.
0, 3
Let u(j) be the second derivative of 2*j**7/21 - 2*j**5/5 + 2*j**3/3 - 3*j. Suppose u(n) = 0. Calculate n.
-1, 0, 1
Let j be (-12)/(-948) + 0/1. Let g = j + 75/316. Factor 1/2*k**2 + 0 + 1/4*k + g*k**3.
k*(k + 1)**2/4
Let x(v) be the second derivative of -v**4/66 + 4*v**2/11 - 12*v. Find k, given that x(k) = 0.
-2, 2
Let l = -1328/7 + 190. Factor 0*m - 2/7 + l*m**2.
2*(m - 1)*(m + 1)/7
Let x(f) be the first derivative of -4*f**5/5 - 4*f**4 - 6*f**3 - 4*f**2 + 5*f + 7. Let i(w) be the first derivative of x(w). Solve i(q) = 0.
-2, -1/2
Let l be (-2)/9 + (-80)/(-36). Factor 264*h**4 - h**3 - 2 + 3*h**l - 265*h**4 - 3*h + 4*h.
-(h - 1)**2*(h + 1)*(h + 2)
Let x(z) = -9*z**3 + 24*z**2 + 15*z - 18. Let r(k) = -17*k**3 + 49*k**2 + 31*k - 35. Let a(d) = -3*r(d) + 5*x(d). What is y in a(y) = 0?
-1, 1/2, 5
Suppose 2*k + 120 + 48 = -d, 168 = -2*k - 2*d. Let c be (-5 - -2)*8/k. Factor 2/7*q - 4/7*q**2 + 0 + c*q**3.
2*q*(q - 1)**2/7
Let n(h) be the first derivative of 1/24*h**3 - 4 - 1/4*h**2 + 1/24*h**4 - 4*h - 1/80*h**5. Let u(j) be the first derivative of n(j). Solve u(i) = 0 for i.
-1, 1, 2
Suppose 0 = 16*r - 20*r + 4. Let c(d) be the first derivative of 3*d + 33/8*d**4 + 27/4*d**2 + 9/10*d**5 + r + 15/2*d**3. Let c(n) = 0. What is n?
-1, -2/3
Find s, given that 0*s**2 - 3/5*s**4 + 3/5 - 6/5*s**3 + 6/5*s = 0.
-1, 1
Let i(p) = 5*p**5 - p**4 + 3*p**3 + p**2 - 4*p - 4. Let v(f) = -14*f**2 + 14*f**2 - f**5 + f + 1 - f**3. Let u(w) = i(w) + 4*v(w). What is l in u(l) = 0?
-1, 0, 1
Let h(r) be the first derivative of 5*r**3/3 + 25*r**2 + 125*r + 21. Let h(j) = 0. What is j?
-5
Factor -10*l**2 + 35*l - 24 + 6*l**3 + 4 - 11*l**3.
-5*(l - 1)**2*(l + 4)
Let q(m) be the third derivative of 1/120*m**5 + 0*m**3 + 0 + 0*m**4 + 0*m - m**2. Factor q(h).
h**2/2
Let q(j) be the second derivative of j**5/300 - j**4/60 - j**2/2 + 2*j. Let i(k) be the first derivative of q(k). Solve i(z) = 0.
0, 2
Let d(c) = c**2 + 1. Suppose 5 + 10 = 3*s. Let v(n) = -3*n**2 + 15*n - 11*n - 5 - 6*n. Let a(r) = s*d(r) + v(r). Find h such that a(h) = 0.
0, 1
Let l be (21/(-22))/7*8/(-6). Find a, given that 0 + 0*a + 2/11*a**5 - 2/11*a**3 + l*a**2 - 2/11*a**4 = 0.
-1, 0, 1
Let h be (10 - 0/2)/2. Let n(v) be the second derivative of -1/6*v**4 + 0*v**2 - 2*v + 0 + 3/20*v**h - 1/6*v**3. Let n(b) = 0. What is b?
-1/3, 0, 1
Factor 3*u**2 - 5 + 4 - 2*u + 0.
(u - 1)*(3*u + 1)
Suppose -49 = -2*d + 5*j, 6*j = -d + j + 32. Let a = 27 - d. Solve 2/5*i**4 - 4/5*i**3 + a*i**2 - 2/5 + 4/5*i = 0.
-1, 1
Let b(s) = 3*s**3 + 5*s**2 + 5*s + 1. Let q(p) = p**3 + p**2 + p. Let k(n) = -b(n) + 2*q(n). Suppose k(z) = 0. What is z?
-1
Let x(j) = -4*j**3 - 56*j**2 + 20*j + 40. Let v(z) = -z**3 - 19*z**2 + 7*z + 13. Let p(r) = 8*v(r) - 3*x(r). What is a in p(a) = 0?
