i**4 - 38*i**2 + 257*i**4 - 22*i**2 + 21*i**3 + 12*i.
3*i*(i - 1)*(i + 2)*(9*i - 2)
Let y(v) be the first derivative of -v**6/180 + v**5/10 - 3*v**4/4 + 8*v**3/3 - 13. Let p(c) be the third derivative of y(c). Let p(g) = 0. Calculate g.
3
Let a(x) = 55*x**4 - 5*x**3 - 220*x**2 - 145*x + 5. Let l(f) = f**5 + 82*f**4 - 8*f**3 - 330*f**2 - 217*f + 8. Let z(v) = -8*a(v) + 5*l(v). Factor z(s).
5*s*(s - 5)*(s - 3)*(s + 1)**2
Factor 5/2*s**4 - 25*s + 15/2*s**2 + 15*s**3 + 0.
5*s*(s - 1)*(s + 2)*(s + 5)/2
Let l be (1 - -3)*(-5 + (-150)/(-24)). Suppose 2/3*n**2 + 2/3*n**l - 2/3*n**4 + 0*n + 0 - 2/3*n**3 = 0. What is n?
-1, 0, 1
Suppose 0 - 32*z**2 - 1/2*z**3 + 0*z = 0. What is z?
-64, 0
Let w be 1*(-4)/6*-6. Suppose -30*j**w - 18*j**5 + 28*j + 4*j**3 + 19*j**2 - 14*j + 9*j**2 + 2 = 0. What is j?
-1, -1/3, 1
Factor -13/4*z**2 - 15/4*z**3 + 0 - 1/4*z**5 - 7/4*z**4 - z.
-z*(z + 1)**3*(z + 4)/4
Let b = 19409/87462 + 3/9718. Factor 2/9*d**5 - 8/9*d**4 + 0 - 8/9*d**2 + 4/3*d**3 + b*d.
2*d*(d - 1)**4/9
Let a be (22/(-12) - -2) + (-263)/(-6). Suppose 38*w - a*w + 18 = 0. Solve 0*n - 5/4*n**2 - 5/4*n**4 + 5/2*n**w + 0 = 0 for n.
0, 1
Suppose -5 = -2*l + 3. Let 4*h**3 - 9*h**4 - 5*h**5 + h**l + 9*h**5 = 0. Calculate h.
0, 1
Let y(x) be the second derivative of x**7/105 - 2*x**5/25 + 24*x. Determine h so that y(h) = 0.
-2, 0, 2
Let p(o) be the second derivative of -9*o + o**3 - 11/4*o**4 + 0*o**2 + 0. Determine r so that p(r) = 0.
0, 2/11
Let j = -1981/3 + 661. Factor 0*c + 0 - j*c**2 - 2/3*c**3.
-2*c**2*(c + 1)/3
Let i(y) = y**2 + 2*y + 2. Let b be i(-2). Determine p so that -3*p**3 + 5*p + 6 - 5*p**2 - 2*p**b + 11*p**2 - 12*p**2 = 0.
-3, -2/3, 1
Let d(x) be the second derivative of x**7/630 + x**6/90 - x**5/10 - 5*x**4/4 - 14*x. Let h(z) be the third derivative of d(z). Find i, given that h(i) = 0.
-3, 1
Let v(j) be the first derivative of -j**7/2520 - j**6/135 - 2*j**5/45 + 4*j**3 + 11. Let x(d) be the third derivative of v(d). Factor x(q).
-q*(q + 4)**2/3
Let o(t) be the first derivative of t**5/5 - 3*t**4 + 16*t**3 - 32*t**2 - 8*t - 37. Let g(z) be the first derivative of o(z). Factor g(w).
4*(w - 4)**2*(w - 1)
Let j(b) = 3*b**2 - 96*b + 288. Let k(x) = -4*x**2 + 144*x - 432. Let a = -21 + 29. Let r(y) = a*j(y) + 5*k(y). Factor r(v).
4*(v - 6)**2
Find s, given that -9*s**5 + 276*s**2 - 10*s**4 + 18*s**4 + 135*s**3 + 120*s + 3*s**4 + 15*s**3 - 8*s**4 = 0.
-2, -2/3, 0, 5
Factor 3/4*d**2 - 1/4*d**4 + 1/2*d + 0*d**3 + 0.
-d*(d - 2)*(d + 1)**2/4
Let t(w) be the second derivative of -w**4/14 + w**3/7 + 6*w**2/7 + 101*w. Factor t(g).
-6*(g - 2)*(g + 1)/7
Find m such that 0 - 2/3*m - 2/3*m**3 + 4/3*m**2 = 0.
0, 1
Let v = 271/10 - 269/10. Factor 1/5 + 0*m - v*m**2.
