3
Let c(o) be the first derivative of -o**4/48 + o**3/24 - o - 3. Let p(v) be the first derivative of c(v). Determine w so that p(w) = 0.
0, 1
Let o(w) be the second derivative of -w**5/210 - 3*w**2/2 - w. Let k(z) be the first derivative of o(z). Factor k(v).
-2*v**2/7
Let k(c) be the third derivative of -c**6/240 + c**5/60 + c**4/16 - c**2. What is b in k(b) = 0?
-1, 0, 3
Let b(g) be the second derivative of g**6/30 + 3*g**5/20 + g**4/4 + g**3/6 - 22*g. Factor b(d).
d*(d + 1)**3
Let c(q) = -3*q**4 + 12*q**3 + 31*q**2 + 24*q + 13. Let o(n) = 5*n**4 - 18*n**3 - 47*n**2 - 36*n - 20. Let v(k) = 8*c(k) + 5*o(k). Factor v(g).
(g + 1)**2*(g + 2)**2
Let o(c) be the first derivative of 21/5*c**5 + 3 - 12*c**3 - 6*c**2 + 0*c + 27/4*c**4. Solve o(m) = 0 for m.
-2, -2/7, 0, 1
Suppose 1084 + 7124 = 19*o. What is j in -1/2 - 108*j**2 - 648*j**4 + o*j**3 + 12*j = 0?
1/6
Factor 8*l + 22*l**2 + 0*l + 11*l**2 + 3*l**2.
4*l*(9*l + 2)
Suppose 15 = 3*g + 3. Let d be (6/(-4))/(4/(-8)). Factor -6*u**d + 4*u**4 - 2*u**5 + 0*u**g + 2*u**4 + 2*u**2.
-2*u**2*(u - 1)**3
Let a be (-42)/(-18) - (-2)/(-6). Factor a*z**2 - 14*z**2 - 5*z**4 + 12*z**3 - z**4 + 3*z**4.
-3*z**2*(z - 2)**2
Let n(l) be the second derivative of -l**7/1260 + l**6/270 - l**5/180 - l**3/3 + 2*l. Let y(o) be the second derivative of n(o). Factor y(s).
-2*s*(s - 1)**2/3
Suppose -4*z + c = -8, z + 8*c - 2 = 5*c. Let p be (-1)/2*4/(-10). Factor p*g**3 - 3/5*g + 2/5 + 0*g**z.
(g - 1)**2*(g + 2)/5
Suppose 5*c - 20 = -5*g, 10 = -0*c + 3*c + 2*g. Suppose 2*f - 3*f = -4*h + 8, 2*f - c*h - 8 = 0. Find a such that 16*a**3 + a + 6*a**4 + f*a**2 - a = 0.
-2, -2/3, 0
Let i(h) be the third derivative of -10*h**2 - 2/35*h**7 - 1/15*h**5 + 0 - 1/6*h**6 + 0*h + 1/6*h**4 + 0*h**3. Find x such that i(x) = 0.
-1, 0, 1/3
Let l be 5/((-50)/(-12))*-10. Let g be l/(-5) + 10/(-25). Factor 1/3*x**g + 0*x - 1/3.
(x - 1)*(x + 1)/3
Let p(z) be the first derivative of 1 + 1/3*z**3 - z + 0*z**2. Factor p(o).
(o - 1)*(o + 1)
Let p = 12 - 9. Suppose -3*q - m - 4*m = -30, q = -5*m + 20. Suppose -2*n**4 + q*n + 8*n**p - n - 12*n**2 + 2*n**2 = 0. Calculate n.
0, 1, 2
Let m(z) = -z**2 + 8*z - 4. Let p be m(7). Suppose -d = -3*i + 9, 5*i - 4*d - 16 = -1. What is b in -14*b**2 + 13*b + i + 1 - p*b = 0?
-2/7, 1
Let v(m) be the second derivative of 1/12*m**4 - 1/2*m**2 + m - 1/6*m**3 - 1/60*m**5 + 0. Let q(i) be the first derivative of v(i). Factor q(l).
-(l - 1)**2
Let 40*z**2 + z**4 - 5*z**4 + 5*z**5 - 10*z**3 - z**4 - 35*z + 10 - 5*z**4 = 0. What is z?
-2, 1
Let l be (20/8 + -2)/4*1. Let j(v) be the third derivative of -l*v**4 - 11/40*v**5 + 0*v + 0*v**3 - 1/5*v**6 - 1/20*v**7 + 0 + v**2. Factor j(o).
-3*o*(o + 1)**2*(7*o + 2)/2
Let r be 2/(-5)*80/(-64). Find z, given that z**2 + r*z - 1 - 1/2*z**3 = 0.
