0. What is h?
-1, -1/4, 1
Let o(n) be the second derivative of -n**6/60 + n**5/30 + n**2 - n. Let k(y) be the first derivative of o(y). Suppose k(l) = 0. What is l?
0, 1
Suppose 10 = 3*s - m, 5*s = 7*m - 2*m + 20. Determine f so that 2/3 - 2*f - 2/3*f**s + 2*f**2 = 0.
1
Let b(t) = 3*t**2 + 14*t + 15. Let s be b(-3). Find m, given that 0*m + s - 1/3*m**3 + 1/6*m**4 + 1/6*m**2 = 0.
0, 1
Let c = 12 - 12. Let g(k) be the second derivative of 0*k**3 + c + 1/18*k**4 + k + 0*k**2. Factor g(b).
2*b**2/3
Let d(w) = 2*w**2 - 4*w. Let k(l) = -l**2 - 5*l - 5. Let b be k(-4). Let q(t) = -t. Let z(g) = b*d(g) + 8*q(g). Find f such that z(f) = 0.
-2, 0
Let j(r) = r - 1. Let o = 30 + -29. Let w(m) be the second derivative of -m**5/10 + m**3 - 2*m**2 - m. Let a(z) = o*w(z) - 4*j(z). Solve a(d) = 0 for d.
-1, 0, 1
Let b(k) = k**4 + k**2 + k. Let u(x) = -11*x**4 - 24*x**3 - 20*x**2 - 2*x + 3. Let y(g) = -2*b(g) - u(g). Factor y(n).
3*(n + 1)**3*(3*n - 1)
Let y be (2/9)/(6/9). Solve y*p**3 + 0 + 1/3*p**2 + 0*p = 0 for p.
-1, 0
Let i(l) = l + 1. Let s be i(5). Suppose 3*q + 0*q = s. Determine u so that -q + 2 + 3*u**3 = 0.
0
Let g(q) be the third derivative of 1/60*q**6 + 0*q + 1/30*q**5 + 2*q**2 - 1/12*q**4 + 0 - 1/3*q**3. Factor g(i).
2*(i - 1)*(i + 1)**2
Let j be (2 + -3)*4*1. Let s be (0 + (-2)/j)*0. Factor s*t + 0*t - 3*t**2 + 0*t**2.
-3*t**2
Let f(k) be the second derivative of -k**7/12600 - k**6/1800 + k**5/200 + k**4/3 + 4*k. Let t(m) be the third derivative of f(m). Find d, given that t(d) = 0.
-3, 1
Factor 4 - 24/5*y + 4/5*y**2.
4*(y - 5)*(y - 1)/5
Let d(k) be the third derivative of -k**7/42 - k**6/12 + k**5/4 + 5*k**4/3 + 10*k**3/3 - 2*k**2 + k. Factor d(r).
-5*(r - 2)*(r + 1)**2*(r + 2)
Find n, given that -1/3 + 2/3*n**2 - 1/3*n = 0.
-1/2, 1
Suppose 3*m - 3*j = 9, 0 = -3*m - 0*m - 5*j - 15. Let v(y) be the second derivative of 0*y**2 + 0 - y - 3/20*y**5 + m*y**3 - 1/24*y**6 - 1/12*y**4. Factor v(g).
-g**2*(g + 2)*(5*g + 2)/4
Let k = -11/8 - -5/4. Let h = 1/8 - k. Solve 0*g**2 + h*g**3 - 1/4*g + 0 = 0 for g.
-1, 0, 1
Let q(l) be the second derivative of l**7/1260 - l**6/360 - l**5/30 - l**4/4 - 2*l. Let u(s) be the third derivative of q(s). Solve u(i) = 0 for i.
-1, 2
Let t(i) be the second derivative of -1/2*i**3 + 0 + 1/12*i**4 - 3*i + i**2. Determine f so that t(f) = 0.
1, 2
Let c(f) be the first derivative of 2*f**3/21 - f**2/7 + 1. Factor c(s).
2*s*(s - 1)/7
Suppose -105*c + 97*c = -24. Let -11*d - d**3 - c - 19/3*d**2 = 0. What is d?
-3, -1/3
Let o(z) be the first derivative of -z**6/75 + 7*z**5/100 - 3*z**4/20 + z**3/6 - z**2/10 - 2*z + 3. Let x(r) be the first derivative of o(r). Factor x(a).
-(a - 1)**3*(2*a - 1)/5
Suppose 3*m + 23 = 5*d, 7*d - 4*m - 20 = 3*d. Find h such that h**d + 0 + 0*h**2 + 2/3*h**3 + 0*h = 0.
-2/3, 0
Let r(g) be the second derivative of -g**6/45 + g**5/30 + g**4/9 + 6*g. Factor r(w).
