be the second derivative of -1/15*u**6 + 0 - 2*u - u**2 + 2/5*u**5 + 4/3*u**3 - u**4. Factor z(n).
-2*(n - 1)**4
Let a(o) be the second derivative of -o**6/10 + 3*o**5/5 - o**4/2 - 2*o**3 + 9*o**2/2 - 13*o. Factor a(y).
-3*(y - 3)*(y - 1)**2*(y + 1)
Let l = -5 + 18. Let f = -9 + l. Find q such that -f*q**2 - 3*q**2 + 3*q + 3*q**2 + 3*q**2 + 1 - 3*q**3 = 0.
-1, -1/3, 1
Find t, given that 6*t**3 - 4*t**2 - 7*t**5 - 12*t**2 + 8*t + 4*t**4 + 5*t**5 = 0.
-2, 0, 1, 2
Let u(f) be the first derivative of -2*f**3/3 + 8*f + 3. Factor u(o).
-2*(o - 2)*(o + 2)
Let h(g) be the first derivative of -g**6/540 + g**5/270 - g**2 - 3. Let d(v) be the second derivative of h(v). Find w, given that d(w) = 0.
0, 1
Let n be 141/(-27) - -5 - 16/(-18). Determine t so that 1/3*t**2 - 29/3*t**3 + n*t + 0 - 28/3*t**4 = 0.
-1, -2/7, 0, 1/4
Suppose 3/4*g**4 - 3/4*g**3 - 3/4*g**2 + 0 + 3/4*g = 0. What is g?
-1, 0, 1
Let u = 22 - 20. Factor 3/4*r + 0*r**u - 1/2 - 1/4*r**3.
-(r - 1)**2*(r + 2)/4
Let c(w) be the second derivative of w**7/98 - 3*w**5/35 - w**4/14 + 3*w**3/14 + 3*w**2/7 - 8*w. Factor c(u).
3*(u - 2)*(u - 1)*(u + 1)**3/7
Let r(t) be the first derivative of 3*t**4/4 - 10*t**3/7 + 9*t**2/14 + 15. Factor r(q).
3*q*(q - 1)*(7*q - 3)/7
Suppose -2*j = -j - 3. Let n(c) = 5*c - 3. Let y be n(1). Factor -1/2*o**j - o + 0 - 3/2*o**y.
-o*(o + 1)*(o + 2)/2
Let w = 21 - 15. Let o(p) = -p**2 - p. Let k(a) = 3*a**2 - 3*a - 6. Let g(c) = w*o(c) + k(c). Factor g(l).
-3*(l + 1)*(l + 2)
Let r = -16912/13 + 1302. Let r*b**2 - 18/13*b + 4/13 = 0. What is b?
2/7, 1
Let n(t) be the second derivative of -2/21*t**3 + 3/70*t**5 - 1/14*t**4 + 1/49*t**7 + 0*t**2 + 1/15*t**6 - 8*t + 0. Find q, given that n(q) = 0.
-1, 0, 2/3
Let v be 3 - -1 - (-45)/(-12). Let k(t) be the second derivative of 2*t - 9/20*t**5 + v*t**3 + 0*t**2 + 2/5*t**6 - 3/28*t**7 + 0 + 0*t**4. Factor k(p).
-3*p*(p - 1)**3*(3*p + 1)/2
Let g(n) = -4*n + 21. Let m be g(5). Let a(o) be the first derivative of -3/4*o**4 - 1/5*o**5 + 0*o**2 - 2/3*o**3 + m + 0*o. Suppose a(w) = 0. Calculate w.
-2, -1, 0
Let q be 7*(2 + (-1 - -2)). Suppose -3*t = -q - 0. Factor -6 - 2*r**5 + 2*r**4 - 4*r**2 - 2*r + t*r**3 + 8 - 3*r**3.
-2*(r - 1)**3*(r + 1)**2
Let i = -6 + -7. Let j(z) = 3*z**3 + z**2 + 3*z + 5. Let d(l) = 6*l**3 + 2*l**2 + 7*l + 11. Let m(r) = i*j(r) + 6*d(r). Factor m(v).
-(v - 1)*(v + 1)*(3*v + 1)
Factor -7/4*u**3 + 0 + 3/4*u + u**2.
-u*(u - 1)*(7*u + 3)/4
Let i(g) = -g**5 + g**3 - g + 1. Let k(c) = 3*c**4 + 7 - 2*c**4 - 5*c - 6*c**5 + 6*c**3 - c**2 - 2*c. Let q(z) = -21*i(z) + 3*k(z). Factor q(n).
3*n**2*(n - 1)*(n + 1)**2
Let d be 4*(-2 + -1)/(-3). Factor 2*v + d*v - 7*v**3 + v**3 - 3*v**4 + 3*v**2.
