3
Let u(h) be the second derivative of 3*h**4/20 + 13*h**3/30 + 2*h**2/5 - 3*h. What is l in u(l) = 0?
-1, -4/9
Let y be (-4*(-1)/12)/(1*63). Let t(l) be the second derivative of 0*l**6 - 2*l - 1/27*l**3 + 0*l**2 + 0 + 0*l**4 + 1/45*l**5 - y*l**7. Factor t(r).
-2*r*(r - 1)**2*(r + 1)**2/9
Let y(d) be the third derivative of -d**6/40 - 21*d**5/20 - 147*d**4/8 - 343*d**3/2 + 28*d**2. Factor y(b).
-3*(b + 7)**3
Let c(a) be the first derivative of -2/7*a**3 + 1/14*a**4 + 4/7*a + 2/35*a**5 + 5 - 1/7*a**2. Find q such that c(q) = 0.
-2, -1, 1
Let a(c) be the second derivative of -c**6/900 - c**5/300 - c**3/3 + 3*c. Let t(i) be the second derivative of a(i). Factor t(q).
-2*q*(q + 1)/5
Let p(v) be the first derivative of -v**6/540 + v**4/108 + v**2/2 - 1. Let d(x) be the second derivative of p(x). Factor d(s).
-2*s*(s - 1)*(s + 1)/9
Let b(o) = -o**2 - 1. Let f(l) = 7*l**2 + 6*l + 5. Let i(t) = -10*b(t) - 2*f(t). Factor i(k).
-4*k*(k + 3)
Let n(z) be the third derivative of z**6/280 - z**5/70 - z**4/56 + z**3/7 - 14*z**2. Determine t, given that n(t) = 0.
-1, 1, 2
Let r(d) = -2*d**2 - 4*d + 4. Let u(o) = 3*o**2 + 8*o - 8. Let f be 6 + ((-4)/4 - 2). Let g(s) = f*u(s) + 5*r(s). Find i such that g(i) = 0.
2
Let y be 3/2 + -1 - 25/(-150). Let d = -220/3 - -74. Let -d*k**2 + 2/3*k**4 + y*k**3 + 0*k - 2/3*k**5 + 0 = 0. Calculate k.
-1, 0, 1
Suppose -2*i + 3 = -3*b, -6*b + b + 11 = 2*i. Suppose i*g - 12 = -3*p + g, g - 16 = -4*p. Factor 9/4*x**3 - 3/4*x**p + 0 - 9/4*x**2 + 3/4*x.
-3*x*(x - 1)**3/4
Let z(k) = -6*k**2 + 11*k - 2. Let t = -2 + 1. Let v(j) = -j**2 + j. Let m(g) = t*z(g) + 2*v(g). Solve m(f) = 0 for f.
1/4, 2
Let p(h) be the first derivative of -3*h**5/80 + h**4/16 - h - 7. Let u(l) be the first derivative of p(l). Factor u(k).
-3*k**2*(k - 1)/4
Factor -4/3*t**2 + 8 - 20/3*t.
-4*(t - 1)*(t + 6)/3
Let m(i) = -7*i**2 - 10*i - 8. Let x(h) = h**2. Suppose 2*p = -2*f + 2, -2*f = -0*f - 4. Let y(s) = p*m(s) - 5*x(s). Factor y(c).
2*(c + 1)*(c + 4)
Let w be (-6)/3 + 0 + 2. Let n(q) be the second derivative of q + 1/60*q**4 + w + 1/15*q**3 + 1/10*q**2. Factor n(o).
(o + 1)**2/5
Let o = -1327 - -139334/105. Let u = o - -851/1155. Factor 16/11*l + 2/11*l**3 + u + 10/11*l**2.
2*(l + 1)*(l + 2)**2/11
Factor -2/7*o**3 + 54/7 - 54/7*o + 18/7*o**2.
-2*(o - 3)**3/7
Determine w, given that 0 + 10/11*w**3 + 8/11*w**2 + 0*w + 2/11*w**4 = 0.
-4, -1, 0
Let j(p) = 5*p**3 - 10*p**2 - 9*p + 6. Let b(w) = 5*w**3 - 10*w**2 - 10*w + 5. Let r(m) = -4*b(m) + 5*j(m). What is k in r(k) = 0?
-1, 1, 2
Let d(m) = -20*m + 302. Let k be d(15). Factor 0*y + 0 - 2/5*y**k.
-2*y**2/5
Let b(f) be the first derivative of -1/15*f**5 - 2/9*f**3 + 0*f**2 - 3 - 1/4*f**4 + 0*f. Find q, given that b(q) = 0.
-2, -1, 0
Let b(f) be the third derivative of f**7/105 - f**5/6 + 4*f**3/3 - 5*f**2. Find o, given that b(o) = 0.
