t c(s) be the second derivative of s**7/147 + s**6/21 + 4*s**5/35 + 2*s**4/21 + 2*s. Find f such that c(f) = 0.
-2, -1, 0
Let r = 27 - 17. Let f = -6 + r. What is g in 2*g**5 + g**3 - 2*g + 4*g**2 - g**3 - 4*g**f = 0?
-1, 0, 1
Let r(c) be the first derivative of 2/3*c**3 + 3 + 0*c + 0*c**2 - 1/2*c**4. Factor r(k).
-2*k**2*(k - 1)
Let u(q) = q**2 - 12*q + 30. Let k be u(3). Find t, given that -8/7*t**k + 2/7*t + 0 + 6/7*t**2 = 0.
-1/4, 0, 1
Suppose -9*r = -0*r. Solve 0*h**3 + 4/7*h**2 + 2/7*h**5 - 2/7*h - 4/7*h**4 + r = 0 for h.
-1, 0, 1
Let b(v) be the first derivative of -v**5/50 + v**4/30 + 3*v + 1. Let q(l) be the first derivative of b(l). Let q(x) = 0. What is x?
0, 1
Let j(l) be the third derivative of -l**6/180 - l**5/45 - l**4/36 - 8*l**2. Factor j(n).
-2*n*(n + 1)**2/3
Solve 5*h**4 + 59*h**2 - 24*h**3 - 4*h + 5*h**4 - 41*h**2 = 0.
0, 2/5, 1
Let i(n) = 23*n**3 + 10*n**2 - 37*n + 30. Let j(u) = -11*u**3 - 5*u**2 + 19*u - 15. Let a(c) = -6*i(c) - 13*j(c). Factor a(l).
5*(l - 1)**2*(l + 3)
Factor 2/5*x**2 + 0 - 3/5*x + 1/5*x**3.
x*(x - 1)*(x + 3)/5
Let i(a) = -2*a**3 - 4*a**2 + 2*a + 4. Suppose 3*w + s = 0, 4*w + s = -0*s + 1. Let x(n) = n**4 - n**2. Let u(k) = w*i(k) + 6*x(k). Factor u(j).
2*(j - 1)**2*(j + 1)*(3*j + 2)
Let t(k) be the third derivative of k**8/288 - k**7/252 - k**6/80 + k**5/72 + k**4/72 - 10*k**2. Suppose t(g) = 0. What is g?
-1, -2/7, 0, 1
Let i(w) = -12*w - 72. Let g be i(-6). Suppose -3*h - 3 = -4*f + 1, 3*h - 3*f = -3. Find s, given that 1/2*s**3 + g*s + h + 1/2*s**2 = 0.
-1, 0
Let b(f) be the second derivative of -f**4/12 + 5*f**3/6 + 2*f**2 + 2*f. Let x be b(5). Factor -2*v**3 + 6*v**x + v**3 - 7*v**2 - v**3 + 3*v**2.
2*v**2*(v - 1)*(3*v + 2)
Let r = 24 + -22. Suppose 18 + 2*d**3 + 3*d + 27*d - 6*d**2 + 18*d**r + 2*d**2 = 0. What is d?
-3, -1
Let j(v) = 2*v - 1. Let a be j(2). Suppose 4*h = a*h. Factor 2/5*i**5 + 0*i - 2/5*i**4 + 0*i**2 + h + 0*i**3.
2*i**4*(i - 1)/5
Let x(a) = -2*a - 7. Let b be x(-7). Let n = b - 2. Factor -n + 5 - p**2 - p.
-p*(p + 1)
Let n(t) be the second derivative of -t**5/60 - 7*t**4/36 - 4*t**3/9 + 8*t**2/3 + 2*t. What is x in n(x) = 0?
-4, 1
Let s = 89 + -89. Let y(t) be the second derivative of -1/10*t**3 + 3/20*t**4 + s - t - 3/5*t**2. Suppose y(h) = 0. What is h?
-2/3, 1
Let u = 18 + -20. Let v(p) = -p. Let r(w) = -2*w**2 - w. Let k(h) = u*v(h) + 2*r(h). Factor k(m).
-4*m**2
Suppose -24*b + 19*b = -10. Factor 0*f - 1/2*f**b + 0.
-f**2/2
Suppose -20*z = -22*z. Let q(t) be the third derivative of 0*t + z - 1/60*t**6 - 1/30*t**5 + 1/6*t**4 + 0*t**3 - 2*t**2. Let q(w) = 0. Calculate w.
-2, 0, 1
Let v(i) be the second derivative of -i**4/42 - 5*i**3/21 - 4*i**2/7 - 14*i. Let v(x) = 0. Calculate x.
-4, -1
Suppose -3*l = -58 + 13. Suppose 3*p + 3 - l = 0. Suppose -z**p - 16*z + z**2 + 2 + 5*z**3 + 14*z - 2 - 3*z**5 = 0. What is z?
