+ 0.
2*s*(s + 2)/5
Suppose 3*w - 8 + 2 = 0. Factor -4*h**2 - h**2 + 7*h**w.
2*h**2
Let x(v) = -v**2 - 2*v + 1. Let t(j) be the first derivative of 4*j**3/3 + 7*j**2/2 - 4*j + 2. Suppose -2*r = -0 - 4. Let n(d) = r*t(d) + 7*x(d). Factor n(u).
(u - 1)*(u + 1)
Let b(c) be the first derivative of c**7/168 + c**6/60 + 6*c + 10. Let a(t) be the first derivative of b(t). Suppose a(z) = 0. What is z?
-2, 0
Let i(r) be the third derivative of -r**9/7560 - r**8/3360 + r**7/1260 + r**6/360 - r**4/8 + 3*r**2. Let o(s) be the second derivative of i(s). Factor o(p).
-2*p*(p - 1)*(p + 1)**2
Let z be (-3 + 3)*(0 - -1). What is g in 2/7*g**3 - 2/7*g**5 + z*g + 0 - 2/7*g**4 + 2/7*g**2 = 0?
-1, 0, 1
Let v(c) be the second derivative of -c**4/42 + 7*c. Solve v(h) = 0 for h.
0
Suppose -4*d = -z - 2*z - 41, -5*z - 3*d = 20. Let v(h) = h**3 + 8*h**2 + 7*h + 2. Let s be v(z). Find t such that 0 + 0*t + 1/2*t**s + 1/4*t**3 = 0.
-2, 0
Let k(q) be the second derivative of 5*q**4/12 + 20*q**3/3 + 40*q**2 - q + 32. Factor k(n).
5*(n + 4)**2
Let y be ((-1)/(-8))/(2/4). Let v = 4/5 - 3/10. Factor -1/4*p + 0*p**2 + 0 - y*p**5 + v*p**3 + 0*p**4.
-p*(p - 1)**2*(p + 1)**2/4
Let k(r) be the first derivative of -10 - 3/2*r**2 - 2*r - 1/3*r**3. What is l in k(l) = 0?
-2, -1
Let n(m) = m**2 + 28*m. Let l be n(0). Find s, given that -2/3*s + 1/3*s**2 + l = 0.
0, 2
Let b(k) be the first derivative of 3*k**5/35 - 9*k**4/14 + 13*k**3/7 - 18*k**2/7 + 12*k/7 + 4. Suppose b(h) = 0. Calculate h.
1, 2
Factor 120 + 100*m + 70/3*m**2 + 5/3*m**3.
5*(m + 2)*(m + 6)**2/3
Factor -2*o**3 - 3*o**3 + 12*o - 14*o + 7*o**3.
2*o*(o - 1)*(o + 1)
Let s(l) = -4*l**3 - 9*l**2 - 30*l + 3. Let c(y) = y**3 + y + 1. Let a(j) = -3*c(j) - s(j). Let w(b) be the first derivative of a(b). Solve w(r) = 0 for r.
-3
Suppose 0 = -d, -4*c + 2*d - 9 = -29. Let l(v) be the first derivative of 2/15*v**3 - 2/25*v**c - 1 - 1/5*v**2 + 0*v + 1/10*v**4. Factor l(s).
-2*s*(s - 1)**2*(s + 1)/5
Suppose -3*j + 2*x + 10 = 0, -x - 2*x - 13 = -4*j. Factor 2*m**3 + 3*m**j - 2*m + m**4 + 4*m**3.
2*m*(m + 1)**2*(2*m - 1)
Let r(x) be the second derivative of x**4/12 + x**3/6 - 13*x. Factor r(h).
h*(h + 1)
Find c such that 5/4*c - 3/2*c**2 + 1/4 = 0.
-1/6, 1
Let u(y) be the third derivative of 0*y**3 - 3*y**2 + 0*y**5 + 1/420*y**6 + 0*y**4 + 0*y + 0. Factor u(c).
2*c**3/7
Let s = 3932/19 + -207. Let q = 33/95 - s. Let 0*y + q*y**2 + 2/5*y**3 + 0 = 0. Calculate y.
-1, 0
What is y in -9/4*y - 21/8 + 3/8*y**2 = 0?
-1, 7
Suppose -5*z = 3*p + 44 - 8, 0 = -2*p - 2*z - 24. Let f be p/10*-2 - 2. Suppose 0 - 2/5*q + f*q**2 = 0. Calculate q.
0, 1
Factor 2*x**5 - 4*x**3 + 2*x**5 - x**2 + 8*x**4 - 3*x**2 - 4*x**2.
4*x**2*(x - 1)*(x + 1)*(x + 2)
Let m(v) be the first derivative of -v**5/12 + v**4/3 + 2*v**3/3 + 2*v**2 + 4. Let f(z) be the second derivative of m(z). Suppose f(s) = 0. Calculate s.
