) = y*f(l) + 5*u(l). Determine i, given that n(i) = 0.
1
Let a(d) = -d**2 - 9*d - 6. Suppose -3 + 35 = -4*n. Let o be a(n). Suppose -4/3*u + 2/3*u**o + 2/3 = 0. Calculate u.
1
Let i(b) be the second derivative of b**5/35 + b**4/7 + 4*b**3/21 - 4*b. Let i(x) = 0. Calculate x.
-2, -1, 0
Let j = -89/3 + 30. Let 2/3*x**2 + j*x + 1/3*x**3 + 0 = 0. Calculate x.
-1, 0
Let m be 18/990 - (-2)/11. Factor 1/5*u**2 - 1/5 - m*u + 1/5*u**3.
(u - 1)*(u + 1)**2/5
Find r such that 4*r**3 + 3*r**4 - 2*r**5 - 2*r + 4*r**4 + 2 - 3*r**4 - 2*r**4 - 4*r**2 = 0.
-1, 1
Factor -4*y**2 - 9*y - y**4 + 6 - 6 + 5*y**3 + y**2.
-y*(y - 3)**2*(y + 1)
Let w(b) be the first derivative of b**4/4 - b**3 + 3*b**2/2 - b + 2. Solve w(x) = 0 for x.
1
Let l = 14 + -20. Let z(p) = 2*p**2 - 2*p - 6*p**2 + 4*p. Let a(j) = j**2 - j. Let k(s) = l*a(s) - 2*z(s). Suppose k(h) = 0. What is h?
-1, 0
Let v be 2/4*(3 + 3). Solve -l**2 - 3*l**3 + l**v + 0*l**3 + 3*l**3 = 0.
0, 1
Let 3*o**2 - 17/7*o**3 + 2/7 - 11/7*o + 5/7*o**4 = 0. Calculate o.
2/5, 1
Determine c, given that -1/2*c**3 + 0*c + 0 + 1/4*c**4 + 0*c**2 = 0.
0, 2
Let a(y) be the first derivative of 4*y**3/3 + 12*y**2 + 36*y + 6. Factor a(c).
4*(c + 3)**2
Let v = 547/5 + -109. Let b(r) be the first derivative of 2/15*r**3 + 2 - v*r**2 + 2/5*r. Factor b(y).
2*(y - 1)**2/5
Let a(g) = 7*g**4 - 16*g**3 + 21*g**2 - 14*g + 2. Let b(r) = -15*r**4 + 32*r**3 - 42*r**2 + 29*r - 4. Let d(v) = 7*a(v) + 3*b(v). Determine k so that d(k) = 0.
1/2, 1, 2
Let u(k) = k**3 + 9*k**2 + k + 13. Let c be u(-9). Factor 8*m**3 + 0*m**2 + 2*m**2 - 7*m**3 - m**c.
-m**2*(m - 2)*(m + 1)
Let n(v) be the first derivative of 14*v**5/15 - 2*v**4 + 2*v**3/3 + 2*v**2/3 - 2. Determine a so that n(a) = 0.
-2/7, 0, 1
Let i be (20/5)/((-4)/10). Let u = -6 - i. Factor -2*p**2 + 2*p + p**2 - u + 2*p.
-(p - 2)**2
Let t(c) be the second derivative of -c**4/20 - c**3/5 - 13*c. Let t(d) = 0. Calculate d.
-2, 0
Let t(d) be the first derivative of 3*d**6/4 - 57*d**5/10 + 47*d**4/4 + d**3/3 - 39*d**2/4 - 9*d/2 - 16. What is a in t(a) = 0?
-1/3, 1, 3
Let y(p) = -p**5 + 3*p**4 - p**3 + 3*p**2 + 2. Let k(l) = -3*l**5 + 9*l**4 - 2*l**3 + 10*l**2 + 7. Let r(b) = 6*k(b) - 21*y(b). Factor r(d).
3*d**2*(d - 1)**3
Determine w, given that 0 - 3/4*w - 3/4*w**2 = 0.
-1, 0
Factor 12/17 + 8/17*n**2 - 2/17*n**3 + 22/17*n.
-2*(n - 6)*(n + 1)**2/17
Let o(m) be the second derivative of -m**6/285 - m**5/190 + m**4/114 + m**3/57 + 8*m. Find j such that o(j) = 0.
-1, 0, 1
Let k(r) be the first derivative of 0*r**5 + 1 - 1/6*r**4 + 0*r + 1/27*r**6 + 0*r**2 - 4/27*r**3. Let k(x) = 0. What is x?
-1, 0, 2
Let j(u) = 13*u**4 - 8*u**3 + 5*u**2 + 5*u. Let r(h) = -84*h**4 + 52*h**3 - 32*h**2 - 32*h. Let q(g) = 32*j(g) + 5*r(g). Factor q(v).
