3*v + 2*v**2 + 3*v + h*v.
2*v*(v + 1)
Suppose 4*a = -4*m - 532, 2*a + 3*m + 534 = -2*a. Let z = 409/3 + a. Factor 1/3*g**3 - z*g + 0 - 1/3*g**4 + 4/3*g**2.
-g*(g - 2)*(g - 1)*(g + 2)/3
Let x(a) be the first derivative of a**4/12 + 13*a**3/3 - 348. Factor x(l).
l**2*(l + 39)/3
Let q = 46 + -42. Let 65 + 3*k**4 + 0*k**q - 65 - 3*k**5 = 0. What is k?
0, 1
Factor 13*j + 7*j**2 - 4*j**2 + 5808 - 23*j + 274*j.
3*(j + 44)**2
Factor 13*w**3 + w - 24*w**3 + 9*w + 9*w**3 + 8*w**2.
-2*w*(w - 5)*(w + 1)
Let m = -5484 + 5486. Let 1/10*h**m - 1/10*h**3 - 1/10*h**4 + 1/10*h + 0 = 0. Calculate h.
-1, 0, 1
Let i(a) be the third derivative of a**5/150 - 2*a**4/5 - 5*a**3/3 + a**2 - 145*a. Determine t, given that i(t) = 0.
-1, 25
Suppose 0 = -k + 4, -5 = y - 2*y - 4*k. Let c be (y/110)/(2/5)*-6. Factor 0*i + c*i**2 + 3/2*i**5 - 3/2*i**4 - 3/2*i**3 + 0.
3*i**2*(i - 1)**2*(i + 1)/2
Factor 6*b**2 - 2*b**2 + 442 + 1002 + 152*b.
4*(b + 19)**2
Let u(w) be the second derivative of -1/3*w**2 + 143/60*w**5 + 13/9*w**3 - 71/24*w**4 - 121/180*w**6 + 0 - 6*w. Factor u(d).
-(d - 1)**2*(11*d - 2)**2/6
Let f(q) be the second derivative of 1/36*q**3 + 0*q**2 + 0 + 30*q + 1/72*q**4 - 1/120*q**5 - 1/180*q**6. Factor f(l).
-l*(l - 1)*(l + 1)**2/6
Let g(q) be the first derivative of -39*q**3/4 - q**2/8 + 514. Factor g(r).
-r*(117*r + 1)/4
Let x(m) = m**2 + 2*m + 3. Let h be -4 + (29 - 1/(-1)). Let j(v) = -4*v**2 - 9*v - 13. Let w(a) = h*x(a) + 6*j(a). Factor w(k).
2*k*(k - 1)
Solve 8*z - 12*z - 49*z**2 - 6 + 48*z**2 - 3*z = 0 for z.
-6, -1
Let w(q) be the first derivative of -q**6/3 + 8*q**5/5 + 9*q**4 + 40*q**3/3 + 7*q**2 - 549. What is j in w(j) = 0?
-1, 0, 7
Let x(k) be the third derivative of k**8/252 + k**7/45 - k**6/90 - 13*k**5/90 + k**4/6 - 2*k**2 + 81. Let x(z) = 0. Calculate z.
-3, -2, 0, 1/2, 1
Suppose 467*b**2 - 15*b - 463*b**2 + 56 - 45*b = 0. What is b?
1, 14
Let g(b) be the third derivative of b**5/60 - 29*b**4/24 - 5*b**3 - 237*b**2. Factor g(x).
(x - 30)*(x + 1)
Suppose 2*i + 4*m - 14 = 10, -4*i + 2*m = 2. Let -15*l**4 + 6*l**i + 0*l**3 + 4*l**3 - 13*l**3 = 0. What is l?
-1, 0, 2/5
Let i(r) be the first derivative of 0*r**3 - 1/9*r**2 + 8*r - 4 + 1/54*r**4. Let y(x) be the first derivative of i(x). Factor y(u).
2*(u - 1)*(u + 1)/9
Suppose -55*z + 115*z = 300. Let k(b) be the second derivative of 0 + 0*b**z - 1/84*b**7 + 1/12*b**4 + 0*b**2 + 8*b + 1/12*b**3 - 1/30*b**6. Factor k(r).
-r*(r - 1)*(r + 1)**3/2
Suppose -212 = 3*s - 224. Let t(u) be the second derivative of u**3 - 4*u - 1/8*u**s + 0 - 3*u**2. Suppose t(l) = 0. Calculate l.
2
Solve -24*g**2 - 1/2*g**3 + 50*g + 0 = 0.
-50, 0, 2
Let t(u) be the third derivative of -u**7/42 + u**5/6 - 5*u**3/6 + 68*u**2. What is j in t(j) = 0?
