5 + 40*c**4/3 + 80*c**3/3 + 32*c**2 - c + 74. Factor l(o).
2*(o + 2)**5
Let x(o) be the second derivative of 4/3*o**3 + 1/3*o**4 + 2*o**2 + 0 + 2*o. Determine s so that x(s) = 0.
-1
Let p be (-16)/1 + (-2)/(-2). Let n = -12 - p. Factor 5*g**3 + 3*g**5 - 2*g**n + 2*g**5 - 6*g**4 - 2*g**5.
3*g**3*(g - 1)**2
Let c(z) = 2*z - 1. Let s(d) = -16*d + 72. Let y(u) = -6*c(u) - s(u). Let t be y(17). Factor -8/7*w + 2/7*w**t + 8/7.
2*(w - 2)**2/7
Let d = 7157 - 7157. Factor -9/4*h + 0*h**4 + d - 6*h**2 - 9/2*h**3 + 3/4*h**5.
3*h*(h - 3)*(h + 1)**3/4
Let s(y) be the second derivative of -y**5/15 - y**4/3 - 7*y**2 + 16*y. Let c(i) be the first derivative of s(i). Factor c(d).
-4*d*(d + 2)
Let w(a) = -12*a**2 + 44*a - 36. Let s(u) = 4*u**2 - 2*u. Let q(g) = 2*s(g) + w(g). Factor q(v).
-4*(v - 9)*(v - 1)
Let f be 135/168 - (-28)/(1568/(-24)). Let p be 5/(-8)*9/(-15). Determine d, given that 3/8*d**4 - 3/8*d**3 - p*d**2 + 0 + f*d = 0.
-1, 0, 1
Let p(m) = 3*m**3 - 4*m**2 - 2. Let d(k) = k**2 - 1. Let a(j) = -j - 1. Let w be a(-3). Let c be (2 - 16/6)/(22/33). Let h(t) = c*p(t) + w*d(t). Factor h(o).
-3*o**2*(o - 2)
Let h(x) be the first derivative of -1/24*x**4 + 1/18*x**3 + 0*x + 24 + 1/12*x**2 - 1/30*x**5. Solve h(r) = 0 for r.
-1, 0, 1
Let b(k) be the third derivative of 1/90*k**6 - 5/504*k**8 - 4*k**2 + 0 + 0*k**4 + 0*k + 0*k**3 - 1/105*k**7 + 0*k**5. What is s in b(s) = 0?
-1, 0, 2/5
Factor 215*r + 160/3 + 20/3*r**2.
5*(r + 32)*(4*r + 1)/3
Let z(d) be the first derivative of -d**6/300 + d**5/50 - d**4/30 - 2*d**2 - 26. Let k(m) be the second derivative of z(m). Factor k(c).
-2*c*(c - 2)*(c - 1)/5
Let b(g) be the third derivative of g**7/50 - 3*g**6/20 + 29*g**5/100 - 3*g**4/20 - 24*g**2. Suppose b(h) = 0. Calculate h.
0, 2/7, 1, 3
Determine v so that -v**2 + 2*v + 997 - 998 + 0*v = 0.
1
Let i be -2 - (30/(-3) - -4). Suppose 9*j + i*j - 52 = 0. Determine h so that -3*h**3 + 3/2*h - 9*h**2 + 3/2*h**5 + 9/2*h**j + 9/2 = 0.
-3, -1, 1
Let f be 6 + 4/(-4) + (-1824)/384. Factor -f*m**2 + m - 1.
-(m - 2)**2/4
Factor -15*x**2 + 12 - 3*x + 39*x**2 + x - 26*x**2.
-2*(x - 2)*(x + 3)
Let c(w) be the third derivative of w**5/20 + 101*w**4/8 + 50*w**3 + 6*w**2 + 34. Find r such that c(r) = 0.
-100, -1
Let x(l) = -2*l**2 + 348*l - 14792. Let g(a) = 4*a**2 - 698*a + 29584. Let j(m) = 2*g(m) + 5*x(m). Factor j(z).
-2*(z - 86)**2
Suppose 204 = 3*o + 198. Let r(s) be the first derivative of 2/35*s**5 - 12/7*s**o + 1 - 3/7*s**4 + 26/21*s**3 + 8/7*s. Factor r(h).
2*(h - 2)**2*(h - 1)**2/7
Let v(q) be the second derivative of -q**5/20 - q**4/2 - 3*q**3/2 - 2*q**2 + 20*q - 3. Suppose v(n) = 0. Calculate n.
-4, -1
Let d(j) be the third derivative of j**8/110880 - 13*j**7/13860 + 169*j**6/3960 + 11*j**5/60 + j**2 - 24. Let z(i) be the third derivative of d(i). Factor z(b).
