 - 1. Let j(i) = 21*i**5 - 24*i**4 - 18*i**3 + 24*i**2 - 9*i + 6. Let w(f) = -j(f) - 6*m(f). Let w(p) = 0. What is p?
-1, 0, 1/3, 1
Let w(q) be the second derivative of -3*q + 1/75*q**6 + 0*q**3 - 1/50*q**5 + 0 - 1/15*q**4 + 0*q**2. Factor w(l).
2*l**2*(l - 2)*(l + 1)/5
Suppose 2 = -w + 6. Factor 2*f**3 + f**2 - 4*f**4 + 2*f**w - f**3.
-f**2*(f - 1)*(2*f + 1)
Let b = 3/20 - -1/20. Let u(w) be the first derivative of -1 + 1/15*w**6 - 2/25*w**5 + b*w**2 - 1/5*w**4 - 2/5*w + 4/15*w**3. Find g, given that u(g) = 0.
-1, 1
Let p be -9 + 0 - (-12)/4. Let d be -1 + p/(-15) - -1. Factor -d - 16/5*t**3 + 12/5*t**2 + 6/5*t**4 + 0*t.
2*(t - 1)**3*(3*t + 1)/5
Let y(b) be the third derivative of -b**7/420 + b**6/120 + b**5/40 - b**4/12 - b**3/3 + 3*b**2. Find u such that y(u) = 0.
-1, 2
Let t(o) be the third derivative of -o**3 - 1/90*o**5 + 0 + 3*o**2 - 1/6*o**4 + 0*o. Solve t(k) = 0.
-3
Let p(r) be the third derivative of r**7/42 - r**6/6 + r**5/2 - 5*r**4/6 + 5*r**3/6 - 25*r**2. Factor p(g).
5*(g - 1)**4
Suppose 0 = -0*d + 6*d - 5*d. Determine x so that 2/3*x**2 - 2/3*x**4 + 2/3*x**5 + d - 2*x**3 + 4/3*x = 0.
-1, 0, 1, 2
Let z(x) be the third derivative of -3*x**2 - 2/33*x**3 + 8/165*x**5 - 1/132*x**4 + 26/1155*x**7 + 0 + 17/330*x**6 + 0*x + 1/264*x**8. Factor z(m).
2*(m + 1)**4*(7*m - 2)/11
Suppose f + 40 = -4*f. Let p(h) = h + 17. Let x be p(f). Factor 3*i**2 - 2 + 0*i**2 + 9*i**2 - x*i**3 - i.
-(i - 1)*(3*i - 2)*(3*i + 1)
Factor 6*a + 2 + 10 - 2*a**2 - 5 + 1.
-2*(a - 4)*(a + 1)
Let k = 30301/60 - 505. Let y(g) be the third derivative of k*g**5 - 1/24*g**4 + 0*g**3 + 0*g - g**2 + 0. Solve y(a) = 0.
0, 1
Let 8/3*r - 4/3*r**2 - 8/3*r**3 + 2 - 2/3*r**4 = 0. Calculate r.
-3, -1, 1
Factor 16*k**2 + 52*k**3 - 59*k**2 - 4*k**4 - 5*k**2.
-4*k**2*(k - 12)*(k - 1)
Let d(a) = 2*a - 1. Let i be d(2). Suppose -4*q + 5*y + 5 = q, -3*q = i*y - 9. Let q*w**4 - w**5 + 0*w**4 - w**5 = 0. What is w?
0, 1
Let x be 11/(-110) - (-147)/70. Factor -x*r**3 + 5/2*r**2 - 1/2*r + 0.
-r*(r - 1)*(4*r - 1)/2
Find s such that 10/13 - 2/13*s - 8/13*s**2 = 0.
-5/4, 1
Determine w, given that 18*w**3 - 5*w**4 + 4*w**4 - w**4 + 5*w**4 + 27*w**2 = 0.
-3, 0
Suppose 0 = -8*p - 2*p. Suppose -2*g + 2 = -2. Factor 1/4*u + p*u**g + 0 - 1/4*u**3.
-u*(u - 1)*(u + 1)/4
Let w(l) be the second derivative of -89/6*l**4 + 0 + 32/3*l**3 - 4*l**2 - 9*l - 17/5*l**6 + 103/10*l**5 + 3/7*l**7. Find h such that w(h) = 0.
1/3, 1, 2
Let v(c) be the third derivative of -1/105*c**5 + 1/21*c**3 + 0*c + 0*c**6 + c**2 + 1/735*c**7 + 0*c**4 + 0. Suppose v(g) = 0. Calculate g.
-1, 1
Suppose -5*y + 7 = -2*r, y + 24 = r + 4*y. Let f(z) = -z**2 + 9*z + 4. Let w be f(r). Factor 18/5*n**2 + 12/5*n**w + 3/5*n + 0 + 27/5*n**3.