-1, 1
Suppose -6*t = -0*t - 24. Let k(z) be the first derivative of -2*z**4 + 6*z**2 + 0*z**2 + z**t - 8*z + 3. Factor k(o).
-4*(o - 1)**2*(o + 2)
Solve 307/2*f**2 - 9/2*f**4 + 16 - 103*f - 62*f**3 = 0.
-16, 2/9, 1
Let p(f) = 8*f**2 + 24*f - 21. Let u(i) = -3*i**2 - 8*i + 7. Suppose -34 = -5*a - 14. Let b(y) = a*p(y) + 11*u(y). What is h in b(h) = 0?
1, 7
Let f(z) be the first derivative of -z**6/6 - 2*z**5 + 13*z**4/4 + 22*z**3/3 - 440. Solve f(v) = 0 for v.
-11, -1, 0, 2
Let a(v) = -3*v - 15. Let q be a(-10). Factor 15*h**2 - q*h**3 + 5*h + 5*h**4 - 8*h - 2*h.
5*h*(h - 1)**3
Let d be 0/(4 + (0 + 9)/(-3)). Let s(o) be the first derivative of d*o - 2/3*o**3 - 1/2*o**2 - 5 - 1/4*o**4. Factor s(t).
-t*(t + 1)**2
Let g = -125/3 + 259/6. Let t(d) be the first derivative of 3 + 1/2*d**3 - 9/2*d + g*d**2. Factor t(y).
3*(y - 1)*(y + 3)/2
Let d(i) be the first derivative of 13*i**5 - 20*i + 85/4*i**4 + 9 + 5/2*i**6 - 20*i**2 + 5*i**3. Factor d(w).
5*(w + 1)**3*(w + 2)*(3*w - 2)
Let a(f) be the third derivative of -f**6/90 + f**5/15 - f**4/6 - 17*f**3/6 + 39*f**2. Let w(j) be the first derivative of a(j). Let w(z) = 0. What is z?
1
Let g(y) = -y**3 + 11*y**2 - 8*y + 20. Let r be g(10). Solve 45*i**4 - 9*i**3 + 45*i**3 - r*i**2 + 3*i**5 - i**5 + 16*i - 59*i**4 = 0 for i.
0, 1, 2
Let 33/4*n + 3/4*n**2 + 0 = 0. What is n?
-11, 0
Let s(k) be the second derivative of 3*k**5/40 + k**4 + 13*k**3/4 + 9*k**2/2 + 457*k. Find i such that s(i) = 0.
-6, -1
Let h(y) be the first derivative of -13 + 1/36*y**4 + y + 4/9*y**3 + 8/3*y**2. Let q(f) be the first derivative of h(f). Solve q(d) = 0.
-4
Let a be -32 + 13 - -36 - 9. Find b such that 0 - 2/3*b**4 - a*b**2 + 4*b**3 + 16/3*b = 0.
0, 2
Let f be 3/(-9) - 56/(-24). Suppose -2*g = -5*s + 11, 2*g + 2*s = -3*s + 19. Factor -g*v**4 + 0 + 4/7*v - 6/7*v**f - 24/7*v**3.
-2*v*(v + 1)**2*(7*v - 2)/7
Suppose -72 = -6*x - 54. Let 450*q**2 + 405*q - 31*q**5 + 55*q**4 + 63*q**5 - 27*q**5 + 135 + 230*q**x = 0. Calculate q.
-3, -1
Let v = -13 - -17. Suppose -2*b = 2*o - 4, -b - 2*o + 7 = 2*b. Suppose -17/2*m**b + 0 + 10*m**v + m - 5/2*m**2 = 0. Calculate m.
-2/5, 0, 1/4, 1
Let s(l) = -15*l**3 - 6*l**2 + 93*l + 444. Let r(n) = 32*n**3 + 11*n**2 - 184*n - 887. Let c(j) = -6*r(j) - 13*s(j). Factor c(q).
3*(q - 6)*(q + 5)**2
Let f(b) be the first derivative of -b**3/9 - 5*b**2/6 - 62. Factor f(a).
-a*(a + 5)/3
Let d(x) be the third derivative of 0 - 1/840*x**7 + 0*x**6 + 0*x**5 + 0*x**3 - 6*x**2 + 0*x + 0*x**4. Solve d(m) = 0.
0
Let w(z) be the first derivative of 2*z**6/3 - z**4 - 63. Factor w(i).
4*i**3*(i - 1)*(i + 1)
Suppose -7*m - m**5 + 1 - 29/2*m**3 + 61/4*m**2 + 25/4*m**4 = 0. What is m?