-1, 1, 2
Let l(z) be the second derivative of -z**7/28 + z**6/3 - 39*z**5/40 + 5*z**4/4 - 2*z**3/3 - 9*z. Find h, given that l(h) = 0.
0, 2/3, 1, 4
Let d(r) be the third derivative of r**6/240 - r**5/20 + r**4/4 - 2*r**3/3 + 13*r**2. Determine o, given that d(o) = 0.
2
Let 12/7*k**3 + 0 + 16/7*k**2 - 16/7*k = 0. What is k?
-2, 0, 2/3
Let t(p) be the second derivative of p**8/1680 - p**7/840 + p**3/6 + 3*p. Let h(l) be the second derivative of t(l). Let h(f) = 0. What is f?
0, 1
Let q(m) be the first derivative of -3*m**4/4 - 7*m**3 - 15*m**2 - 31. Suppose q(l) = 0. Calculate l.
-5, -2, 0
Let c = 475/6 + -79. Let d(o) be the second derivative of 0*o**2 - 1/12*o**4 - 3*o + 1/30*o**6 - c*o**3 + 1/20*o**5 + 0. Let d(g) = 0. Calculate g.
-1, 0, 1
Let v = 1 - -1. Factor -4*o**3 + o**5 - 4*o**4 + 2*o**v - 1 + 2*o**3 + o + 3*o**4 + 0*o**3.
(o - 1)**3*(o + 1)**2
Let o(y) be the first derivative of y**4/4 + 4*y**3/3 + 5*y**2/2 + 2*y - 4. Factor o(i).
(i + 1)**2*(i + 2)
Let f be ((3 - 3)/(-2))/(-3). Let v(h) be the third derivative of h**2 + 1/240*h**5 + f*h**4 + 0*h + 0 + 0*h**3. Factor v(x).
x**2/4
Let h = -1/6 + 5/18. Let f(q) be the second derivative of 1/12*q**2 - h*q**3 + 0 + 1/30*q**5 - 1/45*q**6 + 1/24*q**4 + 2*q. What is g in f(g) = 0?
-1, 1/2, 1
Let a(z) be the first derivative of -z**4/10 - 4*z**3/15 + 7*z**2/5 - 8*z/5 - 20. Factor a(t).
-2*(t - 1)**2*(t + 4)/5
Let c(n) be the first derivative of 1/3*n**4 + 0*n**3 - 2/3*n**2 + 2/15*n**5 + 2 - 2/3*n. Factor c(s).
2*(s - 1)*(s + 1)**3/3
Let p(u) = -13*u**3 + 57*u**2 - 153*u. Let z(x) = 3*x**3 - 14*x**2 + 38*x. Let d(f) = -2*p(f) - 9*z(f). Factor d(j).
-j*(j - 6)**2
Let o(y) be the second derivative of -y**6/30 + 3*y**5/20 - y**4/4 + y**3/6 - y + 11. Solve o(v) = 0 for v.
0, 1
Let g = 51/8 + -137/24. Find x, given that 5/3*x**3 + 2/3*x**4 + 1/3*x**2 - g*x + 0 = 0.
-2, -1, 0, 1/2
Let j(c) = -c**4 - c**3 + c**2 - c - 1. Let x(y) = 10*y**4 + 20*y**3 - 22*y**2 + 16*y + 12. Let u(p) = -12*j(p) - x(p). Find t, given that u(t) = 0.
0, 1, 2
Let j(i) = 5*i**2 + 2*i + 2. Let n be j(-1). Let q(g) be the first derivative of 2*g + 0*g**3 - 2 - 2*g**2 + g**4 - 2/5*g**n. Factor q(a).
-2*(a - 1)**3*(a + 1)
Let l(p) = p - 7. Let y be l(12). Let i be (6/18)/(y/3). Solve 1/5*t**2 + 0*t + 4/5*t**3 - i*t**4 - 4/5*t**5 + 0 = 0.
-1, -1/4, 0, 1
Let j(c) be the second derivative of 9*c**5/70 + 5*c**4/42 - 4*c**3/21 - 30*c. Find r such that j(r) = 0.
-1, 0, 4/9
Let f(k) be the first derivative of -k**4/10 + 3*k**2/5 - 4*k/5 - 9. Find g such that f(g) = 0.
-2, 1
Factor -2/7*a**2 + 2/7*a**4 + 6/7*a**3 - 6/7*a + 0.
2*a*(a - 1)*(a + 1)*(a + 3)/7
Let c be (3/15 - 0) + (-18)/(-10). Let u(t) be the second derivative of 0*t**3 - 1/5*t**2 + 0 + 1/30*t**4 - c*t. What is l in u(l) = 0?
-1, 1
Let i(u) be the first derivative of -4*u - 20/3*u**3 - 6 + 3/2*u**4 + 9*u**2. Factor i(t).
