5*f**i + 0.
4*f*(f - 1)/5
Let f(n) = -n**4 + n**2 + n + 2. Let h(c) = c**5 - 7*c**4 - 2*c**3 + 6*c**2 + 9*c + 17. Let m(p) = -24*f(p) + 3*h(p). Factor m(k).
3*(k - 1)**2*(k + 1)**3
Let s(h) be the third derivative of 2/5*h**5 + 0 - 5/6*h**4 - 14*h**2 + 0*h + 0*h**3 - 1/30*h**6. Factor s(q).
-4*q*(q - 5)*(q - 1)
Let w(c) be the second derivative of -c**6/270 + c**5/45 + 5*c**4/108 + 7*c + 1. Factor w(y).
-y**2*(y - 5)*(y + 1)/9
Solve 9/2*g**4 + 35/2*g**3 + 6*g - 49/2*g**2 + 2 - 11/2*g**5 = 0.
-2, -2/11, 1
Let x(m) be the second derivative of 1/24*m**4 + 0 - 1/12*m**3 - 12*m - 1/4*m**2 + 1/40*m**5. Suppose x(c) = 0. What is c?
-1, 1
Let j be -7 - (-133)/21 - 16/(-6). Let h(l) be the first derivative of -1/2*l**3 - 9/16*l**4 + 9/8*l**2 + 3/2*l - j. Factor h(x).
-3*(x - 1)*(x + 1)*(3*x + 2)/4
Let w(f) be the first derivative of -f**4/5 - 4*f**3/15 + 4*f**2 - 32*f/5 + 100. Factor w(c).
-4*(c - 2)*(c - 1)*(c + 4)/5
Let g(t) = 5*t**3 + 2*t**2 + 5*t - 6. Let k(s) = 6*s**3 + 3*s**2 + 6*s - 8. Let p(r) = -7*g(r) + 6*k(r). Factor p(h).
(h - 1)*(h + 2)*(h + 3)
Suppose -u + 4*u = 4*y + 5, 16 = 4*y. Let g(c) = c - 7. Let k be g(u). Factor k*q - 2 + 0 + q**2 - q + 0*q.
(q - 2)*(q + 1)
Factor 8*a - 96/5 + 8/5*a**2 - 2/5*a**3.
-2*(a - 6)*(a - 2)*(a + 4)/5
Let r(g) be the first derivative of -3*g**4/20 + g**3/5 + 9*g**2/5 - 85. Factor r(n).
-3*n*(n - 3)*(n + 2)/5
Let u(v) be the third derivative of -v**5/90 + 16*v**4/9 - 61*v**3/3 - 2*v**2 + 30*v. Factor u(i).
-2*(i - 61)*(i - 3)/3
Let r be 60452/(-1258) - -48 - (-43)/111. Determine o, given that r*o - 1/2*o**2 + 0 = 0.
0, 2/3
Let b(k) be the third derivative of 7*k**5/510 - 41*k**4/204 - 2*k**3/17 + 3*k**2 + 13. Factor b(v).
2*(v - 6)*(7*v + 1)/17
Let k(b) be the second derivative of -b**6/50 - 9*b**5/10 - 56*b**4/5 + 3*b**3 + 135*b**2/2 + 228*b + 2. Suppose k(s) = 0. Calculate s.
-15, -1, 1
Let c be (-34)/(-40) + (-21)/28. Let l(m) be the first derivative of 1/20*m**4 + c*m**2 + 0*m + 2/15*m**3 + 1. Factor l(i).
i*(i + 1)**2/5
Find a, given that -55*a**5 - 395*a**3 + 59*a**5 - 4*a**4 + 387*a**3 = 0.
-1, 0, 2
Let o be 1 + -1 - (-3)/27. Factor -5/9*a**4 + 0*a - o*a**2 + 4/9*a**3 + 0 + 2/9*a**5.
a**2*(a - 1)**2*(2*a - 1)/9
Let d(z) be the first derivative of 2*z**3/3 - 29*z**2 + 53. What is p in d(p) = 0?
0, 29
Let g(k) = 16*k**3 + k**2 + k + 1. Let w be g(-1). Let m = -12 - w. Determine n so that 3 + 14*n - 5*n**3 - 2 + 3*n**m - 12*n - n**4 = 0.
-1, 1
Let f(y) be the first derivative of y**5 + 5*y**4 + 10*y**3/3 - 10*y**2 - 15*y + 11. Factor f(x).
5*(x - 1)*(x + 1)**2*(x + 3)
What is v in 0 + 0*v + 49/2*v**2 - 3*v**4 - 1/4*v**5 - 21/4*v**3 = 0?
-7, 0, 2
Let s(j) be the second derivative of 16*j**2 + 20*j**4 + 5 + 5/2*j**5 + 28*j**3 - 2*j. Factor s(b).
