*h**4 + 0*h + 8 + k*h**2. Suppose o(q) = 0. What is q?
0, 1
Let y be 6/129 - (-21546)/28595. Find j, given that -2/5 - 2/5*j**2 + y*j = 0.
1
Let o(d) = d**2 + 7*d - 1173. Let h be o(31). Solve -9/7*z**4 + 0*z**2 + 0*z + 3/7*z**3 + 6/7*z**h + 0 = 0 for z.
0, 1/2, 1
Let s(a) = 6*a - 34. Let h be s(16). Let m = -60 + h. Factor 21/5*f + 9/5 + 3*f**m + 3/5*f**3.
3*(f + 1)**2*(f + 3)/5
Let x(w) be the third derivative of -w**5/90 + 25*w**4/36 - 195*w**2. Factor x(k).
-2*k*(k - 25)/3
Solve -28*r**5 - 15*r**4 - 24*r**4 + 16*r**4 + 136*r**2 - 52*r**3 - 46*r**4 - 32 + 80*r - 35*r**4 = 0.
-2, -1, 2/7, 1
Let o(b) be the first derivative of 2/25*b**5 - 1/5*b**4 - 2/5*b**3 - 20 + 0*b**2 + 0*b. Factor o(q).
2*q**2*(q - 3)*(q + 1)/5
Let q = -4393/642 + 750/107. Factor 0*k + q*k**3 - k**2 + 16/3.
(k - 4)**2*(k + 2)/6
Let q = -136 + 54. Let o = q + 576/7. Solve 0*n**2 - o*n**3 + 2/7*n + 1/7*n**4 - 1/7 = 0 for n.
-1, 1
Let p = -20 - -86. Let t = p - 64. What is m in 15/2*m - 3/4*m**t - 75/4 = 0?
5
Let v(i) be the second derivative of -i**5/60 + 5*i**4/36 + 13*i**3/18 + 7*i**2/6 + i. Factor v(q).
-(q - 7)*(q + 1)**2/3
Factor -4/5 - 6/5*h**3 + 2/5*h**2 + 6/5*h + 2/5*h**4.
2*(h - 2)*(h - 1)**2*(h + 1)/5
Let s(o) be the second derivative of 3*o + 0 - 5*o**3 - 45/2*o**2 - 5/12*o**4. Determine b so that s(b) = 0.
-3
Let d(g) be the third derivative of g**5/60 + g**4/2 + 10*g**3/3 - 12*g**2. Suppose d(a) = 0. What is a?
-10, -2
Let m(j) = j - 2. Let a(x) = x**3 - 2*x**2 - 3*x - 1. Let n be a(0). Let i(k) = 14*k**2 + 3*k + 2. Let o(v) = n*i(v) - m(v). Factor o(u).
-2*u*(7*u + 2)
Let u(z) be the second derivative of -z**7/231 - z**6/55 - 3*z**5/110 - z**4/66 - 37*z**2/2 + 28*z. Let c(d) be the first derivative of u(d). Factor c(k).
-2*k*(k + 1)**2*(5*k + 2)/11
Let l(n) = 142*n - 847. Let p be l(6). Solve 6/19*w**4 + 18/19*w - 26/19*w**3 - 4/19 + 8/19*w**p - 2/19*w**2 = 0.
-2, -1, 1/4, 1
Solve 20*d**3 - 13*d**5 + 18*d**3 - 14*d**4 - 18*d**2 + 11*d**5 - 4*d**3 = 0 for d.
-9, 0, 1
Suppose 15*h**2 + 0*h**3 - 10*h**2 + h**3 - 2*h + 6*h**3 = 0. What is h?
-1, 0, 2/7
Let h(m) = 3*m**4 + 2*m**3 - 41*m**2 - 2*m - 4. Let y(f) = 12*f**4 + 6*f**3 - 162*f**2 - 9*f - 18. Let j(q) = 9*h(q) - 2*y(q). Factor j(z).
3*z**2*(z - 3)*(z + 5)
Let x(u) = u**3 + 6*u**2 - 8*u + 5. Suppose 0 = -4*r + 7 - 35. Let c be x(r). Find o, given that 0*o - 9 - 5 + c + 7*o - 3*o**2 = 0.
1/3, 2
Let u = -7 - -7. Suppose u*w = 6*w - 54. Factor -23 - 3*d**2 + 23 + 3*d**4 + 9*d**3 + w*d**2.
3*d**2*(d + 1)*(d + 2)
Let t(z) be the first derivative of -2*z**3/3 - 10*z**2 - 50*z - 70. Solve t(x) = 0 for x.
-5
Let h(l) = -l**2 - 2*l + 1. Let f(w) = 72*w + 404. Let r(c) = -f(c) + 4*h(c). Factor r(i).