-2*w**2*(w - 2)*(w + 1)/3
Factor 4/7*w**4 + 0 - 16/7*w**3 + 0*w - 20/7*w**2.
4*w**2*(w - 5)*(w + 1)/7
Let i(h) be the third derivative of h**6/30 - 7*h**5/15 + h**4 - h**2. Factor i(n).
4*n*(n - 6)*(n - 1)
Let g(r) be the first derivative of -r**7/7 - 8*r**6/15 - 3*r**5/5 + r**3/3 + 2*r - 4. Let i(a) be the first derivative of g(a). Factor i(x).
-2*x*(x + 1)**3*(3*x - 1)
Let p(m) be the first derivative of m**4/6 - 8*m**3/9 + 5*m**2/3 - 4*m/3 - 9. Factor p(l).
2*(l - 2)*(l - 1)**2/3
Factor 0*x**2 - 2/15*x**4 + 0 + 2/15*x**5 + 0*x**3 + 0*x.
2*x**4*(x - 1)/15
Let t(w) be the first derivative of -4 - 1/24*w**4 - 1/15*w**5 + 0*w**3 + 0*w - 1/36*w**6 + 0*w**2. Solve t(m) = 0 for m.
-1, 0
Let b = -1229/4830 + 17/276. Let o = 2/35 - b. What is h in 3/4*h**3 + 0 - h**2 + o*h = 0?
0, 1/3, 1
Let w = -1/275 - -279/1100. Suppose w - g - g**3 + 1/4*g**4 + 3/2*g**2 = 0. What is g?
1
Let o be 0/(0 + -1 + 0). Suppose -x + 4*x - 12 = o. Factor 2*v - v**2 + 3*v**3 + v**x - 3*v - 2*v**3.
v*(v - 1)*(v + 1)**2
Let f(c) be the second derivative of c**5/330 + c**4/22 + 3*c**3/11 - c**2/2 + 4*c. Let d(l) be the first derivative of f(l). Determine u, given that d(u) = 0.
-3
Let h = 19/2 - 129/14. Factor 0 + 2/7*b - h*b**2.
-2*b*(b - 1)/7
Let y(x) be the second derivative of x**4/18 + x**3/3 + 18*x. Find w such that y(w) = 0.
-3, 0
Let w(t) be the first derivative of t**8/560 - 3*t**7/280 + t**6/40 - t**5/40 + t**3 - 1. Let p(n) be the third derivative of w(n). Factor p(l).
3*l*(l - 1)**3
Let k(a) = -4*a**4 + 8*a**3 + 4*a**2 + 4*a + 4. Let d(p) = 4*p**4 - 8*p**3 - 5*p**2 - 5*p - 5. Let i(m) = 4*d(m) + 5*k(m). Factor i(b).
-4*b**3*(b - 2)
Let b(f) = 6*f. Let c(g) = g**2 - 7*g. Let k(d) = -2*b(d) - 3*c(d). Factor k(m).
-3*m*(m - 3)
What is t in -t**4 + 2*t**3 + 0*t**2 + 9*t**4 + 0*t**2 = 0?
-1/4, 0
Let i = 15 + -33. Let h(c) = -c**3. Let z(l) = -3*l**5 - 12*l**3 - 3*l. Let m(b) = i*h(b) + z(b). Find u, given that m(u) = 0.
-1, 0, 1
Let s(b) be the first derivative of -2 + 4*b - b**3 - b**2 + 5 + 0 - b**3. Factor s(a).
-2*(a + 1)*(3*a - 2)
Let r(i) be the first derivative of -2*i**5/5 - i**4/2 - 4. Suppose r(j) = 0. What is j?
-1, 0
Let j = 50 + -46. Let w(h) be the first derivative of 1/2*h**j + 0*h**3 + 0*h**2 + 0*h - 2/5*h**5 - 2. Determine q, given that w(q) = 0.
0, 1
Let g = 26 + -21. Suppose 8 = g*v - 12. Factor 2/3*x**3 + 2/3*x**v + 4/3 - 2/3*x - 2*x**2.
2*(x - 1)**2*(x + 1)*(x + 2)/3
Let i(x) be the first derivative of 4*x**3/3 + 4*x**2 + 4*x + 7. Solve i(r) = 0 for r.
-1
Let o(h) = -2*h - 9. Let v be (-80)/12 - 2/(-3). Let b be o(v). Factor -6*m**5 + m**2 + 8*m**5 - 3*m**2 - 2*m**b + 2*m**4.
2*m**2*(m - 1)*(m + 1)**2
Let k(y) be the first derivative of y**3/6 - 2*y**2 + 7*y/2 - 16. Determine r so that k(r) = 0.