3*n*(n + 1)**2*(4*n + 1)/5
Suppose 4*a - 4*u - 4 = 0, 2*u = 4*a + 3*u - 14. Let i(r) = -2*r**3 + 5*r**2 - 4*r - 2. Let d(x) = x**3 - x**2 + x. Let f(n) = a*d(n) + i(n). Factor f(v).
(v - 1)*(v + 1)*(v + 2)
Let x(z) be the third derivative of z**9/648 + z**8/210 + z**7/420 - z**6/270 + 3*z**3/2 - 6*z**2. Let d(g) be the first derivative of x(g). Factor d(q).
2*q**2*(q + 1)**2*(7*q - 2)/3
Let g(s) = 2*s - 20. Let i be g(10). Factor -1/2*u**2 - 1/2*u**4 + 0 - u**3 + i*u.
-u**2*(u + 1)**2/2
Let f(k) be the second derivative of k**4/66 - 2*k**3/33 - 25*k. Factor f(c).
2*c*(c - 2)/11
Let g(y) be the third derivative of y**9/241920 - y**8/40320 + y**5/60 + 2*y**2. Let c(o) be the third derivative of g(o). Factor c(u).
u**2*(u - 2)/4
Let d(n) be the second derivative of -n**6/75 - n**5/50 + n**4/30 + n**3/15 - 25*n. Factor d(v).
-2*v*(v - 1)*(v + 1)**2/5
Let o(q) be the third derivative of -q**5/20 + 7*q**4/8 - 6*q**2 + 4*q. Factor o(s).
-3*s*(s - 7)
Suppose -23 = 5*u - 8. Let w = -1 - u. Determine c so that -2*c**4 - 2 - 3*c**2 + 3 + 3*c**4 + c**w = 0.
-1, 1
Let v = 75 - 374/5. Suppose -v*b + 0 - 2/5*b**2 = 0. What is b?
-1/2, 0
Let d be 6/9*(-18)/4. Let a be (-12)/d*9/60. Factor 6/5 - 3/5*v - a*v**2.
-3*(v - 1)*(v + 2)/5
Let 3/2*f**3 + 3/4 + 1/4*f**4 + 5/2*f + 3*f**2 = 0. Calculate f.
-3, -1
Let f(r) = r**3 + r**2 - r. Let g(x) = -6*x**3 - x**2 + 6*x. Let p(z) = f(z) + g(z). Let p(d) = 0. Calculate d.
-1, 0, 1
Let p(l) be the second derivative of l**6/120 - l**5/60 + 3*l**2/2 + 2*l. Let j(g) be the first derivative of p(g). Find u, given that j(u) = 0.
0, 1
Suppose -2*l = -3*l + 4. Suppose -33*i + 29*i + 3*i**2 + 0*i**2 - l = 0. What is i?
-2/3, 2
Let z(d) = -4*d**3 - 27*d**2 - 96*d - 64. Let h(w) = w**3 + 7*w**2 + 24*w + 16. Let i(r) = -9*h(r) - 2*z(r). Factor i(u).
-(u + 1)*(u + 4)**2
Let o be 0*-1*5/(-10). Solve -1/2 + 3/4*c + o*c**2 - 1/4*c**3 = 0.
-2, 1
Suppose -f + 6 = 2*f. Let m be 3/18*3/f. Determine h, given that -m*h + 1/2*h**3 - 1/4*h**5 + 0*h**2 + 0*h**4 + 0 = 0.
-1, 0, 1
Determine f so that 0 - 2*f - 10*f**2 - 25/2*f**3 = 0.
-2/5, 0
Let f be 6/8 + (-1)/4. Let g(a) be the first derivative of f*a**4 + 2*a + 3*a**2 - 2 + 2*a**3. Factor g(u).
2*(u + 1)**3
Let l be 2/(-2)*(0 + 0). Suppose 0 = -x - l*x. Suppose x*d + 0*d - 6*d**2 + 2*d + 6*d**3 - 2*d**4 = 0. What is d?
0, 1
Let h be ((-5)/190)/(2/(-4)). Let g = 16/57 + h. Factor 2/3*y - g*y**3 + 0 - 1/3*y**2.
-y*(y - 1)*(y + 2)/3
Let y(f) = -2*f - 2. Let q be y(-6). Let m be 26/10 + q/25. Factor 0*d + 2/5*d**2 + 0 - 2/5*d**m.
-2*d**2*(d - 1)/5
Let t(o) = o**3 + o**2 + o. Let p(r) = -9*r**2 + 18. Let g(i) = -p(i) + 3*t(i). Factor g(x).
3*(x - 1)*(x + 2)*(x + 3)
Let m(a) be the first derivative of -a**4/24 + a**3/18 + a**2/12 - a/6 - 7. Factor m(f).