-2, -1, 1, 2
Suppose 0 = -5*q - 8 - 7, x = -3*q - 3. Let y be x*(-3)/(-8 + 2). Find a, given that 6*a**y + 2*a**4 - 3*a + 4*a**2 + 2*a**2 + 5*a = 0.
-1, 0
Let a(v) be the third derivative of 9*v**7/350 + 3*v**6/20 + 37*v**5/100 + v**4/2 + 2*v**3/5 + 5*v**2. Factor a(m).
3*(m + 1)**2*(3*m + 2)**2/5
Suppose 0 = n - 5, -4*r - 5 = r - n. Suppose r = -3*c - 0 + 12. Solve l + 2*l**4 + 0*l + 5*l**4 - 5*l**c - l**5 - 2*l**2 = 0 for l.
-1, 0, 1
Let l(j) = j + 10. Let n be l(-8). Let d be (46/27 - n)*-15. Let 16/9 - d*m + 28/9*m**2 - 2/3*m**3 = 0. What is m?
2/3, 2
Let -15*h**3 + 143*h**2 - 143*h**2 + h**4 - 4*h**4 = 0. Calculate h.
-5, 0
Let q(s) = -5*s**3 + 3*s**2 - 3*s + 3. Let d(c) = 4*c**3 - 4*c**2 + 2*c - 2. Let g(i) = -3*d(i) - 2*q(i). Factor g(h).
-2*h**2*(h - 3)
Factor -18/7 - 12/7*v**3 + 16/7*v**2 + 2/7*v**4 + 12/7*v.
2*(v - 3)**2*(v - 1)*(v + 1)/7
Suppose 0 = 12*r - 7*r. Find t, given that 2/9*t**2 + r - 2/9*t = 0.
0, 1
Let c(b) be the first derivative of 5*b**3/7 + 9*b**2/14 - 6*b/7 - 1. Let c(z) = 0. Calculate z.
-1, 2/5
Let f(p) = 4*p - 2. Let v(t) be the third derivative of t**5/60 + t**4/24 - t**3/6 - t**2. Let c(h) = -f(h) + 2*v(h). Find g such that c(g) = 0.
0, 1
Find d such that -16/3 - 52/3*d - 26/3*d**2 + 10/3*d**3 = 0.
-1, -2/5, 4
Let j be ((-2)/(-7) - (-10)/14) + 5. Suppose -14/3*i + 4/3 + j*i**2 - 10/3*i**3 + 2/3*i**4 = 0. What is i?
1, 2
Let t(n) be the third derivative of 1/12*n**3 - 1/16*n**4 + 1/672*n**8 - n**2 - 1/140*n**7 + 0 + 1/120*n**6 + 0*n + 1/60*n**5. Factor t(k).
(k - 1)**4*(k + 1)/2
Let h be (-2)/5*(-15)/12. Let d(q) be the first derivative of -8*q**2 - 8*q - 10/3*q**3 - 2 - h*q**4. Factor d(g).
-2*(g + 1)*(g + 2)**2
Let k(y) be the second derivative of y**7/126 + y**6/90 - y**5/30 - y**4/18 + y**3/18 + y**2/6 - y. Factor k(u).
(u - 1)**2*(u + 1)**3/3
Let g(i) = i**2 + 2*i + 1. Let z(s) = 2*s**2 + 3*s + 1. Let f(w) = -3*g(w) + 2*z(w). Find p, given that f(p) = 0.
-1, 1
Let w(o) = 10*o**2 + 20*o + 10. Let g(r) = -5*r**2 - 10*r - 5. Let i(a) = -5*g(a) - 2*w(a). Factor i(k).
5*(k + 1)**2
Let u(x) = x**2 + 10*x + 10. Let n be u(-5). Let p = 17 + n. Factor 3/4 - 3/4*c + 3/4*c**3 - 3/4*c**p.
3*(c - 1)**2*(c + 1)/4
Suppose 2*x - 25 = 3*w, -3*w - 7*x = -3*x - 5. Let j be (1/3)/(w/(-6)). Factor 0 - 16/5*k**2 - 32/5*k**3 - j*k.
-2*k*(4*k + 1)**2/5
Factor 0*d**2 + 0 - 4/5*d**3 + 4/5*d.
-4*d*(d - 1)*(d + 1)/5
Let b(t) = -2*t**2 - 6*t - 24. Let x(y) = -2*y**2 - 5*y - 25. Let j(c) = 7*b(c) - 6*x(c). Factor j(l).
-2*(l + 3)**2
Let b(x) be the third derivative of -1/180*x**6 - 1/315*x**7 + 0*x**3 - 1/1512*x**8 - 2*x**2 + 0*x**4 - 1/270*x**5 + 0*x + 0. Let b(a) = 0. Calculate a.
