*q**4 + 0 + 1/168*q**7 + 1/40*q**6 - 1/80*q**5 + 0*q**2 + 20*q. Factor t(v).
v**2*(v - 1)*(v + 1)*(v + 3)/4
Factor -7*x - 2*x**2 + 12*x + 9*x - 20.
-2*(x - 5)*(x - 2)
Let t(a) = 3*a**2 - 9*a. Suppose -5*i = -4 - 6. Let v(g) = 8*g**i + 8*g**2 - 19*g**2 + 9*g. Let o(r) = -3*t(r) - 4*v(r). Determine n, given that o(n) = 0.
0, 3
Let v(g) be the second derivative of 0 - 19*g - 27/8*g**2 + 3/4*g**3 - 1/16*g**4. Factor v(c).
-3*(c - 3)**2/4
Let v be ((-52)/(-39))/(20/45). Suppose -5/3*d**v - 4/3*d**2 - 2/3*d**4 - 1/3*d + 0 = 0. What is d?
-1, -1/2, 0
Factor -62/9*x**3 + 0 + 2/9*x**4 - 50*x + 170/3*x**2.
2*x*(x - 15)**2*(x - 1)/9
Let a be 4/(-4) - (-3)/2. Let m(n) = n**3 - 3*n**2 + 3*n - 2. Let j be m(3). Factor -j*u**2 - 1/4*u + a.
-(4*u - 1)*(7*u + 2)/4
Solve 5*n**2 + 7*n**3 + 32*n**2 + 17*n**3 + 3*n**4 + 8*n**2 = 0.
-5, -3, 0
Factor 2/3*n**4 - 2/3*n**2 + 0 + 4/3*n**3 - 4/3*n.
2*n*(n - 1)*(n + 1)*(n + 2)/3
Let t(w) be the first derivative of 2/3*w + 2/45*w**3 + 4 + 2/5*w**2. Determine r so that t(r) = 0.
-5, -1
Let k be (3/(6/452))/(68/34). Let c = 113 - k. What is x in -1/2*x**4 + c*x + 0 + 0*x**3 + 0*x**2 = 0?
0
Suppose u = 2*u - 4. Let z = u + -5. Let v(t) = -t**2 + t + 1. Let j(w) = -3*w**3 + w**2 + w + 7. Let r(l) = z*j(l) + 6*v(l). Factor r(d).
(d - 1)**2*(3*d - 1)
Let f(i) be the first derivative of 1/20*i**5 + 0*i**4 + 0*i**2 + 0*i + 17 + 1/24*i**6 + 0*i**3. Factor f(t).
t**4*(t + 1)/4
Let g(u) be the second derivative of -u**7/42 + 49*u**6/120 - 13*u**5/5 + 361*u**4/48 - 119*u**3/12 + 5*u**2 + 7*u - 39. Find k, given that g(k) = 0.
1/4, 1, 2, 4, 5
Let n be -1 + 4/((-12)/(-15)). Suppose -5*x - 4 = -w - 69, 2*x - 8 = n*w. Find o, given that -1 - 8*o + x + 2*o**2 - 5 = 0.
2
Factor -3/7*v**2 - 36/7*v - 81/7.
-3*(v + 3)*(v + 9)/7
Find z such that 278/9*z + 92/3 + 2/9*z**2 = 0.
-138, -1
Suppose -18*o**3 + 6*o**2 + 44*o**3 - 17*o**3 + 3*o**4 = 0. Calculate o.
-2, -1, 0
Let v(d) be the first derivative of d**4/2 - 4*d**3/3 + d**2 - 40. Factor v(q).
2*q*(q - 1)**2
Let u(w) = 20*w**2 - 2*w + 3. Let s be u(1). Suppose 10*h - 5*h**2 - 5*h**2 - 4*h**2 - s*h**2 + 25*h**3 = 0. What is h?
0, 2/5, 1
Let i = 413 - 4121/10. Let w = i - 2/5. What is z in -1/2 + w*z**2 + 0*z = 0?
-1, 1
Let b(r) be the first derivative of -1 + 1/5*r**4 + 1/15*r**3 - 1/5*r - 2/5*r**2. Factor b(q).
(q - 1)*(q + 1)*(4*q + 1)/5
Let f(l) be the first derivative of l**7/280 + l**6/120 - l**3/3 - 4*l - 7. Let s(z) be the third derivative of f(z). What is n in s(n) = 0?
-1, 0
Factor -216/7 + 30/7*g + 6/7*g**2.
6*(g - 4)*(g + 9)/7
Let u(t) = t**2 - 8*t. Let b(q) = q**2 - 16*q. Let p(g) = 3*b(g) - 7*u(g). Let p(v) = 0. What is v?