-1, 0, 2/3, 1
Let n be (9/(-24))/(18/4). Let c = 35/132 + n. Find v such that 0 + 0*v**2 + 0*v**4 - c*v - 2/11*v**5 + 4/11*v**3 = 0.
-1, 0, 1
Suppose w**2 - w - 2*w - 3*w**2 + 3*w**2 = 0. What is w?
0, 3
Suppose -78*o = -67*o. Solve 0*q + 3/5*q**3 - 6/5*q**4 + o + 0*q**2 + 3/5*q**5 = 0 for q.
0, 1
Solve 8*m**2 + m**2 - 7*m**2 - 8 = 0 for m.
-2, 2
Let j(a) be the second derivative of -a**4/72 + a**3/36 + a**2/6 - 9*a. Let j(k) = 0. What is k?
-1, 2
Determine j so that 93*j**2 + 94*j**2 - 4*j - 191*j**2 = 0.
-1, 0
Factor 28/5*r + 2/5 + 98/5*r**2.
2*(7*r + 1)**2/5
Let p(v) = -5*v**3 + 5*v - 6. Let c(t) = -t**3 + t. Let l(w) = 17*w**3 - 17*w + 13. Let f(x) = -6*c(x) - l(x). Let o(y) = 6*f(y) - 13*p(y). Factor o(z).
-z*(z - 1)*(z + 1)
Let 2/3*b**3 + 7/6*b**5 - 8/3*b**4 - 11/6*b + 7/3*b**2 + 1/3 = 0. What is b?
-1, 2/7, 1
Factor -i**2 + 1/5*i**4 + 0 - 1/5*i**5 + 2/5*i + 3/5*i**3.
-i*(i - 1)**3*(i + 2)/5
Let x(l) be the first derivative of 1/18*l**3 + 1/8*l**4 + 0*l + 1 + 1/36*l**6 + 1/10*l**5 + 0*l**2. Let x(n) = 0. Calculate n.
-1, 0
Suppose 15*k = 53 + 22. Suppose 0 + 2/5*a**3 + 2/5*a**k + 6/5*a**4 - 6/5*a**2 - 4/5*a = 0. What is a?
-2, -1, 0, 1
Let l(v) be the third derivative of 0 - 1/180*v**5 + 4*v**2 + 0*v**3 - 1/72*v**4 + 0*v. Solve l(d) = 0 for d.
-1, 0
Factor 8/5 + 2/5*w**2 + 8/5*w.
2*(w + 2)**2/5
Solve 7*d**3 + 0*d**3 - 5*d**3 = 0.
0
Factor 0*b**2 + 2/3*b**3 + 0*b + 0 - 2/3*b**4.
-2*b**3*(b - 1)/3
Let c(z) be the first derivative of z**6/120 + z**3 + 4. Let r(k) be the third derivative of c(k). Factor r(w).
3*w**2
Suppose -1/2*l**2 + 0*l + 1/6*l**3 + 2/3 = 0. What is l?
-1, 2
Let d(j) be the third derivative of -j**6/60 - 7*j**2. Determine r, given that d(r) = 0.
0
Determine v, given that 0*v - 6*v**4 + 8*v**3 + 14*v**2 + 0*v**3 - 8*v - 8 = 0.
-1, -2/3, 1, 2
Let w(c) = -c**3 + 3*c**2 + 2*c - 2. Let f be w(3). Suppose -j - 9 = -f*j. Factor k**j + k**3 - 4*k**3 + 2*k.
-2*k*(k - 1)*(k + 1)
Let p be (-2)/9 - (-116)/36. Suppose -2*s - p*j + 2 = 0, 5*s - j - 22 = -0*j. Factor -1/2*n**s - 2*n - 3*n**2 - 2*n**3 - 1/2.
-(n + 1)**4/2
Let -57/7*z**3 + 0 + 99/7*z**2 - 27/7*z + 9/7*z**4 = 0. Calculate z.
0, 1/3, 3
Let u be -8*-2*(-3)/(-12). Factor 0*f**u + f**3 + f**4 + f**4 + 2*f**3 - f.
f*(f + 1)**2*(2*f - 1)
Let k(u) = -u**4 - u**3 + u + 1. Let l(w) = -w**4 - 12*w**3 - 4*w**2 + 12*w + 5. Let d(q) = -6*k(q) + l(q). Factor d(i).
(i - 1)**2*(i + 1)*(5*i - 1)
Let d(j) be the second derivative of j**5/30 - j**4/9 + j**3/9 - j. Factor d(k).
2*k*(k - 1)**2/3
Suppose 121*t = 116*t. Factor -2/3*o**3 + t*o**2 + 1/3*o**4 + 0 + 0*o.
o**3*(o - 2)/3
Let o(j) be the third derivative of -j**8/40320 - j**7/5040 - j**6/1440 - j**5/30 - 3*j**2. Let a(b) be the third derivative of o(b). Factor a(t).