2*(b - 13)**2/11
Let c(f) = 2*f**3 + 2*f**2 + 6*f - 2. Let i(v) = v**3 + v**2 + v - 1. Let n be (-4)/5 + 27/15. Let d(z) = n*c(z) - 4*i(z). Solve d(g) = 0 for g.
-1, 1
Let f = -12/13 + 135/104. Let s(l) be the first derivative of 1/36*l**6 + 2 + 0*l + f*l**4 + 7/18*l**3 + 1/6*l**2 + 1/6*l**5. Solve s(h) = 0.
-2, -1, 0
Let x = 0 + -5. Let p be (-2)/x + (-340)/(-25). Factor 18*l**2 + p*l - 4*l**2 + 4*l - 8*l - 4.
2*(l + 1)*(7*l - 2)
Let m be (-8)/2 + 3485/(-35). Let v = 104 + m. Determine g, given that 0*g + 3/7*g**3 + 0 + 3/7*g**2 - v*g**5 - 3/7*g**4 = 0.
-1, 0, 1
Let d be 11/(((-6)/18)/((-2)/6)). Let 14 - 25 - 20*t**2 + 8*t + d = 0. Calculate t.
0, 2/5
Let w(l) = -7 + 2*l + 18*l**2 + 3*l - 19*l**2 + 5*l. Let a be w(9). Determine v so that 12*v + 23 + 3*v**2 + 2 + 6*v + a = 0.
-3
Suppose 0*t + 4*t = 11*t. Let f(p) be the first derivative of 1/3*p**4 - 2/3*p + t*p**3 - 2/3*p**2 + 2/15*p**5 - 3. Factor f(s).
2*(s - 1)*(s + 1)**3/3
Suppose -165*t = -167*t + 12. Let o be 6 - -1*(-28)/t. Factor 4/3 - o*i**3 - 10/3*i**2 - 2/3*i.
-2*(i + 1)*(i + 2)*(2*i - 1)/3
Let u = -2072/3 + 691. Let a(s) be the first derivative of -u*s**2 + 0*s + 7 + 2/9*s**3. Factor a(j).
2*j*(j - 1)/3
Let x(p) be the second derivative of -3*p**5/40 - 5*p**4/8 + 11*p**3/2 - 12*p**2 + 19*p. Determine k so that x(k) = 0.
-8, 1, 2
Let b(q) be the first derivative of -4*q**7/105 + 17*q**6/60 - 8*q**5/15 + q**4/4 + q**2 - 1. Let z(u) be the second derivative of b(u). Factor z(i).
-2*i*(i - 3)*(i - 1)*(4*i - 1)
Let b(p) be the third derivative of -1/84*p**4 + 0 - 1/210*p**5 + 17*p**2 + 0*p + 0*p**3. Factor b(h).
-2*h*(h + 1)/7
Let i(m) be the third derivative of -m**9/3402 - m**8/840 - m**7/630 - m**6/1620 - 7*m**3/2 + 6*m**2. Let k(f) be the first derivative of i(f). Factor k(g).
-2*g**2*(g + 1)**2*(4*g + 1)/9
Let c(d) = 3*d - 2. Let p be c(2). Suppose s = -p*o - 13, 4*o + 31 = 4*s + s. Determine u, given that -u**2 - 9*u**3 + 2*u**2 + 5*u**2 + s*u**4 = 0.
0, 1, 2
Let -6*q - 33*q - 2502*q**2 + 320 - 100*q - 31*q + 2507*q**2 = 0. Calculate q.
2, 32
Let s = -18/23 + 259/184. Let q(l) be the third derivative of -s*l**4 + 0 - l**3 - 3/20*l**5 + 0*l - 3*l**2. Factor q(r).
-3*(r + 1)*(3*r + 2)
Let 57*o**4 - 212*o**4 - 2*o + 0*o**2 - 2*o - 13*o**3 + 68*o**2 - 70*o**3 = 0. Calculate o.
-1, 0, 2/31, 2/5
Let o(j) be the third derivative of -j**7/1890 + j**6/216 - j**5/180 - 5*j**4/216 + 2*j**3/27 - 107*j**2. Let o(x) = 0. What is x?
-1, 1, 4
Find t such that 0 - 12/5*t**4 - 3/5*t**5 - 9/5*t**3 + 0*t**2 + 0*t = 0.
-3, -1, 0
Let n(q) be the second derivative of q**4/4 + 14*q**3 + 81*q**2/2 + 25*q - 4. Factor n(p).
3*(p + 1)*(p + 27)
Let c(s) be the third derivative of -s**7/7560 - s**6/270 - 2*s**5/45 - 13*s**4/24 + 16*s**2. Let k(p) be the second derivative of c(p). Solve k(j) = 0.
