*y = 0.
0, 5
Factor -9/5 - 12/5*j**3 - 28/5*j - 6*j**2 - 1/5*j**4.
-(j + 1)**3*(j + 9)/5
Let w be 12/(-24)*18 - -14. Let v(q) be the third derivative of 0 + 0*q - 13*q**2 + 0*q**4 + 1/100*q**w + 0*q**3. Factor v(s).
3*s**2/5
Let f(h) be the third derivative of h**6/40 - h**5/10 + h**4/8 - 3*h**2 - 23*h. Factor f(b).
3*b*(b - 1)**2
Factor 7569/5 + 176/5*u**3 + 15312/5*u + 7918/5*u**2 + 1/5*u**4.
(u + 1)**2*(u + 87)**2/5
Let p(o) be the first derivative of o**3/3 + 3*o**2 + 9*o + 68. Factor p(u).
(u + 3)**2
Let k(u) be the third derivative of -u**6/540 + 7*u**5/270 - 11*u**4/108 + 5*u**3/27 - 8*u**2 + 7*u. Factor k(m).
-2*(m - 5)*(m - 1)**2/9
Determine h, given that -55*h + 46 + 96 + 40*h**2 + 5*h**3 - 232 = 0.
-9, -1, 2
Suppose 2*w = -12 + 28. Let l = -1 - -16. What is n in 2*n**2 - n**3 - w*n - l*n**3 - 15*n**2 - 4*n**4 - 7*n**2 = 0?
-2, -1, 0
Let p(d) be the second derivative of -4/3*d**3 - 1/3*d**4 + 0 + 0*d**2 - d. Factor p(u).
-4*u*(u + 2)
Suppose -4*y + 5*p - 2*p + 160 = 0, 5*p = 0. Factor -53 - 14*j**3 - y*j - j**4 + 69 + 3*j**4 + 36*j**2.
2*(j - 2)**3*(j - 1)
Let j(r) be the second derivative of r**7/147 + 3*r**6/35 + r**5/5 - 179*r. Find h such that j(h) = 0.
-7, -2, 0
Let u = -2237 - -17897/8. Let y(x) be the first derivative of 1/40*x**5 - 1/16*x**4 - u*x + 0*x**3 + 1/8*x**2 + 5. Determine j so that y(j) = 0.
-1, 1
Let w(m) be the third derivative of -m**6/180 + m**5/20 + m**4/3 + m**3/2 - 20*m**2. Let s(g) be the first derivative of w(g). Factor s(v).
-2*(v - 4)*(v + 1)
Let f = -12/53 + 419/212. Let t(q) be the first derivative of -q**2 - 5/6*q**6 - 3/5*q**5 - 1 + q**3 + 0*q + f*q**4. Let t(o) = 0. Calculate o.
-1, 0, 2/5, 1
Suppose -5*f + 3*v + 35 = 0, -6*v = -2*v + 20. Factor -9*p**3 + 21*p**2 + 2*p**f + 3*p**4 - 12*p**2 - 2*p**4 - 3*p.
3*p*(p - 1)**3
Let t(a) be the third derivative of a**5/48 - 5*a**4/16 - 4*a**2 + 17*a. Factor t(j).
5*j*(j - 6)/4
Let d(i) be the first derivative of 16/3*i**3 + 23 - 42*i**2 + 20*i. Find c, given that d(c) = 0.
1/4, 5
Suppose 2*t - 6 = -3*l - 3, 2*t + 2*l = 0. Let v be ((-2)/12)/(1/t). Determine y so that v*y**2 + 2*y + 2 = 0.
-2
Let m be (-4 - -28)/6 + 1*-2. Factor 38*d**5 - 4*d**4 + 10*d**3 - 40*d**5 + 6*d**m + 6*d**4.
-2*d**2*(d - 3)*(d + 1)**2
Let n(w) = 12*w - 48. Let f be n(4). Let s(z) be the second derivative of 1/30*z**4 - 1/5*z**2 + z + 0*z**3 + f. Determine q, given that s(q) = 0.
-1, 1
Let -3*k**3 - 111/2 + 423/4*k**2 + 783/4*k = 0. What is k?
-2, 1/4, 37
Let j(p) be the third derivative of -6*p**2 + 0*p - 1/240*p**6 + 0 + 1/60*p**5 - 1/48*p**4 + 0*p**3. Factor j(t).
-t*(t - 1)**2/2
Factor -16*r**3 + r**3 - 52*r**4 + 30*r**3 + 33*r**3 - 8*r**2 + 12*r**3.
-4*r**2*(r - 1)*(13*r - 2)
Let j(q) = 17*q**4 - 63*q**3 - 39*q**2 + 115*q + 30. Let y(i) = -i**4 + i**3 - i**2 - i - 2. Let m(v) = -2*j(v) - 30*y(v). Suppose m(a) = 0. What is a?