2*(b + 4)*(5*b + 2)**2
Let c(x) = -x**5 - x**2 - 1. Let o(b) = -7*b**5 - 6*b**4 + 3*b**3 + 2*b**2 - 4. Let h(j) = -4*c(j) + o(j). Determine u so that h(u) = 0.
-2, -1, 0, 1
Let r(w) be the first derivative of -w**5/20 + w**4/6 - 10*w - 1. Let x(s) be the first derivative of r(s). Suppose x(d) = 0. Calculate d.
0, 2
Let m = -1685 + 1687. Let x(t) be the first derivative of 1/3*t**3 + 4 + 1/2*t**m - 2*t. Suppose x(f) = 0. What is f?
-2, 1
Let f = 3541/14 - 282. Let y = f - -61/2. Solve 50/7*t**5 + 32/7*t + 2/7*t**2 - 82/7*t**3 + 8/7 - y*t**4 = 0 for t.
-1, -2/5, 1
Let i(a) be the third derivative of 0 - 11/8*a**4 + 0*a**3 + 25*a**2 + 1/20*a**5 + 0*a. What is c in i(c) = 0?
0, 11
What is u in -5*u - 26*u + 4 - 15*u + 50*u**2 - 19 + 11*u = 0?
-3/10, 1
Let v(r) = 3*r**4 + r**4 + 8*r**3 + 0*r**4 - 6*r**2 - 5*r + 5*r**2. Let u(w) = -2*w**4 - 4*w**3 + 2*w. Let q(h) = -5*u(h) - 2*v(h). Solve q(k) = 0 for k.
-1, 0
Let t(h) be the first derivative of 348*h**5/5 - 52*h**4 - 16*h**3/3 + 28. Factor t(a).
4*a**2*(3*a - 2)*(29*a + 2)
Let w = 61 + -36. Suppose 4*p - 3 - w = 0. Factor 2*j**2 + p*j**2 - 5*j**2 - j**2.
3*j**2
Let c(h) be the third derivative of -h**6/540 - 34*h**5/135 + h**4/108 + 68*h**3/27 + 223*h**2. Suppose c(y) = 0. Calculate y.
-68, -1, 1
Let t(k) be the third derivative of k**7/70 - 3*k**6/40 + k**5/10 - k**2 - 147*k. Factor t(r).
3*r**2*(r - 2)*(r - 1)
Let g = -1802 + 1805. Let v(a) be the second derivative of 2/3*a**2 + 4*a + 0 - 1/18*a**4 + 1/9*a**g. Find s such that v(s) = 0.
-1, 2
Let u be 21/49*(-1428)/(-459). Factor u + 2*o + 2/3*o**2.
2*(o + 1)*(o + 2)/3
Let o(k) be the first derivative of k**4/54 + k**3/27 - 2*k + 3. Let v(n) be the first derivative of o(n). Factor v(j).
2*j*(j + 1)/9
Let l be 4/(-10) - (-7616)/7840. Find x, given that -l + 2*x - 10/7*x**2 = 0.
2/5, 1
Let n = -4288 - -4290. Solve -6/11*f**3 + 0 - 2/11*f - 2/11*f**4 - 6/11*f**n = 0.
-1, 0
Let n be (-10)/(-6)*-1 - 156/(-72). Suppose -6*z + 13/2*z**2 + n*z**4 + 2 - 3*z**3 = 0. What is z?
1, 2
Factor -1/2*l**2 + 9/2 - 3/2*l + 1/6*l**3.
(l - 3)**2*(l + 3)/6
Suppose -60*y + 30 = -54*y. Let t(z) = z + 9. Let j be t(-7). Solve y*m**2 - 4*m**4 + 5*m**2 + 4*m**3 - 10*m**j = 0 for m.
0, 1
Let p(v) be the third derivative of 45/112*v**8 - 25/2*v**4 + 71/6*v**5 + 0*v + 20/3*v**3 + 0 - 31/8*v**6 - 6/7*v**7 - 10*v**2. Solve p(i) = 0 for i.
-2, 1/3, 2/3, 2
Let c be (-48)/36*(6 - 296/32). Factor -1/3*d**3 - 16*d - 12 - c*d**2.
-(d + 1)*(d + 6)**2/3
Factor 8/11 + 2/11*k + 3/11*k**3 - 13/11*k**2.
(k - 4)*(k - 1)*(3*k + 2)/11
Let s(u) = -u**2 - 10*u - 9. Let r be s(-6). Let m be (r/25)/(-3)*-2. Solve 4/5 - 6/5*z**4 + 2*z + m*z**2 - 2*z**3 = 0.