-(m - 1)*(m + 1)/5
Let y(w) be the first derivative of -w**6/24 - 3*w**5/20 + w**3/3 + 327. Factor y(h).
-h**2*(h - 1)*(h + 2)**2/4
Let y be ((-112)/21)/(1/(54/(-60))). Let z(o) be the second derivative of -8/5*o**2 - 9*o - y*o**3 + 0 - 27/5*o**4. Factor z(g).
-4*(9*g + 2)**2/5
Suppose -7*r + 8*r = 40. Suppose -5*n + 25 = m, r = -0*n + 5*n + 4*m. Solve 5*c**2 + n*c - c - c**3 - c - 6*c**2 = 0.
-2, 0, 1
Let n(h) be the first derivative of 4*h**6/9 - 83*h**5/15 + 115*h**4/6 - 25*h**3/3 + 698. What is y in n(y) = 0?
0, 3/8, 5
Let k(m) be the second derivative of -3*m**5/140 + 3*m**4/28 + 13*m**3/14 - 45*m**2/14 + 192*m. Find t, given that k(t) = 0.
-3, 1, 5
Let z be 6/5616*488 + 1/(-13). Suppose -26/9*b**2 + 22/9*b - z + 8/9*b**3 = 0. What is b?
1/4, 1, 2
Let r(d) be the first derivative of d**6/1260 - d**5/120 + d**4/56 - 7*d**3/3 + 15. Let k(g) be the third derivative of r(g). Find i such that k(i) = 0.
1/2, 3
Let w(n) = -3*n - 10. Let o be w(-5). Suppose o - 17 = -4*z. Let -6*y**2 + 2 - 4*y**3 + 3*y**3 + 4 + 4*y**z - 3*y = 0. Calculate y.
-1, 1, 2
Let 22*k**2 - 229*k**2 + k**3 - 243*k**2 - 2515456 + 55488*k + 42*k**2 = 0. What is k?
136
Suppose 4*x**4 - 64*x**2 - 8*x**3 + 8*x - 64*x**2 + 124*x**2 = 0. What is x?
-1, 0, 1, 2
Let l be (-1 - (-40)/55)/((-1)/11). Find n such that -1/3*n**5 - 14/3*n**3 - l*n + 2/3 + 16/3*n**2 + 2*n**4 = 0.
1, 2
Suppose -11*h = -8*h. Let o(q) be the second derivative of h*q**2 + 0*q**3 + 0 - 6*q - 1/20*q**5 - 1/12*q**4. Factor o(t).
-t**2*(t + 1)
Suppose -4*o + 123 - 103 = 0. Solve -28*f**2 - 2*f**3 - 2*f**3 + 9*f**4 - o*f**4 + 8*f**2 - 12*f = 0.
-1, 0, 3
Let x(q) be the second derivative of q**6/6 - 5*q**5/4 + 5*q**4/4 + 15*q**3/2 + 3*q - 4. Let x(m) = 0. Calculate m.
-1, 0, 3
Let f(o) = -6*o**3 - 4*o**2 - 10*o + 30. Let y(q) = -q**3 + q**2 + q - 5. Let j(p) = -1. Let z(x) = 6*j(x) - y(x). Let r(t) = -f(t) - 5*z(t). Factor r(m).
(m - 1)*(m + 5)**2
Let c(o) be the third derivative of o**6/168 - 3*o**5/70 - o**4/21 - 4*o**2 - 1. Solve c(x) = 0.
-2/5, 0, 4
Let b(a) be the first derivative of 2*a**3/3 + 4*a**2 + 8*a + 304. Factor b(m).
2*(m + 2)**2
Suppose -3*c - 4*k = -5, 11*k = 2*c + 16*k + 6. Factor -49*h + 343/3 - 1/3*h**3 + c*h**2.
-(h - 7)**3/3
Let f(z) be the second derivative of -1/6*z**4 + 2/9*z**3 + 1/60*z**5 - 30*z + 0*z**2 + 1/60*z**6 + 0 - 1/252*z**7. Determine l, given that f(l) = 0.
-2, 0, 1, 2
Let r = -33969/88 - -386. Let p = 85/264 - r. What is n in 1/3*n**2 + 0 - p*n**3 + 1/3*n - 1/3*n**4 = 0?
-1, 0, 1
Suppose m - 2*b = 1, -402*b + 405*b = 4*m - 9. Factor 1/4*q + 1/4 - 1/4*q**m - 1/4*q**2.
-(q - 1)*(q + 1)**2/4
Find z, given that 5*z**3 + 154 - 403 + 89 - 20*z**2 - 140*z = 0.
