2)/6
Let j be 4/(-20) - 42/(-10). Factor 16*o**5 + 13*o**5 - 31*o**5 - 8*o**3 - 8*o**j.
-2*o**3*(o + 2)**2
Factor 28/3*i**3 + 8 + 116/3*i + 40*i**2.
4*(i + 1)*(i + 3)*(7*i + 2)/3
Let h(k) be the third derivative of k**6/210 + 3*k**5/140 + k**4/84 - 30*k**2. Suppose h(q) = 0. What is q?
-2, -1/4, 0
Let l(s) = -s - s + s + 0. Let f(g) = -2*g**4 - 4*g**3 - 2*g**2 + 5*g. Let y = -4 - -5. Let d(u) = y*f(u) + 5*l(u). Factor d(v).
-2*v**2*(v + 1)**2
Solve 2/15*u**3 - 2/5*u**2 + 0 + 4/15*u = 0 for u.
0, 1, 2
Determine r, given that -2/15*r**3 + 0 - 4/15*r - 2/5*r**2 = 0.
-2, -1, 0
Let m(g) = 11*g**5 - 17*g**3 - 5*g**2 + 6*g - 5. Let w(x) = 17*x**5 - 26*x**3 - 8*x**2 + 9*x - 8. Let s = 9 + -4. Let z(j) = s*w(j) - 8*m(j). Factor z(p).
-3*p*(p - 1)**2*(p + 1)**2
Let g(b) = -b**3 + 4*b**2 + 6*b - 5. Let t be g(5). Let y(d) be the second derivative of -1/8*d**2 + t + 1/12*d**3 + d - 1/48*d**4. Find p such that y(p) = 0.
1
Let i(k) = -2*k**2 - 7*k + 4. Let w be i(-4). Factor 0*m**2 + w + 0*m + 1/6*m**3.
m**3/6
Let n(f) be the first derivative of f**5/15 + f**4/36 - 2*f**3/9 - f**2/6 + f - 3. Let w(i) be the first derivative of n(i). Find o such that w(o) = 0.
-1, -1/4, 1
Let h be 4*-4*(-1)/24. Solve 2/3*s**3 - 2/3*s**2 - 2/3*s + h = 0.
-1, 1
Let -41*j - 245 - 5*j - 24*j - 5*j**2 = 0. Calculate j.
-7
Let o(y) be the second derivative of -y**5/210 + y**4/42 - y**3/21 - 2*y**2 + 2*y. Let p(x) be the first derivative of o(x). Let p(n) = 0. What is n?
1
Let w(c) be the third derivative of 0*c + c**2 - 1/360*c**5 + 1/18*c**3 + 0 + 1/144*c**4. Suppose w(r) = 0. What is r?
-1, 2
Suppose 0 = -4*o - 3*w + 19, -8*w + 3*w = -25. Let h be o/((-1)/(4/(-16))). Factor 1/2 - 1/4*a**2 - h*a.
-(a - 1)*(a + 2)/4
Suppose 0 = 3*v - 3 - 6. Suppose 2 = v*q - 4. What is a in -3 + 3 + q*a + a**2 + 1 = 0?
-1
Let c(a) be the first derivative of -7*a**6/36 + 19*a**5/30 - a**4/3 - 2*a**3/9 + 24. Determine n so that c(n) = 0.
-2/7, 0, 1, 2
Let r(f) be the first derivative of f**7/280 - 3*f**5/40 + f**4/4 - 5*f**3/3 - 2. Let g(n) be the third derivative of r(n). Let g(x) = 0. What is x?
-2, 1
Let m = 35 - 33. Factor 1/2*i + i**m - i**4 + 0*i**3 - 1/2*i**5 + 0.
-i*(i - 1)*(i + 1)**3/2
Let s(v) be the first derivative of -v**3/33 - 3*v**2/11 + 7*v/11 + 24. Factor s(i).
-(i - 1)*(i + 7)/11
Suppose -145*l - 6 = -148*l. Factor 9/4*q**l - 3*q**3 + 3/4*q**4 + 0*q + 0.
3*q**2*(q - 3)*(q - 1)/4
Let z(s) be the second derivative of -s**4/6 - 9*s. Determine y, given that z(y) = 0.
0
Let o = -1027/7 + 147. Factor -4/7 + o*u + 2/7*u**2.
2*(u - 1)*(u + 2)/7
Suppose -2/7*d**5 - 4/7*d**4 - 2/7*d**3 + 0*d**2 + 0 + 0*d = 0. What is d?
-1, 0
Find w, given that -5/7*w**3 + 0 + 4/7*w**2 + 1/7*w = 0.
-1/5, 0, 1
Suppose 19*h - 17*h = 0. Let s(l) be the first derivative of -3 - l**2 + 2/3*l**3 + h*l. Factor s(f).
