4
Let t(p) be the first derivative of p**4/8 + 5*p**3/6 + 2*p**2 + 2*p + 4. Find g, given that t(g) = 0.
-2, -1
Let l(a) be the third derivative of 2/9*a**3 - 1/36*a**4 + 0*a - 2*a**2 - 1/30*a**5 + 0. Suppose l(f) = 0. What is f?
-1, 2/3
Let m(y) be the first derivative of 1/15*y**6 + 4/25*y**5 + 0*y**2 + 0*y**3 + 1 + 1/10*y**4 + 0*y. Factor m(l).
2*l**3*(l + 1)**2/5
Suppose -11 = -5*t - 4*u, 5*t + u = -0*u + 14. Determine j, given that 2*j**t + 6*j**4 + 3*j**2 - 5*j**4 - 7*j**2 - 2*j**5 + 3*j**4 = 0.
-1, 0, 1, 2
Let h(z) be the first derivative of z**4/9 - 14*z**3/27 + 8*z**2/9 - 2*z/3 - 54. Factor h(g).
2*(g - 1)**2*(2*g - 3)/9
Let s(q) be the second derivative of -q**4/28 - 3*q**3/14 + 25*q + 1. Factor s(l).
-3*l*(l + 3)/7
Let l(b) = -99*b + 1. Let r be l(-1). Let d be (-12)/(-20) - (-15)/r. Suppose -3/4*j + 1/4 + d*j**2 - 1/4*j**3 = 0. Calculate j.
1
Let g(w) be the second derivative of -w**6/20 + w**5/6 - w**4/6 + w**2/2 - 2*w. Let t(q) be the first derivative of g(q). Factor t(s).
-2*s*(s - 1)*(3*s - 2)
Let d(m) = -3*m**2 - 2*m + 2. Let k(t) = t**2 + t - 1. Let y be (-6)/(-5)*(-80)/32. Let b(q) = y*d(q) - 6*k(q). Factor b(z).
3*z**2
Let q(d) be the first derivative of -d**4/14 - 8*d**3/21 - 5*d**2/7 - 4*d/7 - 9. Factor q(k).
-2*(k + 1)**2*(k + 2)/7
Let c be (-6)/351*-9*1. Factor 2/13*f - 2/13 + 2/13*f**2 - c*f**3.
-2*(f - 1)**2*(f + 1)/13
Find t, given that 0*t**3 - 4*t - 36 - 27*t**2 + 3*t**3 + 64*t = 0.
1, 2, 6
Let x(b) be the third derivative of b**6/180 - b**5/30 + b**4/12 - b**3/6 - 2*b**2. Let z(s) be the first derivative of x(s). Determine q so that z(q) = 0.
1
Let p be ((-36)/(-24))/((-1)/(-2)). Let w**p + 4*w**2 + 4*w + w + 3 + 0*w**3 - 1 = 0. What is w?
-2, -1
Factor 9*r**2 + 22*r**3 + 5*r**3 + 3*r - 12 - 4*r - 23*r.
3*(r - 1)*(3*r + 2)**2
Let a(z) = 59*z**3 + 321*z**2 + 351*z - 200. Let r(n) = -29*n**3 - 161*n**2 - 176*n + 100. Let w(v) = 4*a(v) + 9*r(v). What is g in w(g) = 0?
-5, -2, 2/5
Let z = -10 + 28. Let q be (-2)/z + 2/6. Factor -q*y**2 + 4/9*y + 0.
-2*y*(y - 2)/9
Let w(g) = -6*g**2 + 17*g - 11. Let v(x) = 9*x**2 - 25*x + 16. Let p(l) = 5*v(l) + 7*w(l). Factor p(b).
3*(b - 1)**2
Let u(n) = 79*n**2 + 301*n + 71. Let x(b) = -16*b**2 - 60*b - 14. Let i(l) = 4*u(l) + 22*x(l). Factor i(a).
-4*(a + 3)*(9*a + 2)
Let m(y) be the second derivative of 1/20*y**5 + 4*y - y**3 - 2*y**2 + 0 - 1/8*y**4. Let a(s) be the first derivative of m(s). Factor a(z).
3*(z - 2)*(z + 1)
Suppose 4*q = b + 20, -4*q - q - 5*b = -25. Factor -4*z**3 + z**4 + 4*z**q + 4 - 17*z**2 + 16*z**2 - 4.
z**2*(z - 1)*(z + 1)*(4*z + 1)
Let y(c) be the first derivative of 0*c**3 - 2/25*c**5 + 1/5*c**4 - 2/5*c**2 + 3 + 2/5*c. Factor y(w).