-2, 8
Let r(a) be the second derivative of -a**4/6 + 4*a**3/3 + 60*a**2 + 420*a. Factor r(d).
-2*(d - 10)*(d + 6)
Let b(u) = u. Let j be b(5). Factor 5*w**2 + 11*w**3 - 9*w**3 - w**j - 14*w**3 + 3*w**2 + 6*w**4.
-w**2*(w - 2)**3
Let y(i) = -1. Let v(o) = -o**3 - 165*o**2 - 9075*o - 166372. Let m(q) = -2*v(q) - 6*y(q). What is u in m(u) = 0?
-55
Let i(c) be the third derivative of 11*c**6/120 + 2*c**2 - 3. Let g(b) = 45*b**3 + b**2. Suppose -1 = 3*y + 26. Let s(u) = y*i(u) + 2*g(u). Solve s(q) = 0.
0, 2/9
Let a = 843 + -840. Determine u, given that -6/5*u + 2/5 - 2/5*u**a + 6/5*u**2 = 0.
1
Let j(p) be the third derivative of -p**5/12 - 85*p**4/24 - 116*p**2. Factor j(u).
-5*u*(u + 17)
Let i(u) be the second derivative of u**6/33 + u**5/110 - 5*u**4/66 - u**3/33 + 99*u. Solve i(m) = 0 for m.
-1, -1/5, 0, 1
Let a(k) be the first derivative of 5*k**7/252 - 9*k - 12. Let m(w) be the first derivative of a(w). Factor m(l).
5*l**5/6
Let y = -1374 + 1377. Let c(q) be the second derivative of 1/2*q**4 + 5/2*q**y - 9/2*q**2 + 10*q + 0. Solve c(d) = 0 for d.
-3, 1/2
Let x(a) be the second derivative of -a**7/273 - a**6/195 + 17*a**5/65 + 5*a**4/3 + 53*a**3/13 + 63*a**2/13 + 200*a. Determine r, given that x(r) = 0.
-3, -1, 7
Let y(b) be the third derivative of -b**8/24 + 4*b**7/21 - 3*b**6/10 + 2*b**5/15 + b**4/12 + 188*b**2. Find s, given that y(s) = 0.
-1/7, 0, 1
Let o(m) be the first derivative of 4/3*m**3 - 1/2*m**2 + 1/240*m**6 + 0*m + 1/6*m**4 + 6 - 7/120*m**5. Let x(d) be the second derivative of o(d). Factor x(r).
(r - 4)**2*(r + 1)/2
Determine n so that -4/3*n - 8/3*n**2 + 2/3*n**4 + 4/3*n**3 + 2 = 0.
-3, -1, 1
Let z(q) be the first derivative of q**7/4200 - q**6/900 - 2*q**3 + 3. Let v(p) be the third derivative of z(p). Factor v(t).
t**2*(t - 2)/5
Solve 12/19*f**3 - 12/19*f - 2/19*f**2 + 0 + 2/19*f**4 = 0 for f.
-6, -1, 0, 1
Let t = 47 - 39. Suppose -4 - t = -4*j. Factor 4*d + d**2 + 0*d**4 - j + 15*d**3 - 7*d + 6*d**4 + 8*d**2.
3*(d + 1)**3*(2*d - 1)
Suppose -z = 2*z + 36. Let m be (36/20 + -2)*z. Solve -9/5*h**2 - 3/5*h**3 + 0*h + m = 0.
-2, 1
Let o(v) be the third derivative of 0 - 16/39*v**3 + 11*v**2 + 0*v + 2/39*v**4 - 1/390*v**5. Find u such that o(u) = 0.
4
Let b be (-3)/12 + (-102)/(-24). Factor -153*x**2 + 160*x**2 - 10*x - b*x - 3*x + 9 + x**3.
(x - 1)**2*(x + 9)
Let a be (2/(-4))/((-1)/63). Let t = a + -311/10. Factor 0 + 0*z - t*z**3 + 2/5*z**2.
-2*z**2*(z - 1)/5
Let o = -5829/10 + 863/2. Let p = 152 + o. Determine i, given that -3/5*i**3 + 0*i**2 + p*i + 0 = 0.
-1, 0, 1
Let p(b) = -b**3 + 16*b**2 - 17*b + 32. Suppose 0 = -5*s + 20, -10 = -2*f + 6*s - s. Let h be p(f). Factor -4/3*a**h + 4/3 + 2/3*a**3 - 2/3*a.
2*(a - 2)*(a - 1)*(a + 1)/3
Let x(o) be the third derivative of -o**5/20 + 10*o**4 - 800*o**3 + 6*o**2 + 7*o. Solve x(t) = 0.
40
Suppose -5*o - 6 = -4*k - 0, k + 4*o +