(y) be the third derivative of -y**5/40 - y**4/4 - y**3 - 32*y**2. Solve d(v) = 0 for v.
-2
Let a(q) = -12*q**4 - 13*q**3 - 14*q**2 + 13*q + 17. Let g(m) = -m**4 + m + 1. Let t(h) = 2*a(h) - 18*g(h). Solve t(u) = 0.
-2, -1, 2/3
Suppose 192/5 + 3/5*l**2 + 48/5*l = 0. What is l?
-8
Let r(n) be the first derivative of 4*n**3/3 + 8*n**2 + 16*n - 17. Find o, given that r(o) = 0.
-2
Let q(l) be the third derivative of 0 - 1/4*l**4 + 1/24*l**8 + 0*l + 2*l**2 + 2/3*l**3 - 7/15*l**5 + 4/35*l**7 - 1/15*l**6. Factor q(r).
2*(r - 1)*(r + 1)**3*(7*r - 2)
What is f in 7/2*f + 4 - 1/2*f**2 = 0?
-1, 8
Let r(b) be the first derivative of 686*b**5/5 - 637*b**4/2 + 252*b**3 - 92*b**2 + 16*b + 5. Solve r(l) = 0 for l.
2/7, 1
Factor 0*q**2 - 2/11*q**3 + 0 + 0*q - 12/11*q**4 - 16/11*q**5.
-2*q**3*(2*q + 1)*(4*q + 1)/11
Let d be 1/2 - (-16)/40. Let o(c) be the first derivative of 7/15*c**6 + 2/5*c**2 + 0*c - d*c**4 - 2/5*c**5 + 2/3*c**3 + 2. Let o(k) = 0. What is k?
-1, -2/7, 0, 1
Suppose 5*m = -0*o + 3*o - 62, 0 = 3*m + 4*o + 14. Let f be (-44)/m + (-4)/1. Factor 2/5*v + f*v**2 + 0.
2*v*(v + 1)/5
Let n(b) be the second derivative of b**8/3360 + b**7/540 - b**5/45 + b**4/4 + 2*b. Let o(j) be the third derivative of n(j). Factor o(v).
2*(v + 1)*(v + 2)*(3*v - 2)/3
Solve -1/5*x**3 + 0*x - 3/5*x**2 + 0 = 0 for x.
-3, 0
Let 0 - 2/7*n**2 + 2/7*n**4 - 2/7*n**3 + 2/7*n**5 + 0*n = 0. Calculate n.
-1, 0, 1
Let s(y) be the third derivative of 2*y**7/105 - y**6/18 + 7*y**5/135 - y**4/54 - 17*y**2. Determine k so that s(k) = 0.
0, 1/3, 1
Let l(m) = -m**2 + 5*m - 2. Let w(c) = c**2 - c + 1. Let t(y) = -l(y) - 2*w(y). Factor t(o).
-o*(o + 3)
Let x(h) be the third derivative of -h**7/1050 - h**6/200 + h**5/300 + h**4/40 - 12*h**2. Find t such that x(t) = 0.
-3, -1, 0, 1
Let p(a) be the second derivative of a**8/4480 + a**7/5040 - a**6/720 + 5*a**4/12 - a. Let l(y) be the third derivative of p(y). Let l(c) = 0. Calculate c.
-1, 0, 2/3
Let k(d) = -d**3 - d**2 - d + 1. Let p(u) = u**4 - 2*u**3 - 4*u**2 - 8*u + 3. Let v(x) = 10*k(x) - 2*p(x). What is m in v(m) = 0?
-2, -1, 1
Let g(s) = -s + 2. Let m be g(-2). Suppose -m*r = -2*r. Suppose 0 + 4/5*t**3 + 2/5*t**2 + r*t + 2/5*t**4 = 0. Calculate t.
-1, 0
Let s(q) be the second derivative of q**6/165 - q**4/66 + q. Find u such that s(u) = 0.
-1, 0, 1
Let j(b) be the second derivative of -b**4 + 2*b**3/3 + 4*b**2 + 4*b. Determine u, given that j(u) = 0.
-2/3, 1
Let q(k) = k**3 - 11*k**2 - 2*k + 24. Let x be q(11). Let -1/3*n**5 + 0 + 0*n**4 + 0*n + n**3 + 2/3*n**x = 0. What is n?
-1, 0, 2
Let f(w) be the first derivative of 0*w - 1/9*w**3 + 1/15*w**5 - 1/18*w**6 + 0*w**2 - 1 + 1/12*w**4. Find v such that f(v) = 0.
-1, 0, 1
Let b = -6 - 2. Let k be ((-10)/b)/(1/4). Factor 4/9*n**3 - 2/3*n - 4/9*n**2 + 2/9*n**k - 2/9 + 2/3*n**4.