2*(t - 2)*(t - 1)*(3*t - 1)
Suppose 5*h = -8 + 33. Suppose -16*w**3 + 2 + h*w - 11*w**2 + 2*w**3 + 0*w**3 = 0. What is w?
-1, -2/7, 1/2
Let y(l) = l**3 - l**2 - l + 3. Let t be y(0). Suppose -t = -2*r + r. Factor 16*s**4 + 2*s + 22*s**2 + 30*s**r - 8*s**2 + 2*s**4.
2*s*(s + 1)*(3*s + 1)**2
Let n be (-1)/(-18)*6*9. Find r, given that 2*r**n - 2*r**2 - 1/2*r + 1/2 = 0.
-1/2, 1/2, 1
Let x(f) be the second derivative of 0 + 1/90*f**5 - f**2 + 2/9*f**3 - 1/12*f**4 - f. Let r(s) be the first derivative of x(s). What is p in r(p) = 0?
1, 2
Let i(q) = -q**3 + 2*q**2 - q + 2. Let a be i(0). Factor -2/7*c**5 - 180/7*c**3 + 486/7 + 30/7*c**4 + 540/7*c**a - 810/7*c.
-2*(c - 3)**5/7
Suppose 3*n + 4*o - 16 = 0, -5*n - o - o = -22. Suppose 0 = u + n*u - 20. Factor -6*m**2 + u*m**4 + 21*m - 4 + 6*m**4 - 14*m**3 - 7*m.
2*(m - 1)**2*(m + 1)*(5*m - 2)
Let t(p) be the third derivative of -2*p**7/315 + p**6/36 - 2*p**5/45 + p**4/36 - p**2. Factor t(g).
-2*g*(g - 1)**2*(2*g - 1)/3
Suppose 32 = 4*i - i - 5*b, 0 = 4*i + 5*b + 4. Suppose -14 = k - 3*k - 4*l, 8 = i*k - 2*l. Factor 1/4*r**k - 1/4 + 1/4*r**2 - 1/4*r.
(r - 1)*(r + 1)**2/4
Let f(z) be the third derivative of 0*z**4 + 1/180*z**6 + 0 + 0*z - 8*z**2 + 0*z**7 + 0*z**5 - 1/504*z**8 + 0*z**3. Factor f(n).
-2*n**3*(n - 1)*(n + 1)/3
Let g(w) be the second derivative of 0*w**2 + 0*w**5 + 1/12*w**4 - 1/30*w**6 + 0 + 0*w**3 - 4*w. Factor g(f).
-f**2*(f - 1)*(f + 1)
Find q, given that -6/5 + 9/5*q + 0*q**2 - 3/5*q**3 = 0.
-2, 1
Let t(s) = s**3 + 9*s**2 + 7*s - 6. Suppose f - 9 = 3*l + 12, -l - 3*f = 17. Let y be t(l). Solve -3 - 1/3*g**y - 2*g = 0 for g.
-3
Let k(j) be the third derivative of -j**8/84 - 8*j**7/105 - j**6/5 - 4*j**5/15 - j**4/6 - 5*j**2. Solve k(p) = 0 for p.
-1, 0
Let u be 4/(-2) - 1 - -1. Let f = u - -2. Factor -2/7*z**4 + 2/7*z**2 + 2/7*z - 2/7*z**3 + f.
-2*z*(z - 1)*(z + 1)**2/7
Suppose -3*z = -3*t - 30, 2*t - 5*t = 2*z - 10. Factor 3*n**2 + 5*n - z*n - 3*n**3 + 1 + 2*n**3.
-(n - 1)**3
Let n(o) be the first derivative of o**6/8 + 3*o**5/20 - 3*o**4/8 - o**3/2 + 3*o**2/8 + 3*o/4 - 2. Let n(x) = 0. What is x?
-1, 1
Suppose 0 + 2/3*u**2 + 2/3*u = 0. What is u?
-1, 0
Let c be -1 - (-2)/(-3) - -2. Suppose 0 = 2*n - 6*n. Factor 0 + c*y + n*y**2 - 1/3*y**3.
-y*(y - 1)*(y + 1)/3
Suppose -4*z = -23 - 9. Suppose -2*j = -6*j + z. What is l in -3*l + 0*l - j*l**2 + l = 0?
-1, 0
Let q = 75/11 - 115/33. Let -4/3*p**2 - q*p**3 + 0*p + 0 = 0. What is p?
-2/5, 0
Let z be 0*(6/(-24) - 3/12). Suppose 1/5*i**3 - 1/5*i**2 + z + 0*i = 0. Calculate i.
0, 1
Let j(b) be the first derivative of -5*b**6/54 + 2*b**5/45 + 3. Let 