1, 7
Let u(f) be the second derivative of 3*f + 0*f**4 + 1/63*f**7 + 1/30*f**5 - 2/45*f**6 + 0 + 0*f**2 + 0*f**3. Factor u(g).
2*g**3*(g - 1)**2/3
Let v(q) be the second derivative of q**7/630 - 2*q**5/15 - 7*q**4/12 - 2*q. Let h(y) be the third derivative of v(y). What is i in h(i) = 0?
-2, 2
Let g(j) be the third derivative of 0*j + j**2 + 0 - 9/100*j**5 - 3/20*j**4 - 1/10*j**3. Factor g(h).
-3*(3*h + 1)**2/5
Let w(o) be the second derivative of o**3/3 + o**2/2 - 2*o. Let c be w(1). Let -6*m + 8/3*m**c + 2*m**2 + 4/3 = 0. Calculate m.
-2, 1/4, 1
Let h(u) be the third derivative of 1/630*u**7 - 1/180*u**5 + 0 + 1/72*u**4 - 1/360*u**6 - 3*u**2 + 0*u**3 + 0*u. Factor h(f).
f*(f - 1)**2*(f + 1)/3
Let r = 913/5 + -181. Let -r*f - 2/5*f**4 + 8/5*f**2 + 2/5*f**3 + 0 = 0. What is f?
-2, 0, 1, 2
Suppose -3*b - b - 4 = 0, 5*z = b + 1. Suppose 0 - 1/4*c**3 + z*c**2 + 0*c = 0. Calculate c.
0
Let j be ((-4)/20)/((-18)/20). Let 2/9*q**2 + 0 + j*q**3 + 0*q - 4/9*q**4 = 0. What is q?
-1/2, 0, 1
Let q be -3 + (-3 - (-2)/(-4)*-12). Solve 2/5*s**2 + 0 + q*s = 0 for s.
0
Let v = 936/2365 + 2/473. Let 0 - 2/5*g**4 + v*g**2 - 2/5*g**3 + 0*g + 2/5*g**5 = 0. Calculate g.
-1, 0, 1
Let a(l) = l**3 - 3*l**2 + 11. Let r(b) = 3*b**3 - 5*b**2 + 23. Let s = -5 + -1. Let d(h) = s*r(h) + 14*a(h). Factor d(u).
-4*(u - 1)*(u + 2)**2
Let h(c) = -c**3 + 5*c**2 + c - 3. Suppose w = 2 + 3. Let k be h(w). Solve d**k + d**3 + 3*d**3 - 5*d**3 = 0.
0, 1
Let v(u) = u**5 - u**4 - u. Let j(r) = -r**5 - 2*r**4 + 3*r**3 + 2*r. Let k(c) = -j(c) - 2*v(c). Factor k(z).
-z**3*(z - 3)*(z - 1)
Let h = -1 + 2. Let a = h + 1. Suppose 4 + c**2 - 6*c + 0 + c**a = 0. Calculate c.
1, 2
Factor 7*m + 0*m - 6*m**2 + 2*m - 3*m**3 + 0*m.
-3*m*(m - 1)*(m + 3)
Let c(o) be the first derivative of -3*o**4/2 - o**3 + 24. Suppose c(d) = 0. Calculate d.
-1/2, 0
Let -38*o**4 + 6*o + o**5 - 2*o**2 + 14*o**3 - 44*o**3 - 2*o - 15*o**5 = 0. What is o?
-1, 0, 2/7
What is z in z**2 - 3/4*z - 1/4 = 0?
-1/4, 1
Let f = -25 + 32. Let c(l) be the third derivative of -1/30*l**5 + 0*l**4 + 0*l + 0*l**3 - 1/210*l**f + 0 + 2*l**2 + 1/40*l**6. Factor c(v).
-v**2*(v - 2)*(v - 1)
Solve 2/3*w**2 + 2/3*w**5 + 16/3*w + 8/3 - 10/3*w**3 - 2/3*w**4 = 0 for w.
-1, 2
Let w(b) be the third derivative of -1/16*b**4 + 0*b - 1/35*b**7 + 10*b**2 + 7/80*b**6 - 1/20*b**5 + 0 + 0*b**3. What is p in w(p) = 0?
-1/4, 0, 1
Let o(l) be the second derivative of l**6/60 + l**5/20 - l**3/6 - l**2/4 - 4*l. What is j in o(j) = 0?
-1, 1
Let n(a) = -2*a**3 - 2*a**2 + 2*a. Let m = 1 + -3. Let f(z) = 4*z**3 + 5*z**2 - 4*z. Let d(i) = m*f(i) - 5*n(i). Factor d(w).
2