-4*v**3*(v - 1)
Let m be -2 + 10 + -3 + -1. Let w(u) be the third derivative of 0*u + 0*u**3 + 0 + 1/72*u**m + 2*u**2 + 1/120*u**6 + 1/60*u**5 + 1/630*u**7. Factor w(f).
f*(f + 1)**3/3
Let i(k) be the third derivative of 8/3*k**4 - 4*k**2 - 2*k**3 + 0*k + 0 - 16/15*k**5. Factor i(s).
-4*(4*s - 3)*(4*s - 1)
Let l(g) be the second derivative of -1/5*g**3 - 1/20*g**4 + 3*g + 0 - 3/10*g**2. Suppose l(x) = 0. What is x?
-1
Let v(f) be the first derivative of -1/6*f**3 + 0*f**2 - 6 + 1/10*f**5 + 1/12*f**6 - 1/8*f**4 + 0*f. Let v(m) = 0. What is m?
-1, 0, 1
Solve 6/7*d**4 + 0 - 6/7*d**2 + 2/7*d**5 - 4/7*d + 2/7*d**3 = 0 for d.
-2, -1, 0, 1
Suppose b = w, -4*w - 3*b = -2*w - 10. Let o(x) be the second derivative of 1/6*x**3 - w*x + 0 + 1/24*x**4 + 1/4*x**2. Determine s so that o(s) = 0.
-1
Let -6/5*q**2 + 4 - 26/5*q = 0. What is q?
-5, 2/3
Let f(t) = -2*t**3 - 8*t**2 - 3*t + 8. Let u(m) = 3*m**3 + 12*m**2 + 5*m - 12. Let q(y) = 8*f(y) + 5*u(y). Suppose q(x) = 0. Calculate x.
-4, -1, 1
Let g(m) be the first derivative of -m**6/15 - 6*m**5/25 + m**4/10 + 2*m**3/5 - 10. Find n such that g(n) = 0.
-3, -1, 0, 1
Suppose 75 = 5*j - o, -j - 4*o + 35 = -1. Suppose j = -3*c + c + 5*r, 3*r = 3*c + 6. Suppose -2*m**3 - 18/5*m**c - 4/5 - 2/5*m**4 - 14/5*m = 0. Calculate m.
-2, -1
Suppose 19 = 3*f + 7. Let n(c) be the first derivative of -c**6 + 11/4*c**f + c**3 - 5/2*c**2 - 1/5*c**5 - 1 - 2*c. Determine y, given that n(y) = 0.
-1, -2/3, -1/2, 1
Let f = -4120 - -3460801/840. Let j(g) be the third derivative of 0*g**6 + 0*g**4 + 1/525*g**7 - 3*g**2 + 0*g**5 + 0*g + f*g**8 + 0*g**3 + 0. Factor j(b).
2*b**4*(b + 1)/5
Let h = 290/9 - 32. Let v be -1 + 0 - (-3 - 0). Factor 0 + 0*b + h*b**4 + 4/9*b**3 + 2/9*b**v.
2*b**2*(b + 1)**2/9
Let r = 25 + -16. Suppose 0 = 3*y - r. Factor 8*w**2 + w - 2*w + y*w.
2*w*(4*w + 1)
Let g(s) = -7*s**3 + 10*s**2 - 16*s + 3. Let p(x) = -x**3 - 1. Suppose 5*h + 4*y = -26, -4*h + 2*h + 2*y = -4. Let q(k) = h*g(k) + 10*p(k). Factor q(o).
4*(o - 2)**2*(o - 1)
Let t(m) be the first derivative of m**4/22 - 2*m**3/11 + 2*m**2/11 - 8. Factor t(b).
2*b*(b - 2)*(b - 1)/11
Let h(v) be the third derivative of v**7/140 + v**6/32 + v**5/80 - v**4/16 - 13*v**2. What is n in h(n) = 0?
-2, -1, 0, 1/2
Let x(m) = m**4 + m**3 - m**2 - m + 1. Let q(v) = -14*v**3 + 26*v**2 - 14*v - 2. Let y(j) = -2*q(j) - 4*x(j). Determine w so that y(w) = 0.
0, 2
What is p in -4/7*p**5 + 12/7*p - 8/7*p**2 + 12/7*p**4 - 8/7*p**3 - 4/7 = 0?
-1, 1
Let k = -106/3 + 36. Let r be 2/(-8) + (-18)/(-8). Factor k*q**2 - r*q + 4/3.
2*(q - 2)*(q - 1)/3
Let c be (2/3)/(4/(-6)). Let g(s) = 4*s**2 - s - 1. Let h be g(c). Factor -2*i**2 + 4 - 2*i + 4*i**2 - h*i.
2*(i - 2)*(i - 1)
Let p be (10/12 - 1)*-3. Factor d**3 + d**2 + p*d**5 - 3/2*d**4 - 3/2*d + 1/2.