2*f*(f - 1)
Let u(p) be the second derivative of p**8/4200 + p**7/700 + p**6/450 - p**3/2 - 4*p. Let i(l) be the second derivative of u(l). Factor i(r).
2*r**2*(r + 1)*(r + 2)/5
Let t(k) be the first derivative of -k**7/840 + k**5/80 + k**4/48 + 5*k**2/2 - 1. Let b(h) be the second derivative of t(h). Determine z so that b(z) = 0.
-1, 0, 2
Let z(v) be the second derivative of v**4/12 + v**3/6 - v**2 - 16*v. Suppose z(h) = 0. What is h?
-2, 1
Let a(u) = u**2 + 8*u + 6. Let x be a(-8). Let y be 16/x - 6/9. Factor 0 + 1 - q**4 + 4*q**3 - 2*q**3 - y*q.
-(q - 1)**3*(q + 1)
Let f = -1 - -4. Let -3*n**2 + 5*n**4 - n - 5*n**f + 3*n**5 - n**2 + 3*n**3 - n**4 = 0. What is n?
-1, -1/3, 0, 1
Suppose 0 = 4*n + 2*o - 18, -5*n - 14 = -2*n - 4*o. Solve 2 - n*v**2 - 4*v - 4 + 3*v**2 - 3*v**2 = 0.
-1
Let b(h) be the third derivative of 1/45*h**5 - 1/36*h**4 + 0*h**3 + 0*h**6 + 0*h + 0 + 3*h**2 + 1/504*h**8 - 2/315*h**7. Find v such that b(v) = 0.
-1, 0, 1
Let i(n) be the second derivative of 25*n**7/14 - 2*n**6/3 - 19*n**5/4 + 5*n**4/3 + 10*n**3/3 - 17*n. Solve i(c) = 0 for c.
-1, -2/5, 0, 2/3, 1
Let f(l) = 13*l**2 + 8*l - 5. Let z(w) = -6*w**2 - 4*w + 2. Let y = 10 - 6. Let j(u) = y*f(u) + 9*z(u). Factor j(x).
-2*(x + 1)**2
Let h(u) = -u**2 - 99*u + 681. Let g(n) = 2*n**2 + 98*n - 682. Let b(y) = 5*g(y) + 6*h(y). Suppose b(t) = 0. Calculate t.
13
Let f be 2 + 2*((3 - 4) + 0). Factor 4/9*c + f - 2/9*c**2.
-2*c*(c - 2)/9
Let i = -8 - -11. Factor -10/7*k**4 + 2/7*k**2 - 2/7*k**i - 6/7*k**5 + 0*k + 0.
-2*k**2*(k + 1)**2*(3*k - 1)/7
Let f be 86/(-10) - 12/30. Let h be ((-1)/3)/(f/81). Find c such that -1/4*c + 0 + 1/4*c**2 + 1/4*c**h - 1/4*c**4 = 0.
-1, 0, 1
Factor 2/3*x**3 - 2*x + 0*x**2 - 4/3.
2*(x - 2)*(x + 1)**2/3
Let l(y) = -383*y**4 - 67*y**3 + 232*y**2 - 60*y. Let t(x) = 128*x**4 + 22*x**3 - 77*x**2 + 20*x. Let b(w) = 3*l(w) + 8*t(w). Let b(r) = 0. Calculate r.
-1, 0, 2/5
Let k(u) = -u + 8. Suppose z = -2 + 10. Let w be k(z). Determine o so that -2*o**2 - 6/5*o**4 + 2/5*o + 14/5*o**3 + w = 0.
0, 1/3, 1
Let u(c) = 12*c + 1. Let w be u(1). Suppose -2*k - 4 = -5*i, 5*i + 4*k - w = 3*k. Factor -2*a + 7*a**2 - 3*a**i + 1 + 0*a**2 - 3.
2*(a - 1)*(2*a + 1)
Let z(l) be the third derivative of -l**7/490 - 3*l**6/280 - l**5/140 + 3*l**4/56 + l**3/7 - 6*l**2. Solve z(v) = 0 for v.
-2, -1, 1
Let o be 2 + 1 + (5 - 3). Let s(d) be the first derivative of -4/3*d**3 + 3/2*d**4 - 1 - 4/5*d**o + 1/2*d**2 + 1/6*d**6 + 0*d. Factor s(l).
l*(l - 1)**4
Let w(o) be the third derivative of o**8/10080 + o**7/1260 + o**6/360 - 7*o**5/60 - 7*o**2. Let h(i) be the third derivative of w(i). Factor h(c).
2*(c + 1)**2
Let a = -35/18 + 22/9. Let -1/2 + 0*g + a*g**2 = 0. What is g?