-3*v*(v - 1)*(v + 1)*(v + 2)
Let a(p) be the second derivative of -1/98*p**7 + 0 + 3/140*p**5 + 1/70*p**6 + 0*p**3 - 1/28*p**4 - 5*p + 0*p**2. Determine v so that a(v) = 0.
-1, 0, 1
Let a(d) be the second derivative of d**7/56 - 3*d**6/40 + 9*d**5/80 - d**4/16 - 14*d. Let a(s) = 0. Calculate s.
0, 1
Let r be 1 + -1 + 28/14. Solve 18*y + y**2 - 6*y + 3*y**r = 0 for y.
-3, 0
Suppose 2*z - 10 = -3*z. Let i be ((-9)/6)/(9/(-48)*6). Let 2/3*p**3 - 2/3*p + i - 4/3*p**z = 0. What is p?
-1, 1, 2
Let f(q) be the second derivative of 5*q**4/12 + 5*q**3/3 - 20*q**2 - 2*q + 9. Find m, given that f(m) = 0.
-4, 2
Factor 9/7 - 6/7*l - 3/7*l**2.
-3*(l - 1)*(l + 3)/7
Let g(x) be the second derivative of -1/9*x**4 + 0 + 1/15*x**6 + 1/63*x**7 + 1/15*x**5 - 1/3*x**2 - 3*x - 1/3*x**3. Let g(a) = 0. Calculate a.
-1, 1
Suppose -1 = 2*k + 3. Let j = k - -2. Factor j + 2/5*n**3 + 0*n + 0*n**2.
2*n**3/5
Let r = -115/4 + 59/2. Factor r*c**2 + 0*c + 0.
3*c**2/4
Let d = -159/7 - -23. Factor 2*t + 4/7 + 10/7*t**3 + 18/7*t**2 + d*t**4.
2*(t + 1)**3*(t + 2)/7
Let f be (-2)/(-3) + 4/(-6). Suppose f = -3*p + 1 + 5. Factor -3*d**5 - 2*d**3 - 3*d**3 - 6*d**p + 5*d + 7*d**4 + 3*d**3 - 1.
-(d - 1)**3*(d + 1)*(3*d - 1)
Let j(u) be the third derivative of -u**6/24 + u**5/3 + 25*u**4/24 - 2*u**2 + u. Factor j(o).
-5*o*(o - 5)*(o + 1)
Let n = -17 + 52/3. Find o such that 1/3*o**2 + n + 2/3*o = 0.
-1
Let y = 51/154 - 1/22. Suppose 5*k + o = -1, k + 7*o + 1 = 6*o. Factor 0*n + k - 2/7*n**3 + 0*n**2 + y*n**4.
2*n**3*(n - 1)/7
Factor 1/4*z**5 + 25/4*z**3 + 2*z**4 + 2 + 19/2*z**2 + 7*z.
(z + 1)**2*(z + 2)**3/4
Let x(p) be the first derivative of -p**6/3 + 4*p**5/5 - p**4/6 - 2*p**3/3 + 3*p + 2. Let o(z) be the first derivative of x(z). Factor o(u).
-2*u*(u - 1)**2*(5*u + 2)
Let s be (11 + -6 + -5)*(-2)/(-4). Factor s*m - 1/5*m**2 + 4/5.
-(m - 2)*(m + 2)/5
Let s = 35 - 14. Let -40*c**2 - 8 + 16*c**3 - c**5 + 10*c**4 + 38*c**4 - 36*c + s*c**5 = 0. What is c?
-1, -2/5, 1
Let r(y) be the first derivative of 9*y**6/2 - 102*y**5/5 + 69*y**4/2 - 24*y**3 + 3*y**2/2 + 6*y - 1. Solve r(o) = 0.
-2/9, 1
Let k(n) be the first derivative of -n**5/25 + 3*n**4/20 - 2*n**2/5 - 15. Factor k(d).
-d*(d - 2)**2*(d + 1)/5
Let i = 1/138 - -25/782. Let w = i + 5/17. Factor w*b**2 - 2/3 + 1/3*b.
(b - 1)*(b + 2)/3
Suppose -k = -6*k. Suppose k*g = -g. Factor 1/3*m + g - 1/3*m**2.
-m*(m - 1)/3
Let m be (5 + -4 - 0) + 4/(-6). Factor m*q**2 + 0*q - 1/3.
(q - 1)*(q + 1)/3
Let l(a) = 3*a**4 + 4*a**3 - a**2 + 2. Let j = -6 + 4. Let k(r) = 10*r**4 + 13*r**3 - 4*r**2 + 7. Let s(g) = j*k(g) + 7*l(g). Factor s(w).
w**2*(w + 1)**2
Let l(t) = -t**2 - 4*t + 7. Let j be -7 + (-4)/(-2) - 0. Let r be l(j). Factor -o + 0*o**3 - o**r + o**3 + 4 - 3.
