p. Solve k(r) = 0 for r.
-1, 1, 2
Let s(y) be the second derivative of y**6/120 - y**4/8 - y**3/3 + y. Let g(m) be the second derivative of s(m). Determine u so that g(u) = 0.
-1, 1
Let f = 16 - 6. Suppose 2 = -2*y + 5*k + 1, 3*y = k + 5. Suppose f*a - 5 + 4 - 3 + 24*a**y = 0. What is a?
-2/3, 1/4
Let w(r) be the second derivative of -r**4/4 - r**3 - 8*r. Determine x so that w(x) = 0.
-2, 0
Let i be 6*(-2 + (-4)/(-6)). Let v be (0 - -3)*i/(-12). Factor 4*s**2 - 14*s**3 - 3*s**5 + 16*s**4 + 0*s**v - 3*s**5.
-2*s**2*(s - 1)**2*(3*s - 2)
Suppose 12 = 7*q - 4*q. Let w(f) be the second derivative of -4*f + 9/50*f**6 + 0*f**2 + 1/5*f**3 + 13/20*f**q + 0 + 3/5*f**5. Solve w(p) = 0.
-1, -2/9, 0
Let j(h) = -h**3 - 10*h**2 - 10*h - 6. Let x be j(-9). Suppose x*i = i + 4. Factor 0 - 2/7*w - 2/7*w**i.
-2*w*(w + 1)/7
Factor 2 + 6*h + h**3 + 2 - 2 + 4*h**2 - h.
(h + 1)**2*(h + 2)
Let p = 15 - 13. Let b(h) be the second derivative of -p*h + 1/45*h**5 + 0*h**4 + 0 + 0*h**2 - 1/135*h**6 + 0*h**3. Let b(l) = 0. What is l?
0, 2
Let u = -69 - -72. Solve 12/7*r - 4/7 - 12/7*r**2 + 4/7*r**u = 0.
1
Let p(a) be the first derivative of -a**7/2520 - a**6/540 - a**5/360 - 4*a**3/3 + 5. Let l(x) be the third derivative of p(x). Suppose l(u) = 0. Calculate u.
-1, 0
Suppose -i + 2*u + 1 = 0, 3*u - 3 + 7 = 2*i. Let -8/3*t**i + 2/3*t**4 + 0*t + 0 + 8/3*t**3 - 2/3*t**2 = 0. Calculate t.
-1, 0, 1/4, 1
Let o = -10/107 - -1645/428. Determine d, given that o*d + 3*d**2 + 3/4 = 0.
-1, -1/4
Let d(h) be the first derivative of -h**6/3 + 2*h**5 - 5*h**4 + 20*h**3/3 - 5*h**2 + 2*h - 10. Factor d(p).
-2*(p - 1)**5
Let m(y) = y**2 - 8*y + 7. Let w be m(9). Find s, given that 5*s - s + 4*s + w*s**3 + 36*s**2 = 0.
-2, -1/4, 0
Suppose -3*k - 4*l + 29 = 0, 2 = -3*k + 2*l + 1. Let -k + 4*x**2 - 4*x**2 + 3*x**2 = 0. Calculate x.
-1, 1
Suppose 4*v + 4*k + 64 = 0, v - 4*k - 4 = 2*v. Let h be (4/(-10))/(4/v). Solve 14*j + j**h - 14*j = 0 for j.
0
Let s(n) = -2*n**2 + 12*n + 2. Let r be s(6). Factor 2/3*p - r*p**2 + 4/3.
-2*(p - 1)*(3*p + 2)/3
Let l(p) be the third derivative of 1/48*p**4 + 1/120*p**5 + 0*p**3 + 0 + 0*p + 3*p**2. Factor l(s).
s*(s + 1)/2
Suppose 38 = -3*f + 4*p, f + 0*p - 5*p = -31. Let n = f + 8. Suppose 12*a + 2*a**3 + n*a - 1 - 5 - 10*a**2 = 0. What is a?
1, 3
Let o(g) be the third derivative of g**8/43680 + g**7/3276 + g**6/1560 - 3*g**5/260 - g**4/6 + 5*g**2. Let c(k) be the second derivative of o(k). Factor c(y).
2*(y - 1)*(y + 3)**2/13
Factor -10*c + 14/3*c**2 - 2/3*c**3 + 6.
-2*(c - 3)**2*(c - 1)/3
Let k = -779/55 + 158/11. Solve 1/5 + 1/5*v - k*v**2 - 1/5*v**3 = 0 for v.
-1, 1
Factor 1/4*g + 0*g**2 + 0 - 1/4*g**3.
-g*(g - 1)*(g + 1)/4
Let v be 10*(-8)/(-160) - 6/28. What is y in 1/7*y**3 + 3/7*y**2 + v*y + 0 = 0?