-2, 0, 1, 25
Suppose 0 = -a + 9 - 6. Suppose -19 + 25 = a*j. Factor 12/5*k**3 + 8/5*k**4 + 2/5*k + 2/5*k**5 + 0 + 8/5*k**j.
2*k*(k + 1)**4/5
Let -6/13*k**3 - 124/13*k**2 - 80/13*k + 0 = 0. Calculate k.
-20, -2/3, 0
Let y(z) be the first derivative of 110*z**3/21 - 163*z**2/7 - 12*z/7 - 42. Factor y(f).
2*(f - 3)*(55*f + 2)/7
Let x(j) be the second derivative of -1/60*j**6 + 1/8*j**4 + 0*j**2 + 0*j**5 + 0 - 22*j - 1/6*j**3. Solve x(l) = 0.
-2, 0, 1
Let p(b) be the first derivative of -b**4 + 80*b**3/3 - 106*b**2 + 136*b + 131. Let p(s) = 0. Calculate s.
1, 2, 17
Let c be -3 - 884/(-330) - (-2)/6. Let h(v) be the second derivative of c*v**6 - 3*v + 0*v**4 + 0*v**3 + 1/231*v**7 + 0 + 1/110*v**5 + 0*v**2. Factor h(w).
2*w**3*(w + 1)**2/11
Let k = 2489 + -2485. Find i, given that 6/13*i**2 + 14/13*i - 12/13 - 2/13*i**k - 6/13*i**3 = 0.
-3, -2, 1
Let z(s) = s**4 - s**3 + 2*s**2 - s. Let h(n) = 12*n**4 - 9*n**3 + 114*n**2 + 123*n + 63. Let d(j) = -h(j) + 15*z(j). Suppose d(g) = 0. What is g?
-3, -1, 7
Let t(y) be the first derivative of y**6/27 + 46*y**5/45 + 28*y**4/3 + 640*y**3/27 - 512*y**2/9 - 185. Solve t(a) = 0 for a.
-8, 0, 1
Let h(z) = -18*z**2 - 111*z + 3. Let j(u) = 13*u**2 + 110*u - 2. Let l(v) = -2*h(v) - 3*j(v). Factor l(t).
-3*t*(t + 36)
Let r(i) = -28*i**3 + 88*i**2 + 17*i - 77. Let n(d) = 15*d**3 - 45*d**2 - 9*d + 39. Let b(u) = 11*n(u) + 6*r(u). Factor b(y).
-3*(y - 11)*(y - 1)*(y + 1)
Let l(o) = o**3 + 15*o**2 + 20*o + 10. Let p be l(-13). Factor p*s**2 - 94*s**2 + 2*s**4 - 2*s**4 - 3*s**4 + 9*s**3.
-3*s**2*(s - 2)*(s - 1)
Let q(w) be the first derivative of -w**2 + 56 + w - 1/5*w**5 + 1/2*w**4 + 0*w**3. Factor q(u).
-(u - 1)**3*(u + 1)
Let x(c) be the second derivative of -c**7/5880 - 3*c**6/560 - 11*c**4/6 + 11*c. Let z(r) be the third derivative of x(r). Determine f, given that z(f) = 0.
-9, 0
Suppose -4*l + 3*t + 40 = 0, -l + t + 9 + 2 = 0. Factor 4*f**2 + 3*f**2 + l*f**2 - 25*f + 10 - 5*f**3 + 6*f**2.
-5*(f - 2)*(f - 1)**2
Let v be (-3 + 5)/(2/13). Let z(f) = f - 11. Let r be z(v). Factor 2 + 6*l - 2*l + 6*l + l + 9*l**r.
(l + 1)*(9*l + 2)
Let u(r) = 2*r**4 + 48*r**3 + 388*r**2 + 1024*r. Let o be 5/(-10) - (-35)/(-10). Let n(g) = -g**2. Let h(d) = o*n(d) - u(d). Suppose h(m) = 0. What is m?
-8, 0
Let g(o) be the second derivative of -o**5/5 - 37*o**4/3 - 290*o**3 - 3150*o**2 + 106*o. Factor g(r).
-4*(r + 7)*(r + 15)**2
Let l(n) = -n**3 + n**2 + 1. Let m(c) = 3*c + 20. Let w be m(-8). Let j(u) = -6*u**3 + 8*u**2 - 2*u + 4. Let y(d) = w*l(d) + j(d). Factor y(z).
-2*z*(z - 1)**2
Let o(c) be the third derivative of c**8/6720 + c**5/20 - 8*c**2. Let m(w) be the third derivative of o(w). Factor m(z).