-(f - 1)**2*(f + 1)/6
Solve -29*d - 4*d**5 - 57*d**3 + 10*d**5 - 21*d**4 - 75*d**2 - 9*d**5 - 19*d - 12 = 0 for d.
-2, -1
Let 0*c**2 - 1/3 + 2/3*c - 2/3*c**3 + 1/3*c**4 = 0. What is c?
-1, 1
Factor -2/17*h**2 - 4/17 + 6/17*h.
-2*(h - 2)*(h - 1)/17
Let n be (16 - 17)*(-3)/(-1). Let c be (24/(-126))/(2/n). Factor 2/7*a**2 + c*a**5 + 16/7*a + 8/7 - 10/7*a**3 - 2/7*a**4.
2*(a - 2)**2*(a + 1)**3/7
Let q(y) = -5*y**3 - 9*y**2. Let v(a) = -6*a**3 - 10*a**2 + a. Let o(b) = 5*q(b) - 4*v(b). Find t such that o(t) = 0.
-4, -1, 0
Let j(f) be the third derivative of -f**8/3024 + 2*f**7/945 - f**6/270 - f**5/270 + 5*f**4/216 - f**3/27 + f**2. What is t in j(t) = 0?
-1, 1, 2
Let u(c) be the first derivative of -6*c**5/25 + c**4/2 - 2*c**3/15 - c**2/5 + 28. Factor u(a).
-2*a*(a - 1)**2*(3*a + 1)/5
Let t(n) = 2*n**3 - 8*n**2 - 6*n - 18. Let s be t(5). Suppose -8/3 - 8/3*z - 2/3*z**s = 0. What is z?
-2
Suppose f - 3*f = -6. Factor -4 + 5*p - 9*p**2 - 5*p - f*p + 10.
-3*(p + 1)*(3*p - 2)
Let v(r) be the third derivative of 0*r + 1/9*r**3 + 2/15*r**5 - 7/36*r**4 - 2*r**2 + 0. Factor v(s).
2*(3*s - 1)*(4*s - 1)/3
Let r be 14/2 + 3*(-5)/3. Factor -1/7*u**r + 1/7 + 1/7*u**3 - 1/7*u.
(u - 1)**2*(u + 1)/7
Let x(p) be the second derivative of p**4/66 - 2*p**3/33 + p**2/11 + 3*p. Determine s so that x(s) = 0.
1
Let s(u) = -u**5 - 12*u**4 - 10*u**3 + 6*u**2 + 13*u + 8. Let i(a) = -12*a**4 - 9*a**3 + 6*a**2 + 12*a + 9. Let v(c) = 2*i(c) - 3*s(c). Factor v(f).
3*(f - 1)*(f + 1)**3*(f + 2)
Let k(a) = -a**3 - 4*a**2 + 5*a + 4. Let o be k(-5). Solve u - 9*u**3 - 12*u**5 - 4 + 3*u**2 + o - 23*u**4 = 0.
-1, -1/4, 0, 1/3
Let r(a) be the second derivative of -1/105*a**6 + 0*a**2 + 0 + 0*a**4 - 1/70*a**5 + 0*a**3 - a. Factor r(q).
-2*q**3*(q + 1)/7
Let v(r) = r**3 - 7*r**2 + 5*r - 4. Let s be v(6). Let o be 8/3 - s/(-15). Suppose 0*g**o - 4*g**2 + 1 - 2*g + 5*g**2 = 0. Calculate g.
1
Let v(z) = -z**3 - 10*z**2 - 17*z - 8. Let j be v(-8). Determine u so that 1/2*u + j + 1/2*u**3 + u**2 = 0.
-1, 0
Let j be 3 + (-3 - -1)/(3 + -4). What is y in 201/5*y**2 - 21/5*y**j - 219/5*y**3 - 84/5*y + 111/5*y**4 + 12/5 = 0?
2/7, 1, 2
Let a be (-589)/(-399) - (-2)/(-14). Let t(s) be the second derivative of -a*s**3 + 0 + 4*s**2 + s + 1/6*s**4. Factor t(r).
2*(r - 2)**2
Let d(g) be the second derivative of -1/60*g**5 + 0*g**2 - 1/36*g**4 + 0*g**3 + 1/126*g**7 + 2*g + 1/90*g**6 + 0. Factor d(t).
t**2*(t - 1)*(t + 1)**2/3
Determine a so that 6/11*a**2 - 4/11*a**3 - 2/11 + 0*a = 0.
-1/2, 1
Let w(j) be the first derivative of 1 + 1/48*j**4 + 1/2*j**2 + 1/240*j**5 + 0*j + 1/24*j**3. Let a(m) be the second derivative of w(m). Factor a(c).
(c + 1)**2/4
Let w = 5 - 2. Factor 1 + 6*t**2 + t**4 + 7*t**3 - t**3 - 2*t**w + 3*t + t.
(t + 1)**4
Let t be (2/4 - -1)/(17/34