2*(n - 1)*(n + 1)**4/9
Let s = -9 + 9. Let w(h) be the first derivative of 1/21*h**6 + 0*h + 2 + s*h**3 + 1/14*h**4 + 4/35*h**5 + 0*h**2. Find u such that w(u) = 0.
-1, 0
Let c(l) be the first derivative of l**5/30 - l**4/8 + l**3/9 - 27. Factor c(p).
p**2*(p - 2)*(p - 1)/6
Let u = 2/351 - -1394/1755. Factor u*s**2 + 0 + 2/5*s.
2*s*(2*s + 1)/5
Suppose 6 = d + i, 4*d + 12 = i + 4*i. Factor 2*k + 3*k**3 + 6*k + 9*k**d + k + 3.
3*(k + 1)**3
Suppose 0 = 2*z - 3*i - 19, 4*z - z + 4*i = -14. Let -1 - 3*g**5 + 6*g**z + 4 - 6*g**3 + 3*g**4 + 9*g - 12*g**4 = 0. What is g?
-1, 1
Let l = -8/77 - -1426/385. Factor l + 2/5*u**3 - 2*u**2 + 6/5*u.
2*(u - 3)**2*(u + 1)/5
Let d(v) = 8*v - 3. Let i be d(6). Let u be 10/i + (-32)/(-18). Solve -8*t**3 + u*t - 8*t**2 - t + 2*t**3 - 3*t = 0.
-1, -1/3, 0
Let l(m) be the first derivative of -m**8/1680 + m**6/180 - m**4/24 + m**3 + 9. Let g(o) be the third derivative of l(o). Factor g(k).
-(k - 1)**2*(k + 1)**2
Factor -2/3*i + 1/3*i**2 + 0.
i*(i - 2)/3
Let o = -177/5 - -179/5. Determine s, given that -2/5*s + 4/5*s**2 - o = 0.
-1/2, 1
Suppose -y - 4 = -3*y. Suppose -1/2*c**4 + 3/2*c**3 + 0*c**2 + 0 - y*c = 0. What is c?
-1, 0, 2
Find b, given that -5/2*b**2 + b + 0 + 5/8*b**5 - 3/4*b**3 + 13/8*b**4 = 0.
-2, 0, 2/5, 1
Let k(a) be the first derivative of -3*a**6/25 + 8*a**5/25 - a**4/6 - 2*a**3/15 - 2*a + 4. Let f(g) be the first derivative of k(g). Factor f(l).
-2*l*(l - 1)**2*(9*l + 2)/5
Let j(h) = -3*h**3 - 2*h**2 + 1. Let i be j(-1). Suppose 0 = l - 6 + 4. Factor -2 - i - 3*q - 49*q**l - 25*q.
-(7*q + 2)**2
Let o = 5839/6 - 973. Find y, given that -5/3*y**2 - 5/6*y**4 + 5/6*y + 5/3*y**3 - 1/6 + o*y**5 = 0.
1
Let h(s) be the third derivative of -s**9/20160 + s**8/5376 - s**7/5040 + s**4/6 - 2*s**2. Let p(t) be the second derivative of h(t). Factor p(g).
-g**2*(g - 1)*(3*g - 2)/4
Suppose -5*f = g - 5, 2*f + 3*g + 13 = 2. Let u(t) be the second derivative of -t**f + 2*t - 2/3*t**4 + 0 - 4/3*t**3. Factor u(i).
-2*(2*i + 1)**2
Factor 0*o**2 + 0 - 2/5*o + 2/5*o**3.
2*o*(o - 1)*(o + 1)/5
Let x(h) = -h**2 - 5*h + 2. Let c(y) = y**2 + 6*y - 3. Let j(z) = -2*c(z) - 3*x(z). Solve j(g) = 0.
-3, 0
Let f(n) = n**3 - 7*n**2 - 8*n + 4. Let b be f(8). Suppose u = -4*u. Let -2/3*x + u*x**3 + 4/3*x**b + 2/3*x**5 + 0 - 4/3*x**2 = 0. Calculate x.
-1, 0, 1
Suppose -95 = -5*r - 85. Factor 1/3*n**r + 1/3*n**3 - 1/6 - 1/6*n**4 - 1/6*n**5 - 1/6*n.
-(n - 1)**2*(n + 1)**3/6
Find g, given that -945*g**3 - 675*g**4 - 306*g**2 - 188/5*g - 8/5 = 0.
-1, -2/15
Let k(v) be the first derivative of v**8/6720 - v**6/1440 - 2*v**3/3 + 7. Let w(p) be the third derivative of k(p). Find t such that w(t) = 0.
-1, 0, 1
Let j be -1 + (3/1 - -2). Suppose -v - 9*v - 20*v**3 - 2*v**5 - 6*v**4 - 20*v**2 - 2 - j*v**4 = 0. Calculate v.