-2, -1, 0
Suppose -3*q = -8*q. Let u(i) be the third derivative of 0*i**4 + 1/60*i**5 + 0 - 1/120*i**6 + i**2 + 1/336*i**8 + q*i + 0*i**3 - 1/210*i**7. Factor u(d).
d**2*(d - 1)**2*(d + 1)
Solve 23*s**2 - 50*s**2 - 12*s + 23*s**2 = 0.
-3, 0
Let s(u) be the second derivative of -u**5/120 - u**4/24 + 9*u**2/2 - 2*u. Let c(i) be the first derivative of s(i). Factor c(n).
-n*(n + 2)/2
Let s(w) = -14*w**2 + 10*w. Let d(q) = 13*q**2 - 11*q. Let h(g) = -4*d(g) - 3*s(g). What is r in h(r) = 0?
0, 7/5
Let d = -17 + -1. Let t be ((-1)/(-3))/((-2)/d). Factor -3*g**t - 11 + g + 8*g + 5.
-3*(g - 1)**2*(g + 2)
Let p(y) be the first derivative of 0*y**2 + 0*y**3 - 1 + 0*y - 1/9*y**4 - 7/27*y**6 - 2/5*y**5. Factor p(u).
-2*u**3*(u + 1)*(7*u + 2)/9
Let v(c) be the second derivative of c**6/150 + c**5/25 + c**4/15 + 3*c. Solve v(o) = 0.
-2, 0
Let x(p) = 2*p**3 - 38*p**2 + 50*p - 24. Let i(m) = -m**3 + 13*m**2 - 17*m + 8. Let q(z) = 10*i(z) + 3*x(z). Factor q(t).
-4*(t - 2)*(t - 1)**2
Let w(s) be the first derivative of 2*s**3/27 - 4*s**2/9 + 8*s/9 + 17. Find g such that w(g) = 0.
2
Let n(u) be the third derivative of u**6/24 - u**5/4 - 5*u**4/6 + 10*u**3 - 40*u**2. Factor n(o).
5*(o - 3)*(o - 2)*(o + 2)
Let a(h) be the second derivative of -h**8/6720 + h**7/2520 + h**6/360 - h**4/6 + 3*h. Let i(k) be the third derivative of a(k). Factor i(d).
-d*(d - 2)*(d + 1)
Let v be 24/132 - 3/(-44). Suppose v*u**2 + 4 - 2*u = 0. Calculate u.
4
Let c(m) = 3*m**3 - 3*m**2 - 3*m - 5. Let l(w) = -w**3 + w**2 + w + 2. Let d(s) = -3*c(s) - 8*l(s). Suppose d(j) = 0. Calculate j.
-1, 1
Let b(x) = x. Let j(q) = -12*q**2 - 42*q - 33. Let s(r) = 6*b(r) + j(r). Let n(p) = -3*p**2 - 9*p - 8. Let d(f) = 9*n(f) - 2*s(f). Suppose d(u) = 0. What is u?
-2, -1
Determine w, given that -3*w + 4*w**2 + 7*w + w**5 + 82*w**4 - 84*w**4 - 3*w**3 = 0.
-1, 0, 2
Let k be ((-12)/27)/(-2 + 0). Suppose -4*s = s. Determine n so that -k*n**2 - 2/9*n + s = 0.
-1, 0
Determine x, given that -47*x + 48 - 30*x**3 - 2*x**4 - 41*x + 5*x**4 + 99*x**2 - 32*x = 0.
1, 4
Let p(d) = 4*d + 52. Let k be p(-13). Let m(o) be the third derivative of 1/180*o**5 + 0 - 1/360*o**6 + 0*o**4 + 0*o**3 + k*o + o**2. Factor m(i).
-i**2*(i - 1)/3
Let h(o) = -11*o**2 - 9*o + 11. Let y(z) = -z**2 - z + 1. Let u(m) = -2*h(m) + 18*y(m). Let u(x) = 0. What is x?
-1, 1
Let l(g) = 9*g - 63. Let n be l(7). Let -2/7*x**3 + 0*x**2 + 0 + n*x = 0. Calculate x.
0
Let r(a) = a - 5. Let t be r(5). Suppose -n - 1 = i, 4 = -n + 4*i + 18. Factor -3/2*z + 3/2*z**n + t.
3*z*(z - 1)/2
Factor -48 - 166*l**2 + 76*l**2 - 32*l + 86*l**2.
-4*(l + 2)*(l + 6)
Let r(m) be the third derivative of m**7/3780 + m**6/540 + m**5/180 + m**4/108 - m**3/6 + 2*m**2. Let a(h) be the first derivative of r(h). Factor a(y).