-1, 1
Let i be 228/16*8/6. Suppose 0 = i*s - 14*s - 20. Find c such that -20/7*c**2 - 10/7*c**s - 2/7 - 2/7*c**5 - 20/7*c**3 - 10/7*c = 0.
-1
Suppose 2*f - 1 = 3. Suppose -f*c**2 + 5*c**3 + 2*c**5 + c**4 + c**3 - 7*c**4 = 0. Calculate c.
0, 1
Solve -5/3*z**2 + 0*z + 0 + 1/3*z**3 = 0 for z.
0, 5
Solve 0 + 16/15*s**3 + 0*s + 2/15*s**5 + 2/3*s**4 + 8/15*s**2 = 0 for s.
-2, -1, 0
Let j be (4/(-10))/((-12)/35). Suppose 33*a = -13*a + 92. Let 1/3*o**3 - 1/3*o + 7/6*o**a - j*o**4 + 0 = 0. Calculate o.
-1, 0, 2/7, 1
Let v = 931 - 929. Factor -6/5*z - 4/5 - 2/5*z**v.
-2*(z + 1)*(z + 2)/5
Determine v, given that 41*v**2 + 29*v**2 + 18*v - 10 - 2*v**3 - 76*v**2 = 0.
-5, 1
Let z(c) = c**3 + 5*c**2 + 4*c + 2. Let f be z(-4). Let h = -62/3 - -257/12. Suppose 1/2*v + 0 + h*v**f = 0. Calculate v.
-2/3, 0
Let m be 325*(-3)/(-252) - 3. Let k = m + -7/12. Factor 0 + 0*z - 2/7*z**5 + 2/7*z**2 + k*z**3 - 2/7*z**4.
-2*z**2*(z - 1)*(z + 1)**2/7
Let r(x) be the second derivative of -3*x**5/20 - x**4/2 - x**3/2 + 16*x. Suppose r(b) = 0. What is b?
-1, 0
Let x(g) be the second derivative of -5*g**4/12 + 5*g**3/6 - g. Find v such that x(v) = 0.
0, 1
Let z be -1 + -2 - 21/(-3). What is k in -2*k**z - 2/5*k + 0 + 6/5*k**3 + 2/5*k**2 + 4/5*k**5 = 0?
-1/2, 0, 1
Let k(g) be the third derivative of -1/180*g**5 + 3*g**2 - 1/12*g**4 + 0*g - 1/2*g**3 + 0. Find i, given that k(i) = 0.
-3
Let f(u) be the third derivative of u**9/7560 - u**8/1680 - u**4/8 + 2*u**2. Let m(v) be the second derivative of f(v). What is z in m(z) = 0?
0, 2
Let i(g) = -g + 1. Let n(t) = 8*t**4 + 2*t**3 - 10*t**2 - 2*t + 2. Let d(j) = 4*i(j) - 2*n(j). Let d(q) = 0. Calculate q.
-5/4, 0, 1
Let x = -31 + 35. Let l(m) be the first derivative of -4/3*m - 14/3*m**3 + 17/6*m**x + 2 + 11/3*m**2 - 2/3*m**5. Let l(r) = 0. Calculate r.
2/5, 1
Let a(w) be the first derivative of -w**4/2 - 4*w**3 + 64*w - 29. Factor a(d).
-2*(d - 2)*(d + 4)**2
Let j = 5 + -2. Let w(n) = -n**3 + 5*n + 0*n**j - 6*n. Let c(r) = -r**4 - 3*r**3 - 5*r**2 - r. Let p(l) = 2*c(l) + 2*w(l). Determine v, given that p(v) = 0.
-2, -1, 0
Let m be -31*1 + (1 - 0). Let p = -208/7 - m. Factor -2/7*k**2 + 0 - p*k.
-2*k*(k + 1)/7
Let q(p) be the second derivative of -1/21*p**7 + 0*p**2 - 1/6*p**5 + 4*p + 0*p**3 + 0 + 1/18*p**4 + 7/45*p**6. Determine h so that q(h) = 0.
0, 1/3, 1
Let v(y) be the first derivative of -y**5/30 - y**4/6 - y**3/3 - 2*y**2 - 1. Let h(s) be the second derivative of v(s). Find p, given that h(p) = 0.
-1
Let u(f) be the first derivative of 5*f**6/12 + f**5/2 - 35*f**4/8 - 65*f**3/6 - 15*f**2/2 + 12. Determine y so that u(y) = 0.
-2, -1, 0, 3
Let v(x) be the first derivative of -x**5/5 + x**4/2 + x**3 + 19. Factor v(w).
-w**2*(w - 3)*(w + 1)
Factor -8/9*m