(d - 1)**4*(d + 1)/2
Let r(k) = -k**2 - 1. Let f be r(0). Let c be (5/30*-2)/f. Find h, given that 3 - 2*h + c*h**2 = 0.
3
Let v(h) be the first derivative of 2*h**3/9 - h**2 + 4*h/3 + 5. Factor v(c).
2*(c - 2)*(c - 1)/3
Let p(l) be the second derivative of l**9/7560 - l**8/1680 + l**6/180 - l**5/60 - 5*l**4/12 - 4*l. Let o(n) be the third derivative of p(n). Factor o(u).
2*(u - 1)**3*(u + 1)
Suppose 2*h + 4*m = 10, 5*m + 4 = 2*h - 33. Suppose 32*w**4 + 2 - h*w - 9*w + 66*w**2 - 71*w**3 - 9*w**3 = 0. What is w?
1/4, 1
Factor j**3 + 4*j**4 + 7/3*j**5 + 0 + 0*j - 2/3*j**2.
j**2*(j + 1)**2*(7*j - 2)/3
Let l(d) = 7*d**4 + 16*d**3 + 8*d**2 - d. Let b = -3 + 2. Let x(w) = -w**2 - w. Let i(j) = b*l(j) + 3*x(j). Factor i(k).
-k*(k + 1)**2*(7*k + 2)
Suppose 2/5*m**3 + 0*m + 0*m**2 + 0 = 0. Calculate m.
0
Let w(o) be the first derivative of 0*o**3 + 1/2*o**4 - 1/3*o**6 + 0*o - 5 + 0*o**2 + 0*o**5. Determine c, given that w(c) = 0.
-1, 0, 1
Let j(v) = -v. Let w be j(3). Let s(m) = -3*m**4 - 2*m**3 + 2*m**2 + 3*m. Let a(d) = -3*d**4 - d**3 + 2*d**2 + 4*d. Let u(f) = w*a(f) + 4*s(f). Factor u(t).
-t**2*(t + 2)*(3*t - 1)
Suppose 7*h = -5*h. Solve -6*o**3 + h + 12/11*o + 14/11*o**5 - 2*o**2 - 18/11*o**4 = 0 for o.
-1, 0, 2/7, 3
Let i(x) be the second derivative of x**5/5 + x**4/3 - 4*x**3/3 - 10*x. Let i(f) = 0. What is f?
-2, 0, 1
Let a be 16*(-4 + 0)/4. Let z = 16 + a. Factor -1/2*p + z + 3/4*p**2.
p*(3*p - 2)/4
Determine r, given that -108/7 + 144/7*r - 27/7*r**5 + 213/7*r**2 - 153/7*r**4 - 165/7*r**3 = 0.
-3, -1, 2/3
Let u(s) be the second derivative of 0 + 1/6*s**4 + 2/3*s**3 + s**2 + 2*s. What is y in u(y) = 0?
-1
Let f = 4 + 27. Suppose -2*z - 9 = -f. Let -5*b**2 + z*b**2 - 4*b**2 + 2*b = 0. What is b?
-1, 0
Let w be 117/6*2/18. Let v(m) be the first derivative of -4/3*m**3 + 1/3*m**2 - 8/5*m**5 + w*m**4 + 0*m + 2 + 4/9*m**6. Suppose v(i) = 0. Calculate i.
0, 1/2, 1
Let p(w) be the second derivative of w**8/3360 - w**7/420 + w**6/120 - w**5/60 - w**4/2 - 5*w. Let d(r) be the third derivative of p(r). Factor d(c).
2*(c - 1)**3
Let g(k) = -6 + 4*k**2 - 4*k**3 - 4*k**3 + 4*k + 0*k**3. Let a = -8 - -2. Let c(s) = -s**3 + s - 1. Let n(t) = a*c(t) + g(t). Factor n(p).
-2*p*(p - 1)**2
Let m(u) be the second derivative of -7*u**5/90 - 5*u**4/54 + 16*u**3/27 - 4*u**2/9 - 7*u. Factor m(t).
-2*(t - 1)*(t + 2)*(7*t - 2)/9
Let q(w) be the second derivative of w**5/140 - w**4/84 - w**3/42 + w**2/14 + 10*w. What is r in q(r) = 0?
-1, 1
Let j(r) = 3*r**4 + 24*r**3 - 27*r**2 + 33*r - 15. Let l(p) = -p**4 - 12*p**3 + 14*p**2 - 16*p + 7. Let d(t) = -4*j(t) - 9*l(t). Factor d(i).
-3*(i - 1)**4
Let q(j) = 3*j**2 + 25*j + 10. Let x be q(-8). Solve 1/2*r**x + 0 + 0*r = 0 for r.
0
Let c = -68 + 70. L