-4, -1, 1
Factor g**3 + 0 - 1/2*g + 1/2*g**2.
g*(g + 1)*(2*g - 1)/2
Let z(w) be the first derivative of -w**7/42 - w**6/10 - 3*w**5/20 - w**4/12 + 3*w + 2. Let s(g) be the first derivative of z(g). Suppose s(b) = 0. Calculate b.
-1, 0
Let i = 1406 + -4211/3. Suppose -i*l**4 - 7/3*l + 5/3*l**3 + 5/3*l**2 + 2/3 + 2/3*l**5 = 0. Calculate l.
-1, 1/2, 1, 2
Let o be ((-21)/(-15))/(5/25). Let r = 7 - o. Factor 1/3*s**3 + r - 1/3*s**2 + 0*s.
s**2*(s - 1)/3
Let u(v) = -v**3 - 3*v**2 + 4*v + 3. Let i be u(-4). What is w in 3*w**3 + 4*w - i*w**2 - 4*w + 3 - 3*w = 0?
-1, 1
Let c(k) = -k**4 + 29*k**3 + 75*k**2 + 71*k + 14. Let q(h) = -5*h**4 + 175*h**3 + 450*h**2 + 425*h + 85. Let j(a) = 35*c(a) - 6*q(a). Factor j(d).
-5*(d + 1)**3*(d + 4)
Let o be 15 - (-9)/(3/1). Suppose 4*v + 17 + 1 = 2*p, o = 4*p - 2*v. Factor -2*j**p + 2*j**3 + j**2 + j**3.
j**2*(j + 1)
Let i(x) = 14*x + 11 + 2*x**2 - x**2 - 2 + 6. Let d be i(-13). Find z, given that -2/7*z**d + 0*z + 2/7 = 0.
-1, 1
Suppose 2*g + 3 = 5. Factor -2 + g + o**3 + o + o**2 - 2*o.
(o - 1)*(o + 1)**2
Suppose 23 - 5 = 9*r. Let j(q) be the first derivative of q**4 + 0*q - r + 14/3*q**3 - 2*q**2 - 14/5*q**5. Factor j(g).
-2*g*(g - 1)*(g + 1)*(7*g - 2)
Let i = -1 + 12. Factor 19 - 18*s - 5 - i + 27*s**2.
3*(3*s - 1)**2
Let q(l) be the third derivative of -l**5/120 - 7*l**4/48 - l**3/2 - 4*l**2. Determine h so that q(h) = 0.
-6, -1
Let w(t) be the first derivative of t**5/270 + t**4/54 + t**3/27 + 2*t**2 + 3. Let o(j) be the second derivative of w(j). Suppose o(y) = 0. Calculate y.
-1
Let r(m) be the first derivative of m**7/735 - m**5/105 + m**3/21 + 3*m**2/2 - 2. Let w(c) be the second derivative of r(c). Factor w(j).
2*(j - 1)**2*(j + 1)**2/7
Let b(w) be the first derivative of 4*w**5/35 + w**4/7 - 4*w**3/7 - 2*w**2/7 + 8*w/7 - 19. Factor b(s).
4*(s - 1)**2*(s + 1)*(s + 2)/7
Let d = -5 + 8. Let q be (-6)/d - 14/(-6). Solve -1/3*l**2 + 2/3 + q*l = 0.
-1, 2
Suppose -40 = -4*g + 16. Suppose r**4 - 5*r**3 + 3*r**4 + g*r**3 - 6*r**3 - r**2 = 0. Calculate r.
-1, 0, 1/4
Let w = -28 + 7. Let m be w/(-36) - 2/6. Factor 1/2*r + m + 1/4*r**2.
(r + 1)**2/4
What is u in 9*u**5 + 27*u**5 + 66*u**4 - 10 + 4*u**3 - 40*u + 2 - 63*u**2 + 5*u**2 = 0?
-1, -2/3, -1/2, 1
Let j(x) = 2*x + 1. Let f be j(1). Suppose -4*m + 20 = 0, 3*v + f = 3*m - 3. Factor -8 + v*o**2 - 3*o**3 + 0*o**3 + 3*o**2 + o**3.
-2*(o - 2)**2*(o + 1)
Let j(i) be the second derivative of -4*i**7/105 + i**6/20 + i**5/30 - i**2/2 + 2*i. Let r(f) be the first derivative of j(f). Factor r(k).
-2*k**2*(k - 1)*(4*k + 1)
Let r be (2*2/(-4))/((-8)/24). Let l(o) be the third derivative of -1/30*o**5 + 1/3*o**r + 3*o**2 + 0*o + 1/60*o**6 + 0 - 1/12*o**4. Let l(u) = 0. Calculate u.
-1, 1
Let u(t) = -t**2 + 5*t - 1. Let q be u(2). Suppose 2 = -g + q. Factor 2*d + 0*d - 3*d**g + d**3.