-2/5, 2
Let l = 25 + -21. Let y(x) be the second derivative of 0 + 1/70*x**5 - x + 0*x**2 + 1/21*x**3 + 1/21*x**l. Factor y(g).
2*g*(g + 1)**2/7
Let j be 1 - -3 - (208/56 - 0). Factor 2/7*k**3 + 4/7 - j*k - 4/7*k**2.
2*(k - 2)*(k - 1)*(k + 1)/7
Let z = 7/38 - -283/114. What is m in -2*m**2 - z + 4*m + 1/3*m**3 = 0?
2
Factor 4/11 - 18/11*v + 14/11*v**2.
2*(v - 1)*(7*v - 2)/11
Let a(i) = 4*i - 3. Let l(r) = -3*r + 2. Let h(c) = 2*a(c) + 3*l(c). Let q be h(-2). Determine b, given that -2*b**q - 2*b + 2*b**3 + 2*b = 0.
0, 1
Let f(y) = -2*y - 2. Let l(u) = u**2 + 8*u + 9. Let h be l(-6). Let v be f(h). Factor 2*x**v + 2*x**2 + x**3 + 4*x**3 - x**3.
2*x**2*(x + 1)**2
Let u(m) be the first derivative of m**6/9 - 6*m**5/5 + 31*m**4/6 - 34*m**3/3 + 40*m**2/3 - 8*m + 25. Solve u(i) = 0.
1, 2, 3
Let i = 1294 - 3878/3. Find r such that -i*r**4 + 4/3*r**2 + 0 + 4/3*r**3 - 4/3*r = 0.
-1, 0, 1
Let k(c) be the third derivative of c**5/80 + 3*c**4/16 + 9*c**3/8 - 21*c**2. Determine r so that k(r) = 0.
-3
Let h(j) be the first derivative of -j**8/8400 + j**7/2100 - j**6/1800 - 2*j**3/3 + 1. Let x(y) be the third derivative of h(y). What is l in x(l) = 0?
0, 1
Let o be (-4)/(-3) - 2/(-3). Suppose 5*b - 3*f - 31 = 0, o*b + 0*b + 2*f - 6 = 0. Factor -8 + q**b + 3*q**3 + 8 + q**2 + 3*q**4.
q**2*(q + 1)**3
Suppose 4*u = -0*q + q - 53, 33 = -4*u - 3*q. Let h = -7 - u. Factor 2*z**2 - z**h - 7*z**3 + z**3 + 6*z**4 - z**5.
-2*z**2*(z - 1)**3
Let n = 5 - -2. Factor -24*k**3 - n*k + 3*k + 16*k**4 - 28*k**5 + 16*k**2 + 24*k**5.
-4*k*(k - 1)**4
Suppose 1/5*c**4 - 8/5*c + 0 + 6/5*c**3 - 4/5*c**2 - 1/5*c**5 = 0. Calculate c.
-2, -1, 0, 2
Let u(k) = -2*k**3 + 3*k**2 + 3*k - 3. Let m(z) = z**3 - 3*z**2 - 2*z + 2. Let j(f) = 3*m(f) + 2*u(f). Factor j(n).
-n**2*(n + 3)
Let k be 1 + -3 - (-98)/48. Let w(b) be the third derivative of 0*b + 0 + b**2 - k*b**4 + 0*b**3 - 7/120*b**5. Let w(h) = 0. Calculate h.
-2/7, 0
Let -4*u**3 + 5*u**4 - 9*u**4 + 6*u**4 = 0. Calculate u.
0, 2
Let w(t) be the third derivative of 0*t + 1/3*t**4 + t**2 + 0*t**3 + 2/3*t**5 + 31/60*t**6 + 1/7*t**7 + 0. Solve w(d) = 0.
-1, -2/3, -2/5, 0
Let l(j) be the first derivative of 4*j**6/105 + j**5/10 + j**4/21 - j**3/21 - 3*j + 4. Let g(b) be the first derivative of l(b). Factor g(u).
2*u*(u + 1)**2*(4*u - 1)/7
Let x(p) = p**4 + p**3 + 1. Let a(y) = y**5 - 4*y**4 - 4*y**3 - 4. Let g = 1 - 5. Let h(d) = g*x(d) - a(d). Factor h(f).
-f**5
Let s be (0 - 3) + (-54)/(-6). What is f in f**2 + 9 - s - 4*f**2 = 0?
-1, 1
Let h(c) be the second derivative of -3*c**5/140 - c**4/14 + c**3/14 + 3*c**2/7 + 7*c. Let h(p) = 0. Calculate p.