0, 2
Suppose 0 = -c - 4*c + 2*r + 20, 4*c + 17 = -5*r. Suppose -4*v + c*v = -4. What is q in -2*q + 0*q**3 - 2*q**2 - v*q**4 + 4*q**2 + 2*q**3 = 0?
-1, 0, 1
Let l(a) be the third derivative of a**7/840 - a**6/60 + 7*a**5/240 - 2*a**2 + 385*a. Determine d so that l(d) = 0.
0, 1, 7
Factor 4*u**2 - 99*u**2 - 2*u**3 + 13*u**2.
-2*u**2*(u + 41)
Let v(r) be the second derivative of -r**7/4620 + r**6/396 - 2*r**5/165 + r**4/33 - 2*r**3 - 5*r. Let c(t) be the second derivative of v(t). Factor c(q).
-2*(q - 2)**2*(q - 1)/11
Determine k, given that 0 - 3/8*k**5 + 15/4*k**2 - 15/4*k**4 - 9*k**3 + 75/8*k = 0.
-5, -1, 0, 1
Let g(q) be the third derivative of q**8/56 - 4*q**7/105 - q**6/15 + q**5/5 + q**4/12 - 2*q**3/3 - 322*q**2. Let g(z) = 0. What is z?
-1, -2/3, 1
Let a(f) be the first derivative of f**6/72 - f**4/48 - 81. Factor a(x).
x**3*(x - 1)*(x + 1)/12
Let a(x) be the second derivative of -x**6/6 - x**5 - 5*x**4/4 + 10*x**3/3 + 10*x**2 + x - 66. Factor a(k).
-5*(k - 1)*(k + 1)*(k + 2)**2
Let k(x) be the first derivative of x**4/10 + 82*x**3/15 + 8*x**2 - 32. Find a such that k(a) = 0.
-40, -1, 0
Let k be (-2 - -3)*1 - -1. Let t = 2 + k. Factor -4*y**2 + 3*y**5 + y**2 + 0*y**t + 19*y**3 - 22*y**3 + 3*y**4.
3*y**2*(y - 1)*(y + 1)**2
Let i be 19/((-95)/30) + 11 + -5. Let n(h) be the first derivative of 3/25*h**5 + 0*h + i*h**2 - 9 + 0*h**4 - 1/5*h**3. Factor n(g).
3*g**2*(g - 1)*(g + 1)/5
Suppose w + w = 5*h - 23, -4*h = -2*w - 20. Let y(a) = a**2 + 4*a + 3. Let u be y(w). Suppose -3*x**3 + u*x**4 + 3*x**2 + 0*x**3 - x - 2*x**4 = 0. Calculate x.
0, 1
Let i(v) be the second derivative of 5/2*v**2 + 1/6*v**6 - 5/3*v**3 - 5/6*v**4 + 5*v - 5/21*v**7 + v**5 + 0. Find z such that i(z) = 0.
-1, 1/2, 1
Let r be 8 - 25/50*(-2 - -2). Let j(y) be the first derivative of -r + 0*y**2 + 1/30*y**6 + 0*y + 0*y**3 - 2/25*y**5 + 1/20*y**4. Find p, given that j(p) = 0.
0, 1
Let k(l) = 3*l**3 + 4*l**2 + l. Let b be k(3). Let w be (24/(-70))/((-18)/b*2). What is d in -10/7*d - w*d**2 - 2/7*d**3 - 4/7 = 0?
-2, -1
Let u(r) be the second derivative of 0*r**2 + 0 + 0*r**3 - 1/30*r**4 - 1/50*r**5 + 14*r. Factor u(a).
-2*a**2*(a + 1)/5
Determine r, given that 5*r**5 + 550*r**4 - 2*r**5 - 16*r**2 - 6*r - 9*r**3 + r**2 - 547*r**4 = 0.
-1, 0, 2
Let l be 8/(-28) - (-16)/56. Let r be ((-6)/28)/((-18)/63). Solve l + 1/4*p**4 - r*p**2 - 1/2*p + 0*p**3 = 0 for p.
-1, 0, 2
Let h(b) = -b**5 + 4*b**4 - 6*b**3 + 20*b**2 - 5*b - 6. Let r(m) = m**4 - m**3 + 3*m**2 - m - 1. Let d(u) = 5*h(u) - 30*r(u). Determine v so that d(v) = 0.
-1, 0, 1
Let x(f) = 12*f - 7*f**2 + 5 - 9*f - 1. Suppose 5*d = 2*w + 14, 0*d - 2*d = w - 11. Let n(u) = -15*u**2 + 6*u + 9. Let i(a) = d*n(a) - 9*x(a). Factor i(o).
3*o*(o - 1)
Let u(r) be the second derivative of -r**4/30 - 2*r**3/5 + 16*r**2/5 + 73*r - 1. What is b in u(b) = 0?
