*a = 0.
-1, -2/7
Factor 3*n**2 + 0*n - n + 6*n + 7*n.
3*n*(n + 4)
Let y(j) be the first derivative of -j**5/80 - j**4/24 - j - 1. Let i(w) be the first derivative of y(w). Determine b so that i(b) = 0.
-2, 0
Let v(i) be the first derivative of 2/5*i - i**2 + 4/3*i**3 + 3 - i**4 - 1/15*i**6 + 2/5*i**5. Let v(d) = 0. What is d?
1
Let p(g) = -g**3 + 6*g**2 + 9*g + 4. Let z be p(7). Factor i**3 + 4*i - 5*i**3 + z*i**4 - 20*i**4 + 8*i**2 - 6.
-2*(i - 1)**2*(i + 1)*(i + 3)
Let n be (-384)/(-14)*(-12)/(-1278). Let f = 2/71 + n. Determine x so that 4/7*x**3 - 4/7*x**2 + 2/7*x**4 - 2/7*x**5 + 2/7 - f*x = 0.
-1, 1
Let f be 7*(-2)/(-14)*2. Let -j**3 + 3*j + 2 + 2*j - 2*j**f - 3*j**3 - j**3 = 0. Calculate j.
-1, -2/5, 1
Let s(t) be the second derivative of t**10/30240 + t**9/5040 + t**8/3360 - t**4/3 - 11*t. Let m(y) be the third derivative of s(y). Find p, given that m(p) = 0.
-2, -1, 0
Let h(o) = 8*o**2 + 32*o + 64. Let j(y) = -7*y**2 - 32*y - 64. Let z = -23 + 27. Let f(d) = z*j(d) + 3*h(d). Solve f(s) = 0.
-4
Let p**3 - 1 - 2*p**2 - 3 + 6 - p = 0. What is p?
-1, 1, 2
Let t = -638/1085 + 20/31. Let b(d) be the first derivative of 0*d - 1/14*d**4 - 2/21*d**3 + 0*d**2 - 2 + 1/21*d**6 + t*d**5. Find q such that b(q) = 0.
-1, 0, 1
Let o = -30 - -61/2. Factor o + 3/4*a + 1/4*a**2.
(a + 1)*(a + 2)/4
Let z(n) be the third derivative of -n**5/90 - n**4/12 - 2*n**3/9 - 13*n**2. Find u, given that z(u) = 0.
-2, -1
Suppose 3*t - 2 - 10 = 0. Let g be (-3)/(-2) - 2/(-4). Factor -l - 2*l**t + 4*l**3 - g + 4 - 3*l.
-2*(l - 1)**3*(l + 1)
Find p, given that -5/2*p**3 + 0*p - p**2 - 2*p**4 + 0 - 1/2*p**5 = 0.
-2, -1, 0
Suppose -21*x - 39 + 81 = 0. What is u in -2/3 + 0*u**x - 1/3*u**3 + u = 0?
-2, 1
Let v = -100 - -100. Determine i, given that -2/5*i**3 + 4/5*i**2 + v + 0*i - 2/5*i**4 = 0.
-2, 0, 1
Factor 4*l + 2/3*l**2 + 6.
2*(l + 3)**2/3
Let h(j) be the third derivative of 0 - 1/108*j**4 + 0*j + 1/270*j**5 + 0*j**3 + 8*j**2. Factor h(b).
2*b*(b - 1)/9
Let g(x) = -3*x**2 + 2*x. Let y(k) = 16*k**2 - 11*k. Let j = 15 - 13. Let w(t) = j*y(t) + 11*g(t). Factor w(s).
-s**2
Factor 5/4 + 25/4*i**2 - 15/2*i.
5*(i - 1)*(5*i - 1)/4
Let u(l) be the first derivative of -l**6/51 - 4*l**5/85 + 3*l**4/17 + 8*l**3/51 - 13*l**2/17 + 12*l/17 + 13. Let u(k) = 0. Calculate k.
-3, -2, 1
Let w be (-4)/1 + 2250/360. Determine m so that 0 - 3*m**4 + 3*m - 3/4*m**5 - w*m**3 + 3*m**2 = 0.
-2, -1, 0, 1
Let l(m) = m**2 - 5*m - 4. Let b be l(6). Let u be (-22)/(-4) - (b - -1). Factor u*h**4 - 1 - 7/2*h**3 + 7/2*h - 3/2*h**2.
(h - 1)**2*(h + 1)*(5*h - 2)/2
Let d(w) = -w + 10. Let z(u) = -6*u + 50. Let k(v) = -11*d(v) + 2*z(v). Let n be k(-12). Factor 6*o**2 + 1 - 6*o + 0 + n*o**2.