-4
Find r, given that -116/3*r**3 - 1/3*r**5 + 39*r + 54 - 142/3*r**2 - 20/3*r**4 = 0.
-9, -2, -1, 1
Let q(g) be the second derivative of 0 - 6/5*g**2 - 30*g + 1/15*g**4 + 11/15*g**3. Factor q(k).
2*(k + 6)*(2*k - 1)/5
Let b(h) be the second derivative of 5*h**7/14 - 13*h**6/6 - 5*h**5/4 + 75*h**4/4 - 95*h**3/3 + 20*h**2 + 12*h + 11. What is i in b(i) = 0?
-2, 1/3, 1, 4
Let n(y) = y**5 - y**4 + y**3 + y - 1. Let t(j) = -10*j**5 - 14*j**4 - 42*j**3 - 28*j**2 - 14*j + 6. Let v(u) = -6*n(u) - t(u). Find q, given that v(q) = 0.
-2, -1, 0
Let d = -3209 + 16053/5. Suppose o - 4 = -2. Factor o*s + d + 2/5*s**2.
2*(s + 1)*(s + 4)/5
Factor 12/7*p**3 - 4/7*p**4 + 20/7*p + 0 + 36/7*p**2.
-4*p*(p - 5)*(p + 1)**2/7
Let f(w) be the first derivative of -7*w**5/5 - 5*w**4/4 + 3*w**3 + 5*w**2/2 - 2*w + 35. Suppose f(r) = 0. What is r?
-1, 2/7, 1
Let d = -33 + 33. Suppose -u + 4*x = -12, 5*x + 15 = -u - d*x. Suppose 0*l**3 + u + 0*l + 3/7*l**4 - 3/7*l**2 = 0. Calculate l.
-1, 0, 1
Let c be (245/50 - 5)/(24/(-40)). Factor -b + 3/2 + c*b**2.
(b - 3)**2/6
Let j(s) = 12*s - 31. Let w be j(3). Let z(m) be the third derivative of 1/480*m**6 + 1/96*m**4 + 0*m - 1/120*m**5 + 0 + 0*m**3 - w*m**2. Factor z(b).
b*(b - 1)**2/4
Suppose 0 = -3*t - 2*g + 32, -2*t = -0*g + 5*g - 25. Let y = t + -8. Solve -3*i + 2*i**2 - 12*i**y - 6 - 2*i**3 - 11*i = 0 for i.
-3, -1
Let s(p) be the third derivative of -p**7/630 - p**6/135 + p**3/2 - 13*p**2. Let g(d) be the first derivative of s(d). Factor g(f).
-4*f**2*(f + 2)/3
Let d be 3/6*2*2. Suppose -306*u + 312*u = 0. Let 0*z**d + 1/6*z**5 + 0 + u*z + 0*z**3 + 1/6*z**4 = 0. Calculate z.
-1, 0
Let h(k) = k**3 - 2*k**2 + 4*k - 44. Let n be h(4). Factor 0 + 5/6*c**n + 0*c - 5/6*c**3 - 5/3*c**2.
5*c**2*(c - 2)*(c + 1)/6
Suppose 5*u = u. Suppose 3*p + c = -p + 10, u = -5*p - 3*c + 9. Suppose -10*h**2 + 10*h**2 - 2 + 4*h + 2*h**4 + 0 - 4*h**p = 0. Calculate h.
-1, 1
Let t = 1/277 + 20495/831. Let -16/3*w + 8/3 - t*w**2 - 68/3*w**3 - 6*w**4 = 0. What is w?
-2, -1, 2/9
Suppose -3*v - 4*t = 0, -2*t + 6*t = 0. Factor v*r**3 + 3*r**4 - 4*r**3 - 4*r**2 + r**4 + 4*r.
4*r*(r - 1)**2*(r + 1)
Let t(g) = g**2 + 12*g + 14. Let x(k) = 84*k + 3 - 10 + 106 + 6*k**2. Let u(m) = -15*t(m) + 2*x(m). Factor u(q).
-3*(q + 2)**2
Let p(c) be the first derivative of -2*c**3/9 + 358*c**2/3 - 64082*c/3 + 43. Suppose p(f) = 0. Calculate f.
179
Determine o, given that -24*o**2 + 2*o**3 - 16*o + 84*o - 46*o**2 = 0.
0, 1, 34
Let n = 0 + 3. Suppose n + 7 = 5*g. Factor 4*j**2 - 4*j - 3 + 3 - 2*j**2 + g.
2*(j - 1)**2
What is l in 2*l - 15/7 + 1/7*l**2 = 0?
-15, 1
Suppose 15*d - 16*d = -4. Factor d*l**4 + 13*l**3 -