-2*(w - 1)**3*(w + 1)/5
Suppose 2*s + 4*j = -8, -4*s + j - 2*j = -5. Factor 1/3*w**s + 0*w + 0.
w**2/3
Let a be ((-25)/175)/((-1)/(21/2)). Solve 0 + a*g**3 - 3/4*g**4 + 0*g - 3/4*g**2 = 0 for g.
0, 1
Let v(b) be the second derivative of 1/3*b**3 + 2*b**2 + 1/15*b**6 + 0 - 1/10*b**5 - 3*b - 1/2*b**4. Solve v(x) = 0.
-1, 1, 2
Let f(w) be the second derivative of w**7/70 + 7*w**6/50 + 57*w**5/100 + 5*w**4/4 + 8*w**3/5 + 6*w**2/5 - w. Suppose f(b) = 0. Calculate b.
-2, -1
Solve -4*g**4 + 39*g**3 - 11*g**3 - 60*g**2 + 59*g**3 + 9*g**5 + 12*g - 44*g**4 = 0 for g.
0, 1/3, 1, 2
Let c(k) = 9*k**5 - 9*k**4 + 12*k**2 - 3*k. Let o(h) = 17*h**5 - 18*h**4 - h**3 + 23*h**2 - 6*h. Let a(v) = -5*c(v) + 3*o(v). Solve a(i) = 0 for i.
-1, 0, 1/2, 1
Let h be (0/(-2))/((-8)/(-4)). Factor -9*m + 6*m**2 + h*m**2 - 3*m**2.
3*m*(m - 3)
Let s(p) be the second derivative of p**6/105 - p**4/21 + p**2/7 - 9*p. Let s(o) = 0. Calculate o.
-1, 1
Let d(x) be the third derivative of -x**6/300 - x**5/10 - 7*x**4/30 + x**2 + 45. Find s such that d(s) = 0.
-14, -1, 0
Let m(b) be the second derivative of -b**6/120 - b**5/40 + b**4/4 - 2*b**3/3 - 4*b. Let o(l) be the second derivative of m(l). Factor o(h).
-3*(h - 1)*(h + 2)
Find o, given that 0*o + 6/5*o**2 + 2/5*o**3 + 0 = 0.
-3, 0
Let a(o) be the first derivative of 1/4*o**4 + 2*o**2 - 4/3*o**3 + 0*o + 4. Determine y so that a(y) = 0.
0, 2
Let v = -9 - -7. Let z be 3 - (4/v - -3). Determine f, given that 3*f**4 - 4*f**z + 2*f**2 - 5*f**3 + f**3 - 5*f**4 = 0.
-1, 0
Let x(p) be the third derivative of -1/36*p**4 + 4*p**2 + 0 - 1/60*p**5 + 1/90*p**7 + 1/120*p**6 + 0*p + 1/336*p**8 + 0*p**3. Factor x(b).
b*(b + 1)**3*(3*b - 2)/3
Let z(x) = 8*x**4 - 13*x**3 - 3*x**2 + 7*x - 2. Let t(p) = -105*p**4 + 170*p**3 + 40*p**2 - 90*p + 25. Let a(l) = -3*t(l) - 40*z(l). Factor a(n).
-5*(n - 1)**3*(n + 1)
Let c(z) = 3*z**2 - z + 4. Let s(x) = 2*x**2 - x + 3. Let r = 2 - -2. Let p(u) = r*s(u) - 3*c(u). Let p(o) = 0. Calculate o.
-1, 0
Let g(u) = 2*u**2 + u + 2. Let s be g(-1). Suppose 4*j - 3*a + 4 = 0, -4*j - a - s*a = -24. What is w in 0*w - 2/3*w**j + 2/3 = 0?
-1, 1
Let z = -4 + 8. Suppose -3*i**2 + z*i**2 - 5*i + 4*i + 0*i**2 - 2 = 0. What is i?
-1, 2
Let r = 13 + 9. Suppose -25 = 5*y, 0 = d + 4*y + y + r. Factor 5*t**3 - t**d - 3*t**3 + 0*t**3.
t**3
Let p(t) = 3*t**2 + 4*t - 2. Let j(f) = 10*f**2 + 13*f - 7. Let a(v) = 6*j(v) - 21*p(v). Factor a(c).
-3*c*(c + 2)
Let n(u) be the first derivative of -u**3 - 3*u**2/2 + 6*u - 9. Determine f so that n(f) = 0.
-2, 1
Let p be 0*(22/66)/(1/3). Factor -3*v**2 + p*v**3 + 0*v + 3/2*v**4 + 3/2.
3*(v - 1)**2*(v + 1)**2/2
Let x(k) = -20*k**3 + 144*k**2 - 252*k + 120. Let c(j) = -7*j**3 + 48*j**2 - 84*j + 40. Let z(u) = -8*c(u) + 3*x(u). Factor z(q).