(2*o - 1)*(4*o - 1)
Let l(a) be the second derivative of -a**5/120 + a**4/8 - 3*a**3/4 - 5*a**2/2 + 7*a. Let r(j) be the first derivative of l(j). Let r(s) = 0. Calculate s.
3
Suppose 0 = -14*l - 12*l + 104. Factor 2/7*p**2 + 0 + 0*p + 2/7*p**3 - 2/7*p**l - 2/7*p**5.
-2*p**2*(p - 1)*(p + 1)**2/7
Let y(k) be the second derivative of k**4/42 - 20*k. Suppose y(l) = 0. What is l?
0
Let a(w) be the second derivative of -w**5/10 - 7*w**4/18 - 5*w**3/9 - w**2/3 + 2*w. Find n, given that a(n) = 0.
-1, -1/3
Let n(y) be the first derivative of -4*y**5/5 + 18. Factor n(d).
-4*d**4
Let j(t) be the first derivative of t**6/2 - 6*t**5 + 75*t**4/4 + 48. Solve j(f) = 0 for f.
0, 5
Let f(r) = 13*r**5 - 9*r**4 - 21*r**3 + 13*r**2 + 3*r - 4. Let u(p) = -p**5 + p**4 + p**3 - p**2 + p. Let o(b) = f(b) + 5*u(b). Find w such that o(w) = 0.
-1, 1/2, 1
Solve -487*p**2 + 486*p**2 - 7*p + 3*p - 3 = 0.
-3, -1
Suppose 5*o - 20 = -0*o. Suppose 17*f**2 - 8 + 2*f**3 + 24*f - 39*f**2 + o*f**3 = 0. Calculate f.
2/3, 1, 2
Let z(h) be the first derivative of 27*h**3/2 - 9*h**2/2 + h/2 - 4. Find b, given that z(b) = 0.
1/9
Suppose -3*f + 1 = -2*b - 1, -f = -b. Suppose p - b*p + 4 = 0. Let 10/11*w - 2/11*w**3 - 6/11*w**2 + 2/11*w**p - 4/11 = 0. Calculate w.
-2, 1
Let h = -150658/9 - -16682. Let w = h + 58. Let -2/9 - w*a + 2/9*a**3 + 2/9*a**2 = 0. What is a?
-1, 1
Suppose 3*y = 4*y - 6. Let g(d) = -5*d**3 + d**2 + 5*d + 5. Let x(h) = 11*h**3 - 2*h**2 - 11*h - 11. Let c(l) = y*x(l) + 13*g(l). Factor c(q).
(q - 1)*(q + 1)**2
Suppose 4*t + 10 = n, -1 = -2*n + 3. Let a be (6/1 - 1) + t. Factor -1/4*v**2 - 1/4*v**a + 1/4*v**4 + 1/4*v + 0.
v*(v - 1)**2*(v + 1)/4
Let z(m) = -6*m**2 + 17*m. Suppose -o + 4 + 0 = 0. Let v(l) = -6*l + l**2 - l**2 + 2*l**2. Let h(k) = o*z(k) + 11*v(k). Determine d, given that h(d) = 0.
0, 1
Let m = -1/29 + 121/145. Factor -2/5 - 2/5*q**2 - m*q.
-2*(q + 1)**2/5
Factor 0*u + 2/13*u**4 + 4/13*u**3 + 0 + 2/13*u**2.
2*u**2*(u + 1)**2/13
Let a be 2 + (-2 + 2)/2. Suppose a*u - 2 = 6. Factor -6*w**4 - 2*w**5 + 2*w**4 - 2*w**3 + 0*w**u.
-2*w**3*(w + 1)**2
Let a(f) = -2*f. Let l be a(1). Let b = l + 4. Solve -z**b + z - 2*z + 0*z = 0 for z.
-1, 0
Let w(i) = -i**3 + 6*i**2 - 4*i - 2. Let g be w(5). Let u be ((-1)/(-1) - 2) + g. Suppose 2*p**3 + 2*p**2 - u*p + 2*p**4 - 4*p**4 + 0*p = 0. What is p?
-1, 0, 1
Suppose -5*h - 4 = -4*u, 0 = -3*h - 4*u + 5*u - 1. Let s = 9 + -4. Let 0 + 1/3*o**s + 2/3*o**4 + h*o**2 + 1/3*o**3 + 0*o = 0. Calculate o.
-1, 0
Let j(z) = -z**3 - 9*z**2 - 7*z + 8. Let b be j(-8). Suppose -3*u + 2*c - 8 = b, u - c = 2 - 6. Factor 2/3*k**2 + u*k + 0.
2*k**2/3
Let z = -4/155 + 1252/465. Factor -z*b**3 + 4/9*b + 0 - 10/9*b**2.
-2*b*(3*b + 2)*(4*b - 1)/9
Let p be (2/(-4))/(4/(-24)). Factor -h**5 + 17*h**4 - 28*h**4 - h**2 + 12*h**4 + h**p.