-2*d*(d - 1)*(d + 1)
Let k(c) = -160*c**2 + 245*c - 55. Let x(q) = -23*q**2 + 35*q - 8. Let m(s) = 2*k(s) - 15*x(s). Suppose m(j) = 0. Calculate j.
2/5, 1
Solve 1/2*f + 0 - 1/4*f**3 - 1/4*f**2 = 0.
-2, 0, 1
Let m(n) be the first derivative of 2/45*n**5 + 4 + 0*n**3 - 1/18*n**4 + 0*n + 0*n**2. Factor m(w).
2*w**3*(w - 1)/9
Let l(v) = -v**3 + 2*v**2 + 3*v. Let y = -3 + 6. Let b be l(y). Factor b + 2/7*h**2 - 2/7*h**3 + 0*h.
-2*h**2*(h - 1)/7
Let f(s) be the first derivative of -s**6/12 + s**5/5 + 5*s**4/8 - 5*s**3/3 - s**2 + 4*s + 8. Solve f(v) = 0.
-2, -1, 1, 2
Let j(f) be the second derivative of -f**6/120 + f**5/60 - 2*f**2 - 2*f. Let r(h) be the first derivative of j(h). Factor r(n).
-n**2*(n - 1)
Let u = 5 + 20. Suppose -4*c + u = -4*j + 1, -24 = -3*c + 5*j. What is m in 2*m**4 + 2*m**3 + 3*m - c*m = 0?
-1, 0
Let 8/5*x**5 + 2/5*x**3 + 0*x**2 - 2*x**4 + 0*x + 0 = 0. What is x?
0, 1/4, 1
Determine k so that 1/3*k**4 - 1/3*k**3 - 4/3*k**2 + 0 + 4/3*k = 0.
-2, 0, 1, 2
Solve 3 - 1/4*q**2 + q = 0.
-2, 6
Let p be (8/20)/(1/10). Factor p*f - 5 - 7*f + 2*f**3 + 1 - 3*f.
2*(f - 2)*(f + 1)**2
Let y = -5/16 - -9/16. Determine h so that -1/4 + 1/4*h - y*h**3 + 1/4*h**2 = 0.
-1, 1
Suppose 5*n = 10, 9 = -3*w - 2*n + 19. Let -6*y**3 + 0 + 11/2*y**4 + 7*y**5 - y - 11/2*y**w = 0. What is y?
-1, -1/2, -2/7, 0, 1
Suppose 85*m - 16*m - 1656 = 0. Let v(g) = g**2 - 6*g. Let d be v(6). Factor d + 12*s + 3/4*s**5 + 6*s**4 + m*s**2 + 18*s**3.
3*s*(s + 2)**4/4
Let d(j) be the second derivative of j**6/10 - 3*j**5/10 + j**4/4 - 7*j. Factor d(q).
3*q**2*(q - 1)**2
Let f = 13/21 - 2/7. Let t(a) be the second derivative of 7/10*a**5 + 1/5*a**6 + f*a**3 + 0 + 5/6*a**4 + 0*a**2 - a. Solve t(r) = 0.
-1, -1/3, 0
Let z = 10 - 6. Suppose 4*r + 2*o + z = 8, 8 = 5*r + 4*o. Factor -2/9*v**2 + 0 + r*v + 2/9*v**4 + 0*v**3.
2*v**2*(v - 1)*(v + 1)/9
Let r(u) = -3*u. Let v be r(2). Let j be (-4 - -6)/((-3)/v). Factor 2/3*p**5 + j*p**4 + 32/3*p**2 + 6*p + 4/3 + 28/3*p**3.
2*(p + 1)**4*(p + 2)/3
Let d(q) = -q**2 + 1. Let z(m) = 30*m**2 - 33*m + 12. Let l(w) = 6*d(w) - z(w). Find y such that l(y) = 0.
1/4, 2/3
Suppose l - 8 = 5*g, 0 = l + g - 1 - 1. Factor t**5 - t**4 - t**4 + 6*t**4 + t**5 + 2*t**l.
2*t**3*(t + 1)**2
Let j = 260 - 260. What is c in j + 1/2*c**3 + 1/2*c**4 + 0*c**2 + 0*c = 0?
-1, 0
Let q = 161/5 - 32. Let s(m) be the first derivative of 1/10*m**4 + 4/15*m**3 + q*m**2 - 2 + 0*m. Suppose s(p) = 0. What is p?
-1, 0
Let l(t) be the third derivative of t**8/28 - 3*t**7/70 - t**6/8 + 3*t**5/20 + t**4/8 + 37*t**2. Solve l(y) = 0.
-1, -1/4, 0, 1
What is f in -6 + 2 - 2*f + 2*f + f**2 = 0?
-2, 2
Let i(g) be the first derivative of -35