-2, -1, 1
Let b(t) be the second derivative of t**6/10 - 3*t**5/20 - 3*t**4/4 + 5*t**3/2 - 3*t**2 + 11*t. Factor b(a).
3*(a - 1)**3*(a + 2)
Suppose -70*x = -65*x - 15. Factor 1/4*h**5 - 1/2*h**2 + 1/2*h**x + 3/4*h**4 - 1/4 - 3/4*h.
(h - 1)*(h + 1)**4/4
Let x(d) be the first derivative of -2*d**3/21 - d**2/7 + 11. Suppose x(z) = 0. What is z?
-1, 0
Let d(k) be the third derivative of -k**8/84 - 2*k**7/105 + k**6/15 + 2*k**5/15 - k**4/6 - 2*k**3/3 + k**2. Find p, given that d(p) = 0.
-1, 1
Factor 2/3*m**4 - 64*m + 128/3 + 104/3*m**2 - 8*m**3.
2*(m - 4)**2*(m - 2)**2/3
Suppose -7*h + 32 = -3*h. Suppose h*y**2 - 2*y**2 - 2*y - 3*y**3 - y = 0. Calculate y.
0, 1
Let t = 70/711 + 1/79. Let m(v) be the second derivative of 0*v**5 + 2*v + 2/45*v**6 + 0*v**3 - t*v**7 + 0 + 0*v**2 + 0*v**4. Suppose m(a) = 0. Calculate a.
0, 2/7
Let b(w) be the second derivative of 2*w - 2/45*w**3 + 1/225*w**6 - 1/30*w**4 + 0*w**2 + 0 + 0*w**5. Factor b(y).
2*y*(y - 2)*(y + 1)**2/15
Let l(v) = v**3. Let n be (-12)/(-6) + 0/2. Let t(o) = -o**3 + 3*o**2 + 2*o. Let h(b) = n*t(b) + 4*l(b). Determine d, given that h(d) = 0.
-2, -1, 0
Let h(g) = -3*g**3 - 34*g**2 - 59*g - 20. Let f(r) = -14*r**3 - 171*r**2 - 296*r - 101. Let o(z) = -2*f(z) + 11*h(z). Suppose o(x) = 0. What is x?
-3, -2/5
Let u(y) = y**2 + 2*y - 5. Let m(s) = 7*s**2 + 11*s - 31. Let x(z) = 6*m(z) - 39*u(z). Let x(r) = 0. Calculate r.
1, 3
Let a(k) be the first derivative of -k**6/2 - 3*k**5 - 27*k**4/4 - 7*k**3 - 3*k**2 + 21. Factor a(l).
-3*l*(l + 1)**3*(l + 2)
Let p(a) be the first derivative of a**3/3 + 6*a**2 + 36*a + 43. Factor p(v).
(v + 6)**2
Suppose r = 10 + 6. Factor 12*n**3 - 3 + 5*n + n + 5*n**2 + r*n**2.
3*(n + 1)**2*(4*n - 1)
Let -1/3*m**4 + 0*m**2 - 1/6*m**3 - 1/6*m**5 + 0*m + 0 = 0. What is m?
-1, 0
Suppose 3*a + 4 = -5. Let s be 18/a*(-4)/6. Factor -6*i**3 + 2*i**2 + 2*i**s + 1 + 7*i - 5 - i.
2*(i - 2)*(i - 1)**2*(i + 1)
Let m(i) = i**2 + 2. Suppose -3*a = -2*l - 0*l + 3, -3*a - 3 = 0. Let c be m(l). Factor 0*g + g**2 - 4*g**2 + 0*g**2 - g**3 + g + c + g**4.
(g - 2)*(g - 1)*(g + 1)**2
Let v(n) be the second derivative of n**8/560 + n**7/175 - n**5/50 - n**4/40 + 5*n**2/2 - 5*n. Let f(q) be the first derivative of v(q). Factor f(o).
3*o*(o - 1)*(o + 1)**3/5
Let l(c) = 2*c**2 + 10*c. Let f(r) = r**2 + 3*r. Let a(q) = -10*f(q) + 3*l(q). Suppose a(o) = 0. What is o?
0
Let s(i) be the first derivative of 2*i**3/39 + i**2/13 - 4*i/13 + 5. Suppose s(c) = 0. Calculate c.
-2, 1
Let x = -75 + 227/3. Let m(o) be the first derivative of -x*o**3 + 2 + 3*o**2 - 4*o. Factor m(d).
-2*(d - 2)*(d - 1)
Let z(r) be the third derivative of r**5/15 - r**4/6 + 2*r**2. Let z(g) = 0. Calculate g.
0, 1
Factor -3*q**2 + 13*q**3 - 10*q**3 + 6*q**2.
3*q**2*(q + 1)
Suppose 9*l = 11*l - 2.