 the first derivative of -m**4/16 - m**3/2 + 7*m**2/8 - 692. Factor o(i).
-i*(i - 1)*(i + 7)/4
Suppose 11 = -2*s - 7*n + 2*n, -s - 3*n = 6. Let b be (0/(-10))/(s + 0/(-1)). Determine j, given that 2/5*j**2 + b*j - 2/5 = 0.
-1, 1
Let a(m) be the third derivative of -m**6/1440 + m**5/240 + 4*m**3 + 10*m**2. Let x(p) be the first derivative of a(p). Factor x(y).
-y*(y - 2)/4
Let l(r) be the first derivative of 0*r + 0*r**2 - 4 + 5/3*r**3. Factor l(p).
5*p**2
Let a(c) = -c**2 + 40*c - 144. Let s be a(36). Let w(n) be the second derivative of -1/30*n**5 + s + 1/9*n**3 + 2/3*n**2 - n - 1/9*n**4. Factor w(u).
-2*(u - 1)*(u + 1)*(u + 2)/3
Let g(b) be the second derivative of -5/36*b**4 + 6*b + 5/9*b**3 + 0 - 5/6*b**2. Factor g(p).
-5*(p - 1)**2/3
Factor -2/7*y**4 + 32/7*y**3 - 176/7*y**2 + 384/7*y - 288/7.
-2*(y - 6)**2*(y - 2)**2/7
Suppose 2*d + 7*a = 5*a - 10, -4*d - 5*a = 25. Let y(g) be the first derivative of 0*g**2 - 3/4*g**4 + 5 - 3*g**3 + d*g. Determine b so that y(b) = 0.
-3, 0
Suppose p + 1 = 2*p. Suppose -5*w + 9 = -p. Factor -t**3 - t - 4*t - 2*t + 5 - w + 5*t**2.
-(t - 3)*(t - 1)**2
Let t(b) be the second derivative of 7225*b**4/4 + 170*b**3 + 6*b**2 - 76*b + 1. What is c in t(c) = 0?
-2/85
Let v(n) = n - 10. Let c be v(13). Factor 15*h**2 + c*h - 10*h**3 - 3*h + 609*h**4 - 614*h**4.
-5*h**2*(h - 1)*(h + 3)
Let i(d) = d**2 + 2*d + 3. Let v be i(-2). Suppose -3*x + 134 = -0*u + 4*u, x = -u + 34. Solve 20*a**2 + 2*a**3 + 0*a**3 + 16 + 2*a**v + u*a = 0.
-2, -1
Let i(v) be the third derivative of -v**7/175 + 7*v**6/150 - 19*v**5/150 + v**4/15 + 4*v**3/15 - 19*v**2 - 2*v. Find z, given that i(z) = 0.
-1/3, 1, 2
Let z(x) be the second derivative of 15*x**6/7 - 93*x**5/14 + 152*x**4/21 - 64*x**3/21 + 2*x - 29. Factor z(f).
2*f*(f - 1)*(15*f - 8)**2/7
Suppose -o - 5*p - 6 = 0, -2*p = -3*o - 2*o - 3. Let v be o + (-6)/4*8/(-12). Suppose 1/2*f**2 + v + 1/4*f**4 + 0*f - 3/4*f**3 = 0. What is f?
0, 1, 2
Let s(k) = k**2 - 6*k - 4. Let q(j) = j**2 + 3. Let w be q(0). Let h(a) = a**2 - 6*a - 3. Let i(p) = w*h(p) - 4*s(p). What is z in i(z) = 0?
-1, 7
Suppose 51/2*r**3 - 52*r**4 - 9/2*r - 1 + 8*r**2 + 24*r**5 = 0. Calculate r.
-1/4, 2/3, 1
Let h(o) = o**2 - o. Let l(p) = -6*p**2. Suppose i + k + k - 3 = 0, i + 5*k - 12 = 0. Let q(v) = i*h(v) - l(v). Solve q(x) = 0 for x.
-1, 0
Let y(g) be the second derivative of g**5/12 - g**4/9 - g**3/18 - 8*g - 14. Factor y(m).
m*(m - 1)*(5*m + 1)/3
Let h(d) be the first derivative of d**3/9 + 22*d**2/3 - 15*d - 253. Let h(f) = 0. Calculate f.
-45, 1
Let g(j) = j**3 - j**2. Let y = 9 + -7. Let o(r) = 27*r**3 - 85*r**2 - 120*r - 32. Let l(k) = y*o(k) + 6*g(k). Find b, given that l(b) = 0.
-2/3, -2/5, 4
Let s be ((-7)/(42/(-8)))/(6/81). Factor 24*k**4 + 16*k**3 - 46*k**3 + 0*k**4 - s*k**3 - 3*k**5.