3*z**2
Suppose -36*g - 18 = -90. Solve 10/3*n**g + 8/3 + 2/3*n**3 + 16/3*n = 0.
-2, -1
Let f = 149/220 - -4/55. Let u be ((-7)/28)/((-11)/(-6) + -2). Suppose -u - 9/4*c - f*c**2 = 0. What is c?
-2, -1
Let k(i) be the first derivative of i + 2/21*i**3 + 0*i**2 + 5 - 1/42*i**4. Let c(n) be the first derivative of k(n). What is r in c(r) = 0?
0, 2
Let l(v) be the third derivative of 0*v**3 + 0*v + 0*v**4 + 0 - v**2 + 1/10*v**6 + 0*v**5 + 2/105*v**7. What is r in l(r) = 0?
-3, 0
What is y in -42*y**4 + 4*y**5 + 39*y**4 + 12*y - 33*y**3 - 395*y**2 + 435*y**2 = 0?
-3, -1/4, 0, 2
Let h be (-4)/38 - 80/(-760). Let y(v) be the first derivative of 1/8*v**2 + 1 + h*v - 1/4*v**3. Factor y(u).
-u*(3*u - 1)/4
Let g be (-6)/(-15)*((-57)/24 - -3). Suppose g*j**3 - 1/8*j**4 + 0*j + 0*j**2 + 0 = 0. Calculate j.
0, 2
Let g(q) be the third derivative of -16*q**2 + 0*q**3 - 1/420*q**7 + 1/24*q**5 + 1/80*q**6 + 1/24*q**4 - 1/672*q**8 + 0*q + 0. Factor g(h).
-h*(h - 2)*(h + 1)**3/2
Let z = -67/126 - -1123/1638. Find k, given that -14/13*k**2 + 0 + 10/13*k**3 + z*k + 14/13*k**4 - 12/13*k**5 = 0.
-1, 0, 1/6, 1
Let z(p) be the second derivative of -p**4/4 + 2*p**3 + 15*p**2/2 - 50*p - 2. Suppose z(k) = 0. Calculate k.
-1, 5
Let d(w) be the second derivative of -w**7/70 - 3*w**6/25 - 3*w**5/100 + 6*w**4/5 - 8*w**3/5 - 72*w. Determine a so that d(a) = 0.
-4, 0, 1
Let g(r) be the third derivative of -r**5/90 + 5*r**4/12 + 16*r**3/9 + 257*r**2 + 2*r. Factor g(p).
-2*(p - 16)*(p + 1)/3
Solve 41*o**2 + 53*o**2 - 180*o + 20*o**3 - 69*o**2 + 180 - 5*o**4 = 0 for o.
-3, 2, 3
Suppose 4*s - s - 12 = 0. Suppose 5*m - s - 11 = 0. Factor -3*o + 3*o + 6*o**2 - 3*o + 0*o**2 - 3*o**m.
-3*o*(o - 1)**2
Determine b, given that -30*b + 10*b**2 + 4*b**5 - 12 - 4*b**4 - 17*b**3 - 4 - 3*b**3 + 46*b + 10*b**2 = 0.
-2, -1, 1, 2
Let v(u) = 2*u + 14. Let g be v(-7). Factor 9 + 3*q**2 + 15*q + g*q**3 - 2*q**3 - q**3.
-3*(q - 3)*(q + 1)**2
Let b(t) be the first derivative of 1/2*t**2 + 0*t**3 + 0*t - 1/4*t**4 - 48. Solve b(p) = 0 for p.
-1, 0, 1
Let h(g) = -g**2 + 2. Let k(i) = i**3 + 11*i**2 + 28*i + 22. Let n(r) = h(r) + k(r). Factor n(x).
(x + 2)**2*(x + 6)
Let 6/5*g**4 + 0 - 2/5*g**5 + 12/5*g + 6*g**3 + 34/5*g**2 = 0. Calculate g.
-1, 0, 6
Let q(y) = -2*y**3 + y**2 - 4*y + 7*y + 3*y**3 - 1 - 2*y. Let v be q(1). Factor d - v - 10 + 16 - 3*d - 2*d**2.
-2*(d - 1)*(d + 2)
Let v(h) be the third derivative of 0*h - 1/420*h**5 - 8/21*h**3 + 0 + 3*h**2 - 1/21*h**4. Factor v(p).
-(p + 4)**2/7
Let i(w) = 2*w**3 - 10*w**2 + 32*w - 18. Let y(f) = -5*f**3 + 19*f**2 - 65*f + 37. Let s(g) = 14*i(g) + 6*y(g). Determine x so that s(x) = 0.
-15, 1
Let r(z) = 2*z**5 - 12*z**4 + 8*z**3 + 6*z**2 - 10*z. Let o(u) = -u**5