**3 - 193*s**2 + 183*s - 18. Let l(r) = 21*r**3 - 96*r**2 + 93*r - 9. Let w(g) = -5*l(g) + 3*z(g). Factor w(x).
3*(x - 3)*(x - 1)*(8*x - 1)
Let s(i) be the first derivative of 13*i**3/3 - i**2/2 - 8*i + 11. Let l(z) = -38*z**2 + 2*z + 23. Let r(k) = 6*l(k) + 17*s(k). Solve r(m) = 0.
-1, 2/7
Suppose -12 = 4*c, -48 = -10*m + 9*m - c. Suppose 4*r = 59 - m. Let 3/4*n**5 - 3/2 - 3/2*n**r + 3*n**4 - 15/4*n + 3*n**3 = 0. Calculate n.
-2, -1, 1
Let k be 0*((-15)/6 - -2). Suppose -s + 7*s - 30 = k. Factor -2*l**2 - l + s*l**2 - 2*l.
3*l*(l - 1)
Let a(q) = q**3 + 8*q**2 + 13*q + 6. Let r be a(-6). Suppose b + 3*u = -11, 2*u = -5*b - r*u + 10. Factor -26/3*k**2 - 8*k - 4*k**3 - 2/3*k**b - 8/3.
-2*(k + 1)**2*(k + 2)**2/3
Suppose 4*v - 7*v + 5*d + 31 = 0, -2 = -2*d. Find o such that o**2 - 48*o + 5*o**2 + 36 + 3*o**2 - v*o = 0.
2/3, 6
Suppose -14 + 25 = l. Suppose 0 = -6*j + l + 25. Solve j*g - 3/2*g**2 - 6 = 0 for g.
2
Factor 0 + 1/6*t**5 - 6*t - 5/6*t**3 - 2/3*t**4 + 6*t**2.
t*(t - 3)*(t - 2)**2*(t + 3)/6
Let f be 194/420 - (-30)/(-70). Let r(p) be the third derivative of -f*p**5 + 0 - 1/180*p**6 + 4/9*p**3 + 6*p**2 + 0*p**4 + 0*p. Determine m so that r(m) = 0.
-2, 1
Let k(l) be the first derivative of -2*l**5/5 + l**4 - 2*l**2 + 2*l + 74. Determine u so that k(u) = 0.
-1, 1
Let l(w) = -w**2 - 23*w - 16. Let f be l(-19). Let i = f - 58. Factor 3/4*y**i + 3/2*y + 3/4.
3*(y + 1)**2/4
Suppose 140/11*b + 2/11*b**2 + 138/11 = 0. Calculate b.
-69, -1
Let k be 6/(-4)*(-96)/18. Suppose -3*s + k = s. Factor 12*u**3 + 4*u**3 - 4*u**4 - 14*u**2 - 5*u**s + 3*u**2.
-4*u**2*(u - 2)**2
Let z(d) = 4*d**3 - 8*d**2 + 4*d - 22. Let i(w) = -2*w**3 + 4*w**2 - 2*w + 12. Let m(r) = -11*i(r) - 6*z(r). Find h, given that m(h) = 0.
0, 1
Let x be 0/(8/4) + 2. Suppose x*o - 2 = 2*l, -2*l = -7*l - 4*o + 31. Factor -2*t - l*t + 4 - 3*t + 4*t**2.
4*(t - 1)**2
Let z(r) be the second derivative of -24*r + 1/30*r**4 + 0 - 1/225*r**6 + 1/75*r**5 - 4/45*r**3 - 4/15*r**2. Solve z(f) = 0 for f.
-1, 2
Suppose 3*s = 5*f - 8, 132*f = -4*s + 126*f + 40. Let -2/3*b**2 - 8/3*b**s + 0*b - 10/3*b**3 + 0 = 0. What is b?
-1, -1/4, 0
Let n = -136/125 + 2018/1625. Factor -n*f**2 + 0 - 2/13*f.
-2*f*(f + 1)/13
Let k be 2*2/2 + -4. Let c(y) = -3*y**2 - y + 2. Let w(z) = -16*z**2 - 5*z + 10. Let u(x) = k*w(x) + 11*c(x). Factor u(t).
-(t - 1)*(t + 2)
Suppose 3/5*a - 1/5*a**2 + 54/5 = 0. What is a?
-6, 9
Suppose 3*w - 10 - 14 = -3*z, 5*w = -10. Let q be (-30)/12*(-12)/z. Factor -43*g + 64*g**4 + 25*g - 60*g**2 + 26*g + 96*g**q.
4*g*(g + 2)*(4*g - 1)**2
Let x(y) be the first derivative of 0*y**4 + 0*y**2 + 0*y + 0*y**3 + 1/5*y**5 + 6. Factor x(q).
q**4
Let b be 30/(-1 + (-10)/(-6)). Let z be b/(-18)*8/(-5). Factor -22*o**3 + 4*o**2 + 18*o**3 + 4*o**4 - 3*o**z.
o**2*(o - 2)**2
Let w = -81 + 81. Factor -4*m**4 + 20 + 8*m**3 + w*m**4 + 51*m**2 + 13*m**2 - 16*m**2 + 56*m.