-3*k**3*(k - 4)**2
Let m(z) = 0 + 7 + 3*z - 2*z + 0*z. Let b be m(-4). Factor 10*g - 6*g**b - 2*g - 6*g + 4*g**2.
-2*g*(g - 1)*(3*g + 1)
Let m(w) be the first derivative of w**5/50 + 7*w**4/60 + 2*w**3/15 - 2*w**2/5 + w + 4. Let n(j) be the first derivative of m(j). Factor n(o).
(o + 2)**2*(2*o - 1)/5
Let i(c) be the first derivative of -c**4/22 + 20. Solve i(k) = 0 for k.
0
Suppose h = 5*p - 10, 4*h = 6*h. Suppose 0 = -r - 0*r + 2, -5*c - 4 = -p*r. Determine t, given that 0 + 5/3*t**5 - 10/3*t**4 - 5/3*t + 10/3*t**2 + c*t**3 = 0.
-1, 0, 1
Let w(d) be the second derivative of -d**6/5 + 129*d**5/40 + 11*d**4/8 - d - 28. Factor w(v).
-3*v**2*(v - 11)*(4*v + 1)/2
Let q(f) be the first derivative of 1/2*f - 3/8*f**2 + 0*f**3 + 1/16*f**4 - 9. Factor q(j).
(j - 1)**2*(j + 2)/4
Suppose -5*l - 9 = -52*y + 49*y, 2*l - 3 = -y. Determine m so that -1/2 - 1/4*m**3 - y*m**2 + 11/4*m + m**4 = 0.
-2, 1/4, 1
Suppose 3*j + 2*f - 12 = 0, -f - 6 = -3*f. Let z be (1*3)/((-45)/(-10)). Determine v, given that z*v**4 - 2/3*v**3 - 2/3*v**j + 2/3*v**5 + 0*v + 0 = 0.
-1, 0, 1
Let l(w) be the first derivative of 2*w**3 + 6 + 5*w + 1/4*w**4 + 6*w**2. Let y(f) be the first derivative of l(f). Suppose y(h) = 0. Calculate h.
-2
Let a(x) = -x**2 + 4*x + 11. Let m be a(6). Let c be 110/33 + -1 + 2*m. Suppose c*n - 2/3 + 1/3*n**2 = 0. Calculate n.
-2, 1
Factor -241588*s - 30*s**3 - 45*s**2 - 5*s**4 + 241588*s.
-5*s**2*(s + 3)**2
Let f(l) = 5*l**3 + l**2 - 2*l - 2. Let o(z) be the first derivative of 13*z**4/2 + 4*z**3/3 - 11*z**2/2 - 11*z - 7. Let g(u) = -11*f(u) + 2*o(u). Factor g(a).
-3*a**2*(a + 1)
Let k(c) = 1. Suppose -6*v + v + 60 = 0. Let n(z) = -2*z**2 + 3. Let y(l) = l**2 - 3. Let t(f) = 2*n(f) + 3*y(f). Let o(u) = v*k(u) + 3*t(u). Factor o(a).
-3*(a - 1)*(a + 1)
Let z be (-3)/(-9) - (-224)/12. Suppose -z*o = -12*o - 14. Factor 3/4*j**o - 1/4*j**3 + 0 + 1/4*j - 3/4*j**4.
-j*(j - 1)*(j + 1)*(3*j + 1)/4
Suppose 38 + 0 = 3*l + b, 5*l - 54 = -4*b. Factor -2*n**2 - 14*n + 6*n**2 - l*n.
4*n*(n - 7)
Let x(q) be the third derivative of 0 - 1/840*q**7 + 0*q + 1/1344*q**8 + 1/120*q**5 - 1/240*q**6 + 9*q**2 + 1/96*q**4 - 1/24*q**3. Factor x(o).
(o - 1)**3*(o + 1)**2/4
Determine c, given that 251*c**5 - 36*c**4 + 250*c**5 + 120*c**3 - 497*c**5 - 176*c**2 + 96*c = 0.
0, 2, 3
Suppose -4*i + 56 = 2*n, -8 = -2*n - 0. Suppose -31*b + 37*b - i = 0. Determine a, given that -2/17*a**3 + 2/17 + 6/17*a**b - 6/17*a = 0.
1
Factor -4/15*h**3 + 2/15*h**5 + 0 - 8/5*h**2 + 8/15*h**4 + 6/5*h.
2*h*(h - 1)**2*(h + 3)**2/15
Let v = -2580 - -12916/5. Factor -8/5 - 2*c**2 - 2/5*c**3 - v*c.
-2*(c + 1)*(c + 2)**2/5
Let z(m) be the first derivative of 2*m**6/15 - m**5/5 - 3*m**4/20 + m**3/3 - m**2/10 - 149. Suppose z(o) = 0. What is o?