-4*(i + 10)**2
Let j be (-48)/(-96) + (-2 - (-28)/8). Factor 0*s**j - 4/9*s**4 + 2/9*s - 2/3*s**3 + 0.
-2*s*(s + 1)**2*(2*s - 1)/9
Let w(o) be the second derivative of -o**5/30 + o**4/4 - 2*o**3/3 - o**2 + 13*o. Let a(k) be the first derivative of w(k). Factor a(p).
-2*(p - 2)*(p - 1)
Suppose 5*h + 7*h = 9*h - 8*h. Factor -4/7*i**3 + h + 4/7*i + 2/7*i**4 - 2/7*i**2.
2*i*(i - 2)*(i - 1)*(i + 1)/7
Let k(m) be the third derivative of 0 - 18*m**2 + 1/100*m**5 + 0*m + 1/200*m**6 - 1/40*m**4 - 1/10*m**3. Factor k(c).
3*(c - 1)*(c + 1)**2/5
Suppose 5*v = -4*k - 5, -k - v - 1 = -5*k. Let s = 3 + k. Find r such that -r - 1 + 11*r - 9*r**2 + 7 - r - 6*r**s = 0.
-2, -1/2, 1
Let c = 34 + -31. Let y(h) be the second derivative of -1/5*h**2 - 1/90*h**4 - 1/9*h**c - 3*h + 0 + 1/150*h**5. Factor y(v).
2*(v - 3)*(v + 1)**2/15
Let q(j) be the second derivative of 0*j**2 + 2/15*j**6 + 11*j + 2/3*j**4 + 0*j**3 + 0 + 3/5*j**5. Factor q(x).
4*x**2*(x + 1)*(x + 2)
Let s = 31 + -66. Let v be (-7)/(s/10) + 9/(-6). Factor -1/2*w**3 + v*w + 0 + 7/4*w**4 - 7/4*w**2.
w*(w - 1)*(w + 1)*(7*w - 2)/4
Let k = 196/645 + -1/258. Let z(d) be the third derivative of 6*d**2 + 0 + 7/30*d**7 + k*d**5 + 11/6*d**4 + 4/3*d**3 + 0*d - 119/120*d**6. Factor z(x).
(x - 2)*(x - 1)*(7*x + 2)**2
Let o(u) be the second derivative of -5*u**4/12 + 80*u**3/3 - 539*u. Let o(k) = 0. What is k?
0, 32
Let j(h) be the first derivative of 4*h**5/5 + 8*h**4 + 68*h**3/3 + 20*h**2 + 200. Suppose j(d) = 0. Calculate d.
-5, -2, -1, 0
Let l(q) = -3*q**3 + 9*q + 6. Let j(d) = -13 - 14 + 26. Let v(w) = -12*j(w) - l(w). Factor v(g).
3*(g - 1)**2*(g + 2)
Let 104/5*l - 2/5*l**2 - 1352/5 = 0. Calculate l.
26
Let w = 1 - -83. Let c(d) = d**2 - 11*d - 10. Let a be c(12). Factor -81*x**4 + 4*x**2 + w*x**4 - 7*x**a.
3*x**2*(x - 1)*(x + 1)
Let p(l) be the second derivative of -l**4/60 - 101*l**3/30 + 8*l - 33. Solve p(h) = 0 for h.
-101, 0
Factor 8/5 + 43/10*y**3 + 28/5*y + 73/10*y**2 + 1/10*y**5 + 11/10*y**4.
(y + 1)**3*(y + 4)**2/10
Let j(w) be the second derivative of w**6/24 + w**5/2 + 15*w**4/8 + 21*w**2/2 + 6*w. Let t(n) be the first derivative of j(n). Factor t(o).
5*o*(o + 3)**2
Let n be (-2223)/117 + 86/4. Determine a, given that 2*a**2 - 1/2*a**3 + 1 - n*a = 0.
1, 2
Let p(u) be the third derivative of u**7/210 - u**6/40 + u**5/30 + 7*u**2 - 2. Suppose p(i) = 0. What is i?
0, 1, 2
Let h(f) be the second derivative of 0*f**2 + 0 - 9/10*f**5 - 2/3*f**3 - 33*f + 11/6*f**4. Suppose h(i) = 0. What is i?
0, 2/9, 1
Let q(s) = 6*s + 4. Let h(w) = w + 1. Let r(v) = -5*h(v) + q(v). Let j be r(3). Factor -11*f**5 + 0*f**4 + 9*f**5 - j*f**4.
-2*f**4*(f + 1)
Let d(x) be the second derivative of 7*x**5/4 + 15*x**4/4 - 100*x**3/3 - 30*x**2 - 22*x - 1. Factor d(l).
5*(l - 2)*(l + 3)*(7*l + 2)
Let p be 30384/3024 + 4/6. What is j in -60/7*j**4 + p*j**5 - 9*j**3 + 0 - 12/7*j + 60/7*j**2 = 0?