-4*(q - 10)*(q - 1)**2
Let m(d) = -7*d**5 - 3*d**4 + 5*d**2. Let s(p) = 6*p**5 + 2*p**4 - 4*p**2. Let k(w) = -4*m(w) - 5*s(w). Factor k(b).
-2*b**4*(b - 1)
Let t(z) be the third derivative of -z**6/900 - 17*z**5/150 - 289*z**4/60 - 4913*z**3/45 - 9*z**2. Suppose t(g) = 0. What is g?
-17
Let j(f) be the third derivative of f**6/180 + f**5/60 - f**3/6 - 6*f**2. Let m(s) be the first derivative of j(s). Factor m(o).
2*o*(o + 1)
Suppose 50 = -2*i + 3*i. Let r be (4 - -1)*4/i. Factor 2/5*c**4 + r*c - 2/5*c**2 + 0 - 2/5*c**3.
2*c*(c - 1)**2*(c + 1)/5
Let l(k) = -k**3 + 3*k**2 - 2*k + 2. Suppose 7*m - 4*m = 6. Let d be l(m). Suppose -n**d + 1 + n - 1 = 0. Calculate n.
0, 1
Let o(h) = 2*h - 1. Let z be o(4). Let p = -4 + z. Find f, given that 0*f**2 + 0 + 2/5*f**5 + 0*f + 2/5*f**4 + 0*f**p = 0.
-1, 0
Let p be ((-10)/(-6) + -1)/((-28)/(-21)). Factor -1/2*j**2 + p*j**3 + 0*j + 0 - 1/2*j**5 + 1/2*j**4.
-j**2*(j - 1)**2*(j + 1)/2
Let g(a) be the second derivative of -a**4/12 + a**3/4 + a**2/2 + 10*a. Find s such that g(s) = 0.
-1/2, 2
Factor 0*k**5 + 0*k**3 + 3*k**4 - 2*k + k**3 - k**5 + 2*k**5 - 3*k**2.
k*(k - 1)*(k + 1)**2*(k + 2)
Let q(r) be the second derivative of r**7/126 + r**6/90 - r**5/60 - r**4/36 + 16*r. Solve q(h) = 0 for h.
-1, 0, 1
Let d = -3 - -8. Let x(t) be the first derivative of 3 - 1/12*t**3 + 1/20*t**d + 0*t**2 + 0*t**4 + 0*t. Factor x(v).
v**2*(v - 1)*(v + 1)/4
Let m(n) be the third derivative of -n**7/735 + n**6/140 - n**5/70 + n**4/84 - 11*n**2. Factor m(q).
-2*q*(q - 1)**3/7
Let k(o) = 6*o**2 + 3*o - 1. Let t(p) = -25*p**2 - 11*p + 5. Let z(a) = 9*k(a) + 2*t(a). Solve z(c) = 0.
-1, -1/4
Let p(o) be the first derivative of o**5/25 + 3*o**4/20 + o**3/15 - 3*o**2/10 - 2*o/5 - 11. Factor p(l).
(l - 1)*(l + 1)**2*(l + 2)/5
Let q be ((-12)/(-18))/(5 + -1). Let l = q + 5/42. Let -2/7*d + 0 - l*d**2 = 0. Calculate d.
-1, 0
Determine i so that 32 - 4*i**3 + 24*i**2 - 46*i + 45*i - 47*i = 0.
2
Let a(g) = 3*g**2 + 8. Let l(m) = m**3 - 10*m**2 - 11*m - 8. Let z be l(11). Let y(w) = -w**2 - 3. Let s(d) = z*y(d) - 3*a(d). Determine x, given that s(x) = 0.
0
Let p(g) = g**2 + 5*g + 6. Let s be p(-4). Factor -l**2 - 15*l**5 + 2*l**4 - l**s + 2*l**3 + 13*l**5.
-2*l**2*(l - 1)**2*(l + 1)
Let f be (-4)/7 + (145314/(-252))/(-23). Factor 12*g + 2 + 21/2*g**2 - f*g**3.
-(g - 1)*(7*g + 2)**2/2
Let y = 33 + -25. Suppose -4*w + y = -12. Factor -w*i**3 - 5*i**2 - 1/2*i**5 - 5/2*i - 1/2 - 5/2*i**4.
-(i + 1)**5/2
Let r = 64546/13445 + -2/2689. Factor 18/5*n - r*n**2 - 4/5 + 2*n**3.
2*(n - 1)**2*(5*n - 2)/5
Let s be 4/16 + (0 - (-1)/(-4)). Let k(z) be the second derivative of -1/10*z**2 - z + s + 0*z**3 + 1/60*z**4. Solve k(h) = 0.
-1, 1
Let f(m) be the first derivative of -3*m**5/35 + 3*m**4/7 - 3*m**3/7 + 15. Factor f(v).
-3*v**2*(v - 3)*(v - 1)/7
Let f(k