-1
Factor 7*t**3 - 2*t - 2*t**5 + 5*t**2 + 8*t**4 - 12*t**3 + 3*t**2 - 7*t**3.
-2*t*(t - 1)**4
Factor 0 + 2/3*i**4 + 2/3*i**3 - 10/3*i**2 + 2*i.
2*i*(i - 1)**2*(i + 3)/3
Suppose -2*q - 5*h + 3 = -3, -4*h + 3 = q. Suppose -4*j + q + 5 = 0. What is l in -2*l**2 + 2*l**2 + 4*l**2 - 3*l**j - 2*l = 0?
0, 2
Let t(c) be the third derivative of 11*c**7/315 - 4*c**6/135 - 2*c**5/135 + 30*c**2. Factor t(h).
2*h**2*(3*h - 2)*(11*h + 2)/9
Let z = -153/5 - -31. Let x be 3 + 219/(-105) + 4/14. Factor -4/5 + z*n + x*n**2.
2*(n + 1)*(3*n - 2)/5
Let a(z) = -4*z**3 + 6*z**2 + z. Let p(c) = 3*c**3 - 5*c**2. Let d(b) = -2*a(b) - 3*p(b). Determine f, given that d(f) = 0.
0, 1, 2
Let j(s) be the first derivative of 2/5*s**5 - 4/3*s**3 - 2 + 2*s + s**4 - s**2 - 1/3*s**6. Suppose j(d) = 0. Calculate d.
-1, 1
Let h = 41 + -40. Let a(x) be the first derivative of 6*x**3 + 3/4*x**4 + 24*x + 18*x**2 - h. Factor a(v).
3*(v + 2)**3
Let h(m) be the first derivative of -m**3/8 - m**2/16 + 19. Let h(d) = 0. Calculate d.
-1/3, 0
Let j(r) be the second derivative of -r**5/180 + r**4/27 - r**3/18 + 23*r. Factor j(x).
-x*(x - 3)*(x - 1)/9
Let w(u) be the second derivative of -u**4/12 - 5*u**3/6 + 3*u**2 + 11*u. Factor w(g).
-(g - 1)*(g + 6)
Let p be (9/((-945)/10))/(6/(-14)). Factor -p*t - 2/9*t**2 + 0.
-2*t*(t + 1)/9
Factor 4*c - 4*c**2 - 4*c + 5*c + 7*c.
-4*c*(c - 3)
Let u = -10 + 10. Let h(j) be the third derivative of -2*j**2 + 1/180*j**5 + 1/360*j**6 + u*j + 0*j**4 + 0 + 0*j**3. Factor h(r).
r**2*(r + 1)/3
Let s(i) be the third derivative of 5*i**8/336 + i**7/14 + i**6/12 - 22*i**2. Let s(g) = 0. Calculate g.
-2, -1, 0
Suppose -x - i = -2*x + 1, -x = -5*i + 19. Suppose 3*f = x*f - 6. Solve -2/7 - 2/7*r**f + 4/7*r = 0 for r.
1
Let r(l) = -2*l**2 + 13*l - 8. Let s(x) = 4 + 0*x**2 - 2 + 2 - 6*x + x**2. Let y(k) = -2*r(k) - 5*s(k). Factor y(g).
-(g - 2)**2
Let w(m) be the first derivative of 2/7*m**3 + 1/14*m**4 - 8/7*m + 0*m**2 + 4. Suppose w(j) = 0. What is j?
-2, 1
Factor 3/2*l**3 + 9/4 - 2*l**2 - 3/2*l - 1/4*l**4.
-(l - 3)**2*(l - 1)*(l + 1)/4
Let s be (6/(-135))/(6/(-9)). Let x = 4/15 + s. Factor 1/3*j**2 - x*j**3 - 1/3*j**4 + 1/3*j + 0.
-j*(j - 1)*(j + 1)**2/3
Let b(m) be the third derivative of -m**8/1176 + m**7/735 + m**6/70 - 2*m**5/105 - 2*m**4/21 + 2*m**2. Find w, given that b(w) = 0.
-2, -1, 0, 2
Let w(z) = 4*z**4 - z**3 + 3*z**2 - 3. Let f(t) = 9*t**4 - 2*t**3 + 7*t**2 - 7. Let p(q) = -6*f(q) + 14*w(q). Factor p(j).
2*j**3*(j - 1)
Let l(w) be the first derivative of -1 + 0*w**2 - 2/5*w**5 + 0*w**3 + 0*w - 1/8*w**4. Suppose l(c) = 0. What is c?
-1/4, 0
Let c(g) = 7*g**2 + 4*g + 19. Let r(n) = -2*n**2 - n - 5. Let a(i) = -6*c(i