-1, 0, 2/5, 1
Factor 12/5*n + 1/5*n**5 - 8/5*n**4 + 0 + 23/5*n**3 - 28/5*n**2.
n*(n - 3)*(n - 2)**2*(n - 1)/5
Let v(l) be the third derivative of l**6/30 + 26*l**5/15 + 169*l**4/6 - l**2 + 27*l. Suppose v(q) = 0. Calculate q.
-13, 0
Let p(m) be the third derivative of -m**6/120 - 3*m**5/20 - 9*m**4/8 + 3*m**3 + 12*m**2. Let y(q) be the first derivative of p(q). Factor y(a).
-3*(a + 3)**2
Let x be (((-10)/(-21))/2)/((-24)/((-864)/20)). Solve -x*t**2 - 2/7*t + 0 = 0 for t.
-2/3, 0
Factor -3*b**3 - 94100 + 80*b + 94012 + b**3 - 14*b**2.
-2*(b - 2)**2*(b + 11)
Factor 16*u + 47*u**2 + 18*u + 38*u - 43*u**2 + 324.
4*(u + 9)**2
Let u(f) = f**3 + 22*f**2 + 41*f + 22. Let l be u(-20). Factor 2/3 + 1/3*x**l + x.
(x + 1)*(x + 2)/3
Factor -72*p + 24*p**2 - 5 + 89*p**3 - 91*p**3 + 39 + 30.
-2*(p - 8)*(p - 2)**2
Let p(m) = -3 + 2*m + 2 - 2*m + m. Let l be p(4). Factor -4*g - 4*g**l - 3*g + 9*g + 14*g.
-4*g*(g - 2)*(g + 2)
Let q = -1/19 - 5/266. Let t = 4/7 + q. Factor -2*v**3 - t - 1/2*v**4 - 2*v - 3*v**2.
-(v + 1)**4/2
Factor -2/11*t**3 + 4/11 - 4/11*t**2 + 2/11*t.
-2*(t - 1)*(t + 1)*(t + 2)/11
Let w(r) be the second derivative of -r**4/3 - 4*r**3 + 4*r - 1. Factor w(j).
-4*j*(j + 6)
Let j(h) = h**3 - h**2 + 2 - 2 + 1 - h. Let w(a) = 22*a**2 - 21*a**2 + a - a**3 - 1 + 0*a**3. Let b(u) = -4*j(u) - 3*w(u). Find r such that b(r) = 0.
-1, 1
Factor -27/4*v**3 + 33*v**2 - 5/2 + 17/4*v.
-(v - 5)*(3*v + 1)*(9*v - 2)/4
Factor 2/7*a + 6/7*a**3 - 6/7*a**2 - 2/7*a**4 + 0.
-2*a*(a - 1)**3/7
Let l(m) be the second derivative of m**6/165 + m**5/55 - m**4/22 - 4*m**3/33 + 4*m**2/11 + 7*m - 3. Find a, given that l(a) = 0.
-2, 1
What is h in 4/7*h + 0 - 5/7*h**2 + 1/7*h**3 = 0?
0, 1, 4
Suppose 138 - 95 = i. Determine m so that 13*m**2 + 0*m + 2*m - i*m**2 + 2*m = 0.
0, 2/15
Let f(p) be the first derivative of -p**4/10 - 4*p**3/15 + 13*p**2/5 - 4*p - 227. Factor f(o).
-2*(o - 2)*(o - 1)*(o + 5)/5
Let t(f) be the third derivative of -f**7/70 - 3*f**6/10 - 7*f**5/4 + 3*f**4/2 + 18*f**3 + 2*f**2 - 114*f. Factor t(p).
-3*(p - 1)*(p + 1)*(p + 6)**2
Determine r so that -36/5*r**4 - 768/5*r + 576/5*r**2 - 12/5*r**3 + 0 - 3/5*r**5 = 0.
-8, 0, 2
Let q(z) be the second derivative of -z**6/15 + z**5/2 - 7*z**4/6 + z**3 + 120*z + 2. Factor q(s).
-2*s*(s - 3)*(s - 1)**2
Suppose -3*d + 5*n + 14 = 0, -3*n - 2*n = 4*d + 28. Let z be (d - -5)/(15/6 + -1). What is x in 5/3*x**z + 0 - 2/3*x = 0?
0, 2/5
Let x(w) = -15*w**4 + 35*w**3 + 160*w**2 + 20*w - 250. Let v(j) = -j**4 - j**3 - 2*j**2 - 1. Let s(m) = 10*v(m) - x(m). Solve s(f) = 0 for f.
-2, 1, 12
Let u be 1/(1/140*4). Determine t, given that -9 - u*t + 23*t + 24*t - 3*t**2 = 0.
1, 3
Let -297*p**2 + 498 - 741*p