-1, -2/3, 1
Suppose o - 4 + 0 = 3*j, -2*j + 4*o = 16. Let p be -5*(j + (-4)/2). Let 6 - p*k**3 + 8*k**4 + 3 - 10*k**2 - 7 + 2*k + 8*k**5 = 0. Calculate k.
-1, -1/2, 1/2, 1
Let u be ((-6)/(-10))/((-35)/(-175)). Let o(j) be the second derivative of 6*j + 3*j**2 + 1/4*j**4 + 0 - 3/2*j**u. Solve o(b) = 0 for b.
1, 2
Let v(u) = -26*u**3 - 226*u**2 - 537*u - 354. Let b(p) = 285*p**3 + 2485*p**2 + 5905*p + 3895. Let s(m) = -6*b(m) - 65*v(m). Factor s(k).
-5*(k + 8)*(2*k + 3)**2
Let x(z) be the first derivative of -7 + 16*z + 4/3*z**3 - 8*z**2. Suppose x(w) = 0. What is w?
2
Let u(y) be the first derivative of y**7/2240 + y**6/320 + y**5/160 - 6*y**3 - 3. Let g(m) be the third derivative of u(m). Factor g(c).
3*c*(c + 1)*(c + 2)/8
Let k(w) = -3*w**2 - 6*w + 9. Let n(u) = -u**2 + 1. Let l be 80/35 - 4/14. Suppose -3 - l = -d. Let q(v) = d*n(v) - k(v). Let q(s) = 0. Calculate s.
1, 2
Let j = -7 - -10. Let h(p) = p**2 + 12*p + 20. Let t be h(-10). Suppose t*o + 0 + j*o**3 - 3/4*o**4 - 3*o**2 = 0. Calculate o.
0, 2
Let y(k) be the second derivative of 2*k**7/21 - 2*k**6/15 - 3*k**5/5 + k**4/3 + 4*k**3/3 + 11*k - 1. What is p in y(p) = 0?
-1, 0, 1, 2
Let m = 12 + -16. Let f(q) = -q**2. Let w(p) be the first derivative of p**3/3 - p**2/2 - p + 3. Let u(d) = m*w(d) - 5*f(d). Suppose u(c) = 0. What is c?
-2
Let x(c) be the second derivative of 11*c + 0*c**2 - 9/10*c**6 + 9/56*c**7 + 2/3*c**3 + 9/5*c**5 - 1 - 5/3*c**4. Suppose x(h) = 0. What is h?
0, 2/3, 2
Let t = -1/114 - -349/798. Let r(k) be the second derivative of -t*k**2 - 3/28*k**5 - 1/2*k**3 + 0 - 1/70*k**6 - 9/28*k**4 - k. Let r(f) = 0. What is f?
-2, -1
Determine g so that -3/5*g**5 - 21/5*g**2 + 0*g + 12/5 + 3/5*g**3 + 9/5*g**4 = 0.
-1, 1, 2
Let k(c) be the second derivative of c**5/10 + 17*c**4/66 + 2*c**3/11 + 276*c. Factor k(x).
2*x*(x + 1)*(11*x + 6)/11
Let w(b) be the first derivative of -7*b**6/10 + 6*b**5/25 + 63*b**4/10 - 68*b**3/5 + 111*b**2/10 - 18*b/5 - 165. Find h, given that w(h) = 0.
-3, 2/7, 1
Let x(q) be the second derivative of -q**4/15 - 262*q**3/15 + 264*q**2/5 + 102*q. Factor x(y).
-4*(y - 1)*(y + 132)/5
Let o(v) = -3*v**3 - 2*v**2 + 53*v + 4. Let w(y) = y**2 + 2*y + 1. Let u(t) = o(t) - 4*w(t). Suppose u(a) = 0. What is a?
-5, 0, 3
Let z = -3/779 + 3131/3895. Suppose 2/5*t**2 - z - 2/5*t = 0. What is t?
-1, 2
Let c(y) = 2*y**4 - 16*y**3 + 38*y**2 + 48*y - 8. Let v(i) = -3*i**4 + 31*i**3 - 76*i**2 - 96*i + 14. Let m(o) = -7*c(o) - 4*v(o). Factor m(j).
-2*j*(j - 3)*(j + 1)*(j + 8)
Let h(f) = -25*f**3 - 364*f**2 + 1289*f - 911. Let y(d) = 5*d**3 + 73*d**2 - 258*d + 182. Let a(b) = -2*h(b) - 11*y(b). Solve a(m) = 0 for m.
-18, 1, 2
Let h(d) = d**5 + 2*d**3 - d**2 - d + 1. Let f(x) = -11*x**5 + 12*x**4 - 36*x**3 + 9*x**2 + 9*x - 9. Let y(q) = -2*f(q) - 18*h(q). Factor y(c).
4*c**3*(c - 3)**2
Let i(d