-(t + 1)**2/2
Determine u, given that -5*u**2 + 2*u**2 - 11*u + 2*u**2 + 12*u = 0.
0, 1
Let o = 24 - 47/2. Suppose -1/2*w**2 + 1 - o*w = 0. Calculate w.
-2, 1
Let m(p) = -35*p**5 + 20*p**4 + 50*p**3 - 20*p**2 - 10*p + 5. Let d(w) = w**4 - w**3 - w**2 - 1. Let i(z) = 5*d(z) + m(z). Let i(g) = 0. What is g?
-1, -2/7, 0, 1
Let f = 5627/63 - 800/9. Let -f*w**2 + 4/7 - 1/7*w**3 + 0*w = 0. What is w?
-2, 1
Let w(l) be the third derivative of l**7/2100 - l**6/1800 - l**4/24 + 3*l**2. Let q(a) be the second derivative of w(a). Find j such that q(j) = 0.
0, 1/3
Factor -2/7*z - 3/7*z**2 + 9/7*z**3 + 0.
z*(3*z - 2)*(3*z + 1)/7
Let q = -2522 + 17686/7. Factor 8/7 + 34/7*y**2 - q*y - 10/7*y**3.
-2*(y - 2)*(y - 1)*(5*y - 2)/7
Let 2*z**4 - 71*z**3 + 138*z**3 - 70*z**3 - 3*z**4 = 0. What is z?
-3, 0
Let g be ((-15)/(-6))/(4 - (-44)/(-16)). Find c, given that 0 - 2/3*c**3 + 0*c**g - 8/3*c**4 + 0*c = 0.
-1/4, 0
Let x = 2/67 + 191/335. Let h(m) be the first derivative of m**3 + 3/4*m**4 + 0*m - 3/2*m**2 - 1 - x*m**5. Factor h(c).
-3*c*(c - 1)**2*(c + 1)
Let o(q) be the second derivative of -q**6/55 + q**5/22 - q**4/33 + 6*q. Determine c, given that o(c) = 0.
0, 2/3, 1
Let q(v) be the first derivative of -4*v**5/5 - 2*v**4 + 4*v**2 + 4*v - 14. Find f such that q(f) = 0.
-1, 1
Suppose n + n + 5*f = 25, 4*f = 5*n + 20. Find q, given that q**3 - q**2 + n*q**2 + q**2 = 0.
0
Let f(l) = 2*l**2 - 2*l - 1. Let w be f(-1). Suppose y - 3*y + 10 = -o, 5*y - 25 = -w*o. Factor 4*q**3 + 0*q - 2*q + 0*q**3 - 2*q**y.
-2*q*(q - 1)**2*(q + 1)**2
Let u be (4 - 55/15)/(2/8). Factor 0 - u*n**3 + 2/3*n**4 + 2/3*n**2 + 0*n.
2*n**2*(n - 1)**2/3
Let c(h) be the third derivative of -h**6/30 + h**4/6 - 2*h**2. Factor c(f).
-4*f*(f - 1)*(f + 1)
Let v = 8074/5 - 1589. Let g = 26 - v. Solve 1/5*d**4 - 2/5*d**2 - g*d - 1/5*d**5 + 2/5*d**3 + 1/5 = 0.
-1, 1
Let d = -611/2 - -306. Factor 0 + 1/2*g**3 - 1/4*g**2 - d*g + 1/4*g**4.
g*(g - 1)*(g + 1)*(g + 2)/4
Let n be 693/(-18) + (-2)/(-4). Let r = -35 - n. Factor -1/3*a**4 - 2/3 + a**2 + 1/3*a - 1/3*a**r.
-(a - 1)**2*(a + 1)*(a + 2)/3
Let a(c) be the second derivative of -c**4/3 + 2*c**3/3 + 4*c**2 - 20*c. Let a(q) = 0. Calculate q.
-1, 2
Suppose -c - 4*d - 7 = -31, 0 = -3*c - 5*d + 37. Let i be (8/14)/(c/14). Factor 2/7 + 4/7*f**i - 6/7*f.
2*(f - 1)*(2*f - 1)/7
Let k(a) be the second derivative of 0 + 1/5*a**4 - 2/15*a**3 + 0*a**2 - a - 9/100*a**5. Factor k(m).
-m*(3*m - 2)**2/5
Let y(k) be the first derivative of 14*k**3/33 + k**2/11 + 3. Solve y(s) = 0.
-1/7, 0
Let z(f) be the third derivative of 1/105*f**7 + 1/90*f**5 - 1/504*f**8 + 0*f**4 + 0 + 0*f**3 - 3*f**2 - 1/60*f**6 + 0*f. Factor z(w).