-1, 0, 1/4, 1
Suppose 0 = 4*k + 4*t + 12, -k - 5 = -2*t + 5*t. Let s be (24/(-7))/(k/7). Determine m, given that 18*m**4 + 15*m**3 - 36*m**2 + 30*m**2 - 15*m**5 - s*m**5 = 0.
-2/3, 0, 1/3, 1
Let m be 2/3 - (-116)/(-12). Let c(z) = -3*z - 25. Let j be c(m). Factor -2/7*r + 8/7*r**3 + 0 - 6/7*r**j.
2*r*(r - 1)*(4*r + 1)/7
Let g = 36 - 32. Let c be (-25)/10*24/21 + g. Factor 10/7*h - c - 2/7*h**2.
-2*(h - 4)*(h - 1)/7
Let f(i) be the second derivative of -i**6/300 - i**5/200 + i**4/120 + i**3/60 + 11*i - 7. Factor f(k).
-k*(k - 1)*(k + 1)**2/10
Let s(m) = 9*m**2 + 15*m + 17. Let n(o) be the second derivative of 5*o**4/12 + 4*o**3/3 + 9*o**2/2 + 11*o. Let v(r) = 11*n(r) - 6*s(r). What is j in v(j) = 0?
-1, 3
Let t(x) be the third derivative of -x**8/504 + 4*x**7/315 - 8*x**5/45 + 4*x**4/9 - 124*x**2. Suppose t(f) = 0. Calculate f.
-2, 0, 2
Let n(j) = -7*j**4 + 90*j**3 - 402*j**2 - 90*j + 403. Let i(t) = -t**4 - t**2 - 1. Let u(q) = -2*i(q) + n(q). Determine m, given that u(m) = 0.
-1, 1, 9
Let n(l) = -7*l**3 - 1 - 9*l**2 + 19*l**3 - 3*l - 4*l. Let s(h) = 13*h**3 - 9*h**2 - 6*h - 2. Let u(g) = 6*n(g) - 5*s(g). Factor u(w).
(w - 2)*(w + 1)*(7*w - 2)
Let l(g) be the third derivative of -g**5/90 - g**4/24 + g**3/9 - g**2 - 11*g. Factor l(z).
-(z + 2)*(2*z - 1)/3
Let q(o) be the first derivative of 28 + 0*o**2 - 4*o**3 + 9*o**4 - 27/5*o**5 + 0*o. Factor q(t).
-3*t**2*(3*t - 2)**2
Let t(o) = o**5 + 3*o**4 + 2*o**3 - 16*o**2 + o + 9. Let y(a) = -a**4 - a**2 + 2*a. Let v(b) = -t(b) + 2*y(b). Factor v(s).
-(s - 1)**2*(s + 1)*(s + 3)**2
Find m such that -29*m - 6*m**2 + 17*m + 3*m**3 + 15*m**2 + 6 - 12*m**2 + 6 = 0.
-2, 1, 2
Let k = -39 - -48. Solve -13*f**2 + 4*f**3 + 5*f**2 - k*f + 9*f = 0 for f.
0, 2
Let u be 1/5*25 - (-9 + -1). Factor -5/4*f**2 - u*f + 0.
-5*f*(f + 12)/4
Let p(b) = -b**2 + 7*b - 1. Let y be (-136)/(-28) - (-1)/7. Let n be p(y). Find t, given that 3*t - 17 + 8 + n + 3*t**2 = 0.
-1, 0
Let x = -72 - -72. Let o = 16 - 16. Determine g so that 0*g + o*g**2 + x - 1/2*g**3 = 0.
0
Let r = -5/1016 + 8193/13208. Let r*j + 2/13*j**2 + 0 = 0. What is j?
-4, 0
Let m(a) = a**3 + 6*a**2 - a - 4. Let t be m(-6). Suppose 5*w**2 - 427 + 425 + w - 4*w**t = 0. What is w?
-2, 1
Let d(q) be the third derivative of -q**5/150 - 23*q**4/60 - 60*q**2. Let d(c) = 0. What is c?
-23, 0
Let v = -2/2969 + 2975/8907. Solve -1/2*m + v + 1/6*m**2 = 0 for m.
1, 2
Let h(b) be the first derivative of b**7/126 + b**6/45 - b**5/15 - 2*b**4/9 - 35*b - 28. Let c(o) be the first derivative of h(o). Factor c(n).
n**2*(n - 2)*(n + 2)**2/3
Let i be (40 + -41)*15/(-7). Suppose i*w - 3/7*w**3 + 9/7*w**2 - 3/7*w**4 + 6/7 = 0. What is w?
-1, 2
Let k(d) be the first derivative of -d**7/21 - 2*