1/4, 1, 2
Let k(i) = i**3 + 2*i**2 - 5*i - 4. Let a be k(-3). Let s be 19/(-28 - -47)*(-1 - -4). Factor 4/3*z**5 - 3*z**4 + 0*z + 2*z**s + 0 - 1/3*z**a.
z**2*(z - 1)**2*(4*z - 1)/3
Let h(l) = 8*l**2 + 172*l + 172. Let a = 19 - -9. Let p(y) = y**2 + 19*y + 19. Let f(d) = a*p(d) - 3*h(d). Factor f(u).
4*(u + 2)**2
Let m(y) be the first derivative of 0*y + 17/3*y**3 + y**2 - 3. Let d(t) = 16*t**2 + t. Let n(u) = -4*d(u) + 5*m(u). Factor n(b).
3*b*(7*b + 2)
Let u = -681 + 683. Let g(v) be the third derivative of 0*v - 2/315*v**7 + 0*v**4 - 1/180*v**6 + 1/90*v**5 + 0 + 7*v**u + 0*v**3. Factor g(b).
-2*b**2*(b + 1)*(2*b - 1)/3
Let m(z) = -3*z + 2. Let q be m(-1). Factor 2*h + 0*h**3 + 12*h**2 - q*h**3 - 22*h + 8*h**2.
-5*h*(h - 2)**2
Let p(j) be the first derivative of -j**4/60 + 2*j**3/15 + 7*j - 7. Let x(n) be the first derivative of p(n). Find l such that x(l) = 0.
0, 4
Suppose 50/3 + 5/3*t**2 - 55/3*t = 0. Calculate t.
1, 10
Suppose 11 = 4*f - 25. Let b be (-25)/(-14) - (-3 + f/2). Factor -6/7*s + 2/7 - b*s**3 + 6/7*s**2.
-2*(s - 1)**3/7
Let s(l) be the first derivative of -l**7/21 + l**6/5 - 2*l**4/3 + 10*l - 35. Let t(j) be the first derivative of s(j). Factor t(z).
-2*z**2*(z - 2)**2*(z + 1)
Let a(f) = -2*f**3 - f**2 + 3*f + 1. Let i(k) = 65*k**3 + 230*k**2 + 45*k + 5. Let o(p) = 5*a(p) - i(p). Factor o(v).
-5*v*(v + 3)*(15*v + 2)
Factor 12/7*v + 24/7*v**2 + 0 + 15/7*v**3 + 3/7*v**4.
3*v*(v + 1)*(v + 2)**2/7
Let w(c) = -c**3 - 25*c**2 + 29*c + 81. Let s be w(-26). Let p(t) be the second derivative of -4*t + 4*t**2 + 0 - 7/6*t**4 - 4*t**s. Solve p(o) = 0.
-2, 2/7
Suppose 33 + 35 = 34*u. Let j(w) be the second derivative of 4*w - 8/33*w**3 + 0 + 5/22*w**4 + 1/11*w**u. Factor j(z).
2*(3*z - 1)*(5*z - 1)/11
Let c = -18 - -20. Let z(p) be the first derivative of 27/4*p**4 + p**6 + 0*p + 3/2*p**c - 5*p**3 - 21/5*p**5 + 7. Factor z(x).
3*x*(x - 1)**3*(2*x - 1)
Let z be (3 - 1 - -3) + 1. Suppose -19 = -3*o - n, z*o + 4*n - 36 = 2*o. Determine q, given that 5*q**2 - 3*q**4 + q**o - 2*q**5 - 3*q**3 - 2*q**2 + 4*q**5 = 0.
-1, 0, 1
Let c(r) be the first derivative of 0*r**2 + 3/16*r**4 + 1/12*r**3 - 1/5*r**5 + 9 + 0*r. Factor c(z).
-z**2*(z - 1)*(4*z + 1)/4
Factor -2*v**5 - 12*v**5 + 18*v**3 - 9*v**3 + 13*v**5.
-v**3*(v - 3)*(v + 3)
Factor -18*c**2 - 1698*c**3 + 32*c + 0*c - 18*c**2 + 1702*c**3.
4*c*(c - 8)*(c - 1)
Factor -8/5*r**2 + 44/5*r + 48/5 - 4/5*r**3.
-4*(r - 3)*(r + 1)*(r + 4)/5
Factor -287/3*m**4 + 1/3*m**5 + 1741825/3*m - 911810/3*m**2 - 857375/3 + 27646/3*m**3.
(m - 95)**3*(m - 1)**2/3
Let w(q) = -15*q**3 - 120*q**2 - 280*q - 80. Let x(t) = -t**2. Let h(y) = w(y) + 5*x(y). Find p such that h(p) = 0.
-4, -1/3
Let z(h) be the first derivative of h**4/22 - 12*h**2/11 + 32*h/11 + 92. Let z(q) = 0. Calculate q.
-4, 2
Let j be (-3)/(66/(-4)) - 795/(-165). Determine p so that -10 + j*p