(o - 1)**2*(o + 1)
Let l(j) = -9*j**3 - 5*j**2 + 9*j - 9. Let d(h) = 5*h**3 + 3*h**2 - 5*h + 5. Let z(t) = 7*d(t) + 4*l(t). Factor z(b).
-(b - 1)**2*(b + 1)
Let p(m) be the third derivative of m**8/1176 - m**7/735 - m**6/420 + m**5/210 - 9*m**2. Solve p(x) = 0.
-1, 0, 1
Let b = 1/2 + -1/4. Suppose 4*z - z = 3. Factor -v - b*v**2 - z.
-(v + 2)**2/4
Let d(p) be the third derivative of 0*p - 3/20*p**6 + 8/5*p**5 + 8*p**2 - 13/3*p**4 + 16/3*p**3 + 0. What is o in d(o) = 0?
2/3, 4
Let y(p) be the second derivative of 1/12*p**4 + 0 + 7*p + 0*p**2 - 1/40*p**5 + 0*p**3. Factor y(t).
-t**2*(t - 2)/2
Suppose -2/9*s**3 + 2/9*s - 4/9*s**2 + 4/9 = 0. What is s?
-2, -1, 1
Determine b so that 0*b + 0 + 0*b**3 + 0*b**2 - 4/13*b**4 + 46/13*b**5 = 0.
0, 2/23
Let q(f) be the third derivative of f**5/72 - 5*f**3/36 - 16*f**2. Solve q(t) = 0 for t.
-1, 1
Let t(u) be the third derivative of -u**7/1680 - u**3/3 + 2*u**2. Let i(l) be the first derivative of t(l). Find a, given that i(a) = 0.
0
Let f(g) be the third derivative of -g**7/70 - g**6/40 + g**5/20 + g**4/8 + 10*g**2. Solve f(q) = 0.
-1, 0, 1
Let u(q) be the third derivative of q**6/180 - q**4/12 + q**3/3 + 4*q**2. Let l(r) be the first derivative of u(r). Let l(c) = 0. What is c?
-1, 1
Let l be 10/4*12/10. Factor -10*n**2 + 2*n**4 - 13*n**l - n**5 - 2*n**4 - 6*n**4 - 4*n - 2*n**2.
-n*(n + 1)**2*(n + 2)**2
Solve -1/4*f + 1/4*f**4 - 3/4*f**3 + 3/4*f**2 + 0 = 0.
0, 1
Let j = -7 - -7. Let p = j - -5. Factor -p*b + 2 + 3*b - b**2 + b.
-(b - 1)*(b + 2)
Suppose 0 = 2*z - 7*z + 15. Suppose 2*g - 8 = z*v, 4*g - 3*g + 4*v - 4 = 0. Factor 2*y + 3*y**2 - y + 0*y**2 + y**g + 3*y**3.
y*(y + 1)**3
Factor -4*t**2 + 81*t**3 - 77*t**3 + 0*t**4 + 4*t**4 - 4*t**5.
-4*t**2*(t - 1)**2*(t + 1)
Let f(d) be the second derivative of -d**7/126 - d**6/18 - 7*d**5/60 + d**4/36 + 4*d**3/9 + 2*d**2/3 + 27*d. Let f(r) = 0. Calculate r.
-2, -1, 1
Suppose q + 8 = -i, 0*q + 4*i + 14 = 2*q. Let f be ((-10)/q)/((-4)/(-6)). Factor 0*l**4 + 3*l**3 + 2*l**4 - f*l**3.
2*l**3*(l - 1)
Let t = -18 + 56/3. Factor -4/3*b**4 - t*b**5 + 4/3*b**2 + 0*b**3 + 2/3*b + 0.
-2*b*(b - 1)*(b + 1)**3/3
Let j(f) = f - 1. Let u(x) = x**2 + 9*x - 11. Let v(s) = 22*j(s) - 2*u(s). Factor v(h).
-2*h*(h - 2)
Let d(v) = -10*v**3 + 9*v**2 + v. Let o(q) = 5*q**3 - 4*q**2 - q. Let p(u) = 4*d(u) + 9*o(u). Find g such that p(g) = 0.
-1, 0, 1
Let u(b) = b - 1. Let j be u(5). Suppose 0*n**2 + 0*n**3 - 2/3*n**j + 0*n - 2/3*n**5 + 0 = 0. What is n?
-1, 0
Let i be 6/(-10) + 90/25. Suppose i*a - 12 = -a. What is g in 4*g**2 - 2*g**2 - 2*g**a + 0*g**3 = 0?
0, 1
Let a(d) be the second derivative of -d**4/36 + d**3/9 - d**2/6 + 4*d. Factor a(h).
-(h - 1)**2/3
Factor 0 - 6/5*m**2 + 8/5*m - 2/5*m**3.
-2*m*(m - 1)*(m + 4)/5
Let a(n) be the third derivative of -n**9/15120 + n**8/6720 + n**7/2520 - n**6/720 - n**4/12 + 