-1, 0
Let x = 2014 - 5981/3. Let k = x + -20. Factor 1/3 + 1/3*i**3 - 1/3*i**2 - k*i.
(i - 1)**2*(i + 1)/3
Factor -6*a**2 + 4*a**2 + a**2.
-a**2
Let j(z) = z**3 + 15*z**2 - 13*z + 48. Let n be j(-16). Factor n - 3/2*m + 1/2*m**2.
m*(m - 3)/2
Let o(f) be the first derivative of 0*f + 1/16*f**4 - 1/6*f**3 + 0*f**2 + 3. Let o(h) = 0. Calculate h.
0, 2
Suppose 0 = 9*c - 13*c. Let u(o) be the third derivative of 0*o + 2*o**2 + 0*o**3 + c - 1/30*o**5 - 1/12*o**4. Let u(v) = 0. What is v?
-1, 0
Let u(p) be the first derivative of -p**3/9 - 3*p**2/2 + 10*p/3 - 63. Determine j so that u(j) = 0.
-10, 1
Let v(l) be the third derivative of -l**8/336 + l**7/210 + 8*l**2. Factor v(n).
-n**4*(n - 1)
Let l(z) be the first derivative of -2*z**5/15 - 5*z**4/6 - 14*z**3/9 - z**2 - 27. Factor l(v).
-2*v*(v + 1)**2*(v + 3)/3
Let a(j) be the first derivative of j**6/27 - 2*j**5/45 - j**4/9 + 4*j**3/27 + j**2/9 - 2*j/9 - 4. Factor a(y).
2*(y - 1)**3*(y + 1)**2/9
Let k(s) = -60*s**2 + 215*s. Let a(d) = 5*d**2 - 18*d. Let g(i) = -25*a(i) - 2*k(i). Factor g(h).
-5*h*(h - 4)
Let x(k) be the first derivative of 2*k**5/45 + k**4/9 + 2*k**3/27 + 14. Factor x(y).
2*y**2*(y + 1)**2/9
Let x(i) be the second derivative of i**4/28 + i**3/2 + 9*i**2/7 + 3*i. Solve x(f) = 0.
-6, -1
Let j = -3/7 + 352/21. Let w(l) be the first derivative of j*l**3 + 4*l - 14*l**2 - 2. Factor w(z).
(7*z - 2)**2
Let l = 1 + 1. Let b = 14 + -10. Suppose y + 8*y**b - 8*y**4 + y**5 - l*y**3 = 0. What is y?
-1, 0, 1
Suppose -3*w = 2*w + 4*y - 48, 2*w - 10 = 3*y. Let u(b) be the first derivative of 1 - w*b - 10/3*b**3 - 1/2*b**4 - 8*b**2. Factor u(m).
-2*(m + 1)*(m + 2)**2
Let q(r) be the third derivative of r**8/336 - r**7/210 - r**6/120 + r**5/60 - 21*r**2. Factor q(m).
m**2*(m - 1)**2*(m + 1)
Determine s so that -36*s**3 + 4*s**2 + 61*s**3 - 10*s - 15*s**5 - 9*s**2 + 5*s**4 = 0.
-1, -2/3, 0, 1
Let q(d) = -9*d**4 + 11*d**3 + 2*d**2 - 11*d - 7. Let p(l) = -l**4 + l**3 - l - 1. Let m(r) = -14*p(r) + 2*q(r). Factor m(v).
-4*v*(v - 2)*(v - 1)*(v + 1)
Factor -13*y**2 + 1 + 16*y**2 - 25*y + 21*y.
(y - 1)*(3*y - 1)
Factor 0 + 3/2*w**2 - 9/2*w.
3*w*(w - 3)/2
Let w(h) be the third derivative of 0 + 0*h**3 + 0*h + 9/40*h**6 + 1/112*h**8 + 1/14*h**7 - 4*h**2 + 7/20*h**5 + 1/4*h**4. Factor w(l).
3*l*(l + 1)**3*(l + 2)
Let s = -1168/3 + 390. Factor s*o + 1/3*o**3 - o**2 + 0.
o*(o - 2)*(o - 1)/3
Let j(q) = -q**3 - q. Let i be j(0). Find p, given that 0*p - 1/5*p**2 + i = 0.
0
Let h(u) be the second derivative of -u**4/12 + u**3/3 + 4*u**2 + 15*u. Let h(i) = 0. What is i?
-2, 4
Let y be ((-1)/(-2))/(5/30). Let h(k) = 12*k**3 + 28*k**2 + 16*k. Let v(c) = -4*c**3 - 9*c**2 - 5*c. Let x(z) = y*h(z) + 8*v(z). Factor x(i).
4*i*(i + 1)*(i + 2)
Factor -g**3 - 2*g + 3*g*