-h**2*(h - 1)**2*(h + 1)
Let n(a) be the third derivative of a**7/315 - a**6/36 + 4*a**5/45 - a**4/9 - a**2 + 29. Factor n(y).
2*y*(y - 2)**2*(y - 1)/3
Let q(b) = 3*b + 52. Let d be q(-16). Suppose 0*j + 1/4*j**3 + 0 + 0*j**2 - 1/4*j**d = 0. Calculate j.
0, 1
Suppose -s = 3*s + 660. Let j be (-10)/(-66) + (-30)/s. Factor 0 + j*t**4 - 1/3*t**2 + 0*t - 1/3*t**3 + 1/3*t**5.
t**2*(t - 1)*(t + 1)**2/3
Let l be (9/3)/(3/4). Suppose 2*k = -2*k + 12. Suppose 3*r**3 - r**l - 2*r**5 - 3*r**k + 3*r**4 = 0. What is r?
0, 1
Let u(b) be the third derivative of b**6/120 - b**5/10 + b**4/24 - b**3/3 - 4*b**2. Let o be u(6). Solve 4 - 13*d - 5 + 15*d + d**o - 2*d**3 = 0 for d.
-1, 1
Let j(n) = n**2. Let l(k) = -15*k**2 + 20*k - 15. Let i(g) = 10*j(g) + l(g). Factor i(v).
-5*(v - 3)*(v - 1)
Let x(r) be the second derivative of -1/42*r**7 - 1/12*r**4 + 1/30*r**6 + 0*r**3 + 0 - 3*r + 1/20*r**5 + 0*r**2. Factor x(f).
-f**2*(f - 1)**2*(f + 1)
Let c(h) = 3*h**4 - 15*h**3 + 21*h**2 - 27*h + 12. Let s(r) = -r**2 - r + 1. Let i(q) = -c(q) + 6*s(q). Solve i(t) = 0 for t.
1, 2
Let f(b) be the third derivative of -b**7/1155 - b**6/330 + b**4/66 + b**3/33 - 3*b**2. Factor f(n).
-2*(n - 1)*(n + 1)**3/11
Let p(r) = 3*r**2 + 6*r + 2. Let d be p(0). Factor 1/3*v**3 + 4*v + 2*v**d + 8/3.
(v + 2)**3/3
Suppose -p - 116 = 3*a, -5*p - 550 = -5*a + 30. Let i be p/(-63) - (-4)/(-14). What is g in -4/9 + i*g**2 + 10/9*g = 0?
-1, 2/7
Let c(l) be the second derivative of l**4/42 + 4*l**3/21 + 3*l**2/7 - 37*l. Determine o so that c(o) = 0.
-3, -1
Let n(o) = -o**4 - 12*o**3 - 12*o**2 - o - 3. Let h(g) = -2*g**4 - 12*g**3 - 12*g**2 - 2*g - 2. Let d(w) = -3*h(w) + 2*n(w). Factor d(c).
4*c*(c + 1)**3
Let v(m) be the first derivative of m**3/15 + 2*m**2/5 + 4*m/5 - 11. Factor v(d).
(d + 2)**2/5
Suppose 56/9*s**2 - 44/9*s + 4/9*s**5 + 4/3 - 8/3*s**3 - 4/9*s**4 = 0. What is s?
-3, 1
Let p(i) be the third derivative of 0*i**3 + 0 - 1/200*i**6 + 0*i + 1/1050*i**7 - 1/120*i**4 - 4*i**2 + 1/100*i**5. Find h such that p(h) = 0.
0, 1
Let w = -197 + 593/3. Solve 0 - w*a**3 + 0*a - 4/3*a**2 = 0 for a.
-2, 0
Let s = -31 + 1093/35. Let j(u) be the first derivative of 3/7*u**4 + 1/21*u**6 - 8/21*u**3 + 1/7*u**2 + 0*u - s*u**5 - 2. Factor j(r).
2*r*(r - 1)**4/7
Let j(k) be the third derivative of -k**6/900 - k**5/225 + k**4/180 + 2*k**3/45 - 12*k**2. Determine a so that j(a) = 0.
-2, -1, 1
Let a = -1729/3 + 577. Factor 4/3*m + a*m**2 + 0.
2*m*(m + 2)/3
Let d = -47/56 - -9/8. Solve d*f**2 + 0 + 2/7*f = 0 for f.
-1, 0
Determine x so that -12*x + 4 - 5*x**2 + 72*x**3 - 4*x - 7*x**2 = 0.
-1/2, 1/3
Let a be 8/(-36) + (-94)/(-18). Let p(l) be the second derivative of 1/70*l**a + 1/21*l**4 + 0*l**2 + 3*l + 0 + 1/21*l**3. Determine b, given that p(b) = 0.
-1, 0
Le