-8, 2
Determine w so that 0 + 0*w - 2/5*w**5 + 6/5*w**3 + 4/5*w**4 + 0*w**2 = 0.
-1, 0, 3
Suppose -4*o = -0*o - 4. Let j be (1 - 1) + 2/o. Factor -3*k**2 + 2*k**j + 5*k**2 + 0*k**2 + 100 + 40*k.
4*(k + 5)**2
Let f(r) be the first derivative of -9 + 0*r - 8/9*r**3 - 1/3*r**2. Factor f(k).
-2*k*(4*k + 1)/3
Suppose 2627*f = 2634*f. Let q(k) be the second derivative of 1/18*k**4 - 1/120*k**5 + k - 1/9*k**3 + 0 + f*k**2. What is m in q(m) = 0?
0, 2
Let x(q) = -74*q + 11. Let s be x(-10). Suppose 2*n**2 - 14 + 4 - 743*n + s*n = 0. Calculate n.
-5, 1
Let o(v) be the second derivative of -v**4/72 - 17*v**3/36 - 13*v. Suppose o(u) = 0. Calculate u.
-17, 0
Let g be 6 - (-12 - (-7 + -7)). Let s(k) be the third derivative of 10*k**2 - 7/6*k**g + 0 + 0*k + 4/3*k**3 - 4/15*k**5. Find z, given that s(z) = 0.
-2, 1/4
Suppose -2*a + 5*o + 29 = 0, a - 9 - 18 = 5*o. Let -3*y**3 + 2*y**2 + 6*y**3 - 4 - 4*y + y**3 + 2*y**a = 0. What is y?
-1, 1
Let t = -299 - -298. Let w be (-530)/(-65) + t - 7. Factor 0 - w*j + 0*j**2 + 2/13*j**3.
2*j*(j - 1)*(j + 1)/13
Let g(q) be the third derivative of -q**6/240 + 67*q**5/60 - 4489*q**4/48 - 461*q**2. Factor g(c).
-c*(c - 67)**2/2
Let m(q) be the third derivative of 0 + 0*q - 256*q**3 - 1/40*q**6 - 18*q**2 - 24*q**4 - 6/5*q**5. Find u such that m(u) = 0.
-8
Let m(w) be the second derivative of w**3/6 + 3*w**2 + 9*w. Let p be m(-3). What is h in h**p - 2*h**2 - 4*h**2 + 5*h**2 = 0?
0, 1
Let o(m) be the second derivative of 2/189*m**7 + 0*m**3 - 1/27*m**6 + 0 - 2/27*m**4 - 17*m + 0*m**2 - 11/90*m**5. What is t in o(t) = 0?
-1, -1/2, 0, 4
Let t(i) = -5*i**4 - 13*i**3 + 35*i**2 + 11*i - 11. Let w(a) = 3*a**4 + 6*a**3 - 18*a**2 - 6*a + 6. Let m(k) = -6*t(k) - 11*w(k). Solve m(s) = 0 for s.
0, 2
Let k(p) = -2*p - 4. Let g be k(-8). What is n in -12 - g*n**2 - 3*n**4 - n**4 + 16*n - 16*n**3 + 11 + 17 = 0?
-2, -1, 1
Let m(q) be the third derivative of -q**8/60480 + q**6/2160 + 13*q**5/60 - 7*q**2. Let o(c) be the third derivative of m(c). Find f such that o(f) = 0.
-1, 1
Suppose 8*m - 23 = 17. Factor -23 + 36 - m*f**2 - 18 + 10*f.
-5*(f - 1)**2
Let u(z) be the first derivative of -z**4/4 + 2*z**3/3 - z**2/2 + 16. Find v, given that u(v) = 0.
0, 1
Let s(n) be the second derivative of n**6/50 + n**5/100 - 7*n**4/60 - n**3/6 + 848*n. Factor s(b).
b*(b + 1)**2*(3*b - 5)/5
Let q(w) be the second derivative of w**7/56 - w**6/10 - 33*w**5/80 - 3*w**4/8 + 527*w. Find a such that q(a) = 0.
-1, 0, 6
Let k(x) be the first derivative of -x**4/4 + 2*x**3 - 5*x**2/2 - 282. Factor k(r).
-r*(r - 5)*(r - 1)
Factor 2*r**2 + 45*r - 5*r**2 + 0*r**2 - 363 + 21*r.
-3*(r - 11)**2
Factor -14/9*a**3 - 20/9*a**2 - 2/9*a**4 + 0*a + 0.
-2*a**2*(a + 2)*(a + 5)/9
Let j = 3221 - 12871/4. Solve -j*d - 3/2 - 2*d**2 - 1/4*d**3 