2*(y + 1)**3/9
Let m = -13 + 13. Let l(x) be the first derivative of 0*x**3 + 0*x**2 + 1/3*x**6 + 1 - 1/2*x**5 + m*x + 1/8*x**4. Factor l(k).
k**3*(k - 1)*(4*k - 1)/2
Let b(c) be the first derivative of -4*c**5/5 + 4*c**4 - 4*c**3 - 8*c**2 + 16*c - 65. Suppose b(x) = 0. What is x?
-1, 1, 2
Let a(f) be the third derivative of f**6/75 - f**5/75 - 2*f**4/15 + 2*f**3/5 + 8*f**2. Factor a(t).
4*(t - 1)**2*(2*t + 3)/5
Let h be 15/1 - (-3)/(-1). Factor 2 - 4*g**3 - 10*g - 3*g**4 + h*g + g**5 + g**5 + 5*g**4 - 4*g**2.
2*(g - 1)**2*(g + 1)**3
Let b = 324 - 1289/4. Let l(s) be the first derivative of 0*s**2 + 7/6*s**6 + 4 + 0*s + 2/3*s**3 - b*s**4 - 2/5*s**5. Factor l(t).
t**2*(t - 1)*(t + 1)*(7*t - 2)
Solve -2*h - 1/4*h**3 - 1 - 5/4*h**2 = 0.
-2, -1
Suppose -9*h = h - 40. Let i(l) be the first derivative of h*l - 2/3*l**3 + l**2 + 2. Suppose i(j) = 0. What is j?
-1, 2
Let z(u) = -7*u + 1. Let t be z(-2). What is l in -17*l**2 - 54*l**4 - 7*l + t*l**5 + 6 + 66*l**3 - 7*l**2 - 2*l = 0?
-2/5, 1
Let y(u) be the second derivative of -2*u**4/3 + 6*u**3 + 10*u**2 + 16*u. Factor y(b).
-4*(b - 5)*(2*b + 1)
Find o such that 1/4*o**2 - 1/2*o - 3/4 = 0.
-1, 3
Let y(c) be the third derivative of -c**6/40 - 3*c**5/4 - 75*c**4/8 - 125*c**3/2 + 4*c**2. Find m, given that y(m) = 0.
-5
Let t(d) = d**2 + 13*d + 3. Let z be t(-13). Solve 2/5*y - 2/5*y**z + 0 + 0*y**2 = 0.
-1, 0, 1
Let a(b) = -7*b**3 + 5. Let v(q) = -6*q**3 + q. Let c be v(-1). Let w(r) = 4*r**3 - 3. Let z(s) = c*w(s) + 3*a(s). Solve z(n) = 0 for n.
0
Let f = -64 + 68. Let a(o) be the third derivative of 0*o - 1/4*o**f + 3*o**2 + 1/20*o**5 + 0 + 1/2*o**3. Suppose a(t) = 0. Calculate t.
1
Let g(t) be the second derivative of -1/36*t**4 + t + 0*t**3 - 1/60*t**5 + 0*t**2 + 0. Solve g(h) = 0 for h.
-1, 0
Suppose -2*q = -0*q - 4. Solve 2*z**4 - 16*z - 25*z**2 - 7 + 13*z**q + 1 = 0 for z.
-1, 3
Suppose 11 = 4*r + 11. Let b = -4 - -8. Let r*l + 1/3*l**2 - 1/2*l**3 + 0 + 1/6*l**b = 0. What is l?
0, 1, 2
Factor 2*h - 8/7*h**3 + 10/7*h**2 - 4/7.
-2*(h - 2)*(h + 1)*(4*h - 1)/7
Suppose 0 = p + 2*j - 2, -19*p + 35 = -15*p - j. Find b such that -14*b**2 - p*b - 8/7 = 0.
-2/7
Factor 0*j + 0*j**2 - 2/5*j**4 + 0 - 8/5*j**3.
-2*j**3*(j + 4)/5
Factor 10/13*o + 2/13*o**3 - 4/13 - 8/13*o**2.
2*(o - 2)*(o - 1)**2/13
Let r(u) be the second derivative of 2*u**7/21 - 2*u**6/5 + 2*u**5/5 + 2*u**4/3 - 2*u**3 + 2*u**2 - 25*u. What is m in r(m) = 0?
-1, 1
Let q(k) be the second derivative of 2*k + 5/9*k**3 - 2/9*k**4 + 0 + 1/30*k**5 - 2/3*k**2. Solve q(c) = 0 for c.
1, 2
Let j(i) be the second derivative of 245*i**4/12 - 35*i**3/3 + 5*i**2/2 - 42*i. Factor j(o).
5*(7*o - 1)**2
Let n(l) be the first derivative of l**4 - 4*l**3/3 - 4*l**2 + 5. Factor n(c).
4*c*(c