-4*(m - 5)*(m + 1)**3
Let k(v) = -241*v**3 + 106*v**2 - 10*v. Let h(p) = p**3 - p**2 + p. Let d be 4/10 + 136/85. Let j(c) = d*h(c) - k(c). Suppose j(s) = 0. What is s?
0, 2/9
Let w(s) = -s**3 + 22*s**2 - 23*s + 47. Let x be w(21). Let -26*f**x + 6*f**3 + 17*f**5 - 18*f**5 + 21*f**4 = 0. What is f?
-2/9, 0, 1
Let v(x) be the first derivative of -6*x**2 - 4/3*x**3 + 2 + 0*x. Solve v(r) = 0.
-3, 0
Determine k, given that 0 - 7/2*k**2 + 7/2*k**4 + 3*k**3 - k - 2*k**5 = 0.
-1, -1/4, 0, 1, 2
Let r(t) = -3*t**2 - 23*t - 27. Let u(p) = 2*p**2 + 15*p + 18. Let s(l) = 5*r(l) + 7*u(l). Factor s(f).
-(f + 1)*(f + 9)
Let o(k) be the third derivative of -k**6/120 + k**5/20 + k**4/8 - 2*k**3/3 - 2*k**2. Let s be o(3). Factor 0*z**5 + z**5 - 2*z**5 - z**4 + 2*z**s.
z**4*(z - 1)
Let o(l) be the first derivative of l**4/5 - 4*l**3/5 - 12*l**2/5 + 32*l/5 + 11. Let o(i) = 0. What is i?
-2, 1, 4
Let r(g) be the third derivative of -g**6/2700 + g**5/300 + g**4/45 - g**3/3 + 8*g**2. Let f(o) be the first derivative of r(o). Find w, given that f(w) = 0.
-1, 4
Let a(q) be the third derivative of -q**7/4620 - q**6/660 - q**5/220 - q**4/132 - 4*q**3 - 10*q**2. Let o(x) be the first derivative of a(x). Factor o(k).
-2*(k + 1)**3/11
Let o(y) be the first derivative of y**7/1260 + y**6/240 + y**5/180 + 3*y**2/2 + 1. Let x(j) be the second derivative of o(j). Factor x(d).
d**2*(d + 1)*(d + 2)/6
Suppose 0 = -70*l + 60*l + 20. Let u(w) be the first derivative of 12 - 50/27*w**3 - 8/9*w + 20/9*w**l. Factor u(i).
-2*(5*i - 2)**2/9
Let n(v) = 55*v**3 + 860*v**2 + 1880*v + 945. Let f(z) = 5*z**3 + 78*z**2 + 171*z + 86. Let m(l) = 65*f(l) - 6*n(l). Factor m(q).
-5*(q + 1)**2*(q + 16)
Let n(r) be the first derivative of -2/25*r**5 - 2/15*r**2 - 12 + 0*r + 2/15*r**3 + 1/45*r**6 + 1/30*r**4. Find l such that n(l) = 0.
-1, 0, 1, 2
Let y(n) be the second derivative of n**6/105 + n**5/10 - 3*n**4/14 - n**3/3 + 8*n**2/7 - 360*n. Solve y(g) = 0 for g.
-8, -1, 1
Let v(k) be the second derivative of 1/12*k**5 + 0 + 5/36*k**4 - 1/9*k**6 + 0*k**2 + 10*k + 0*k**3. Solve v(t) = 0.
-1/2, 0, 1
Let q(n) be the second derivative of -7*n**5/10 - n**4/3 + 21*n**3 + 18*n**2 - 585*n. Factor q(z).
-2*(z - 3)*(z + 3)*(7*z + 2)
Let k be (-2)/(-6)*(-99)/3. Let b = k - -17. Factor 3*m**2 - m**2 - 4*m**2 + b*m**2 - 4.
4*(m - 1)*(m + 1)
Let j(v) = -12*v**2 + 41*v + 21. Let n(z) = -7*z**2 + 21*z + 12. Let s(c) = 4*j(c) - 7*n(c). What is x in s(x) = 0?
-17, 0
Let i be 12*(50/12 + (-16)/4). Solve 3/2*n**2 - i + 1/2*n = 0.
-4/3, 1
Let j(b) = -b**2 + b - 12. Let d(t) = -t**2 - 12*t + 9. Let n(c) = -2*d(c) + 4*j(c). Solve n(r) = 0.
3, 11
Find u, given that 55*u + 135 - 2*u**2 - 7*u**2 + 5 + 14*u**2 = 0.
-7, -4
Let c be 10 + (-3 - 2) + -5. Let a(q) be the second derivative of -q**3 + 0 - 1/4*q**4 + c*q**2 - 10*q. Let a(z) = 0. What is z?
-2, 0
Let h(b) be the first derivative of b**3/3 + b**2/2 + 3*b + 12. Let r(j) = 8*j**2 + 6*j + 20. Let u(z) = -44*h(z) + 6*r(z). Suppose u(s) = 0. Calculate s.
-1, 3
Let r = 8/3511 - -10493/17555. Factor 2/5*h**3 + r*h**2 - 1/5*h**4 - 4/5 -