at 0*w + 10/3*w**4 + 0 + 4/3*w**3 + 2*w**5 + z*w**2 = 0.
-1, -2/3, 0
Let h(l) be the second derivative of l**5/5 - l**4/2 + l**3/3 - 4*l. Factor h(a).
2*a*(a - 1)*(2*a - 1)
Let n(u) be the second derivative of -u**5/10 + u**4/6 + u**3/3 - u**2 + 28*u. Factor n(r).
-2*(r - 1)**2*(r + 1)
Find j, given that -2/3*j**3 + 2/3*j + 0*j**2 + 0 = 0.
-1, 0, 1
Let w(l) = 4*l + 2. Let m(d) = -5*d - 1. Let t(i) = -3*m(i) - 4*w(i). Let n be t(-5). Factor -2*v**5 + 2*v + 0*v**5 - 4*v**2 + 4*v**4 + n*v**4.
-2*v*(v - 1)**3*(v + 1)
Let r = -5 - -8. Let i = r + 1. What is k in -1/2*k**i + 0*k - 1/2*k**5 + 0 + 1/2*k**2 + 1/2*k**3 = 0?
-1, 0, 1
Suppose 14*s = 10*s + 44. Let d be (-48)/(-18)*3/s. Factor 6/11*f**2 + 2/11 + d*f.
2*(f + 1)*(3*f + 1)/11
Let m(b) be the second derivative of b**6/60 - b**5/8 + 3*b**4/8 - 7*b**3/12 + b**2/2 - 6*b. Solve m(y) = 0 for y.
1, 2
Let a(c) = -14*c**3 + 20*c**2 + 14*c - 20. Let s(f) = 9*f**3 - 13*f**2 - 9*f + 13. Let w(g) = 5*a(g) + 8*s(g). Find y such that w(y) = 0.
-1, 1, 2
Let i(y) be the third derivative of y**8/5040 - y**6/540 + y**4/72 - y**3/6 + 4*y**2. Let l(x) be the first derivative of i(x). What is b in l(b) = 0?
-1, 1
Let n = -30 - -20. Let t be 0 + n/(-9) + 2. What is h in -8/9*h**3 + 4/9 + 22/9*h - 14/9*h**5 + t*h**2 - 32/9*h**4 = 0?
-1, -2/7, 1
Let u(o) be the second derivative of -9*o**5/4 + 17*o**4/12 + 4*o**3 + 2*o**2 + 38*o. Factor u(k).
-(k - 1)*(5*k + 2)*(9*k + 2)
Let k = 5 + -3. Let q(s) be the second derivative of 0*s**2 + 0 + k*s + 1/35*s**5 + 1/49*s**7 + 0*s**3 + 1/21*s**6 + 0*s**4. Let q(w) = 0. What is w?
-1, -2/3, 0
Let c(f) = -2*f**2 + 18*f - 6. Let g(z) = z**2 - z + 1. Let l(p) = -c(p) - 6*g(p). Find r, given that l(r) = 0.
-3, 0
Let p(k) = k**3 + k**2 - 2*k + 24. Let v be p(0). Let s = v - 19. Factor 0 - 2/7*x**3 - 8/7*x**s - 10/7*x**4 + 0*x**2 + 0*x.
-2*x**3*(x + 1)*(4*x + 1)/7
Let r(g) be the third derivative of -g**7/490 + g**6/280 - 6*g**2. Factor r(m).
-3*m**3*(m - 1)/7
Let b(r) = -5*r - 25. Let p be b(-5). Factor p*s**3 + 2/5*s**5 + 4/5*s**2 - 4/5*s**4 - 2/5*s + 0.
2*s*(s - 1)**3*(s + 1)/5
Let x = 50 + -48. Factor -1/4 - 3/4*u**x + 3/4*u + 1/4*u**3.
(u - 1)**3/4
Let n(s) be the second derivative of s**7/840 + s**6/240 - s**5/20 + s**4/3 - s. Let m(h) be the third derivative of n(h). Solve m(l) = 0.
-2, 1
Let y(i) = 2*i - 5. Suppose -4*g + 8 + 2 = 3*d, -5*g = -4*d - 28. Let o be y(g). Determine b, given that -2/7*b**o - 4/7*b**2 - 2/7*b + 0 = 0.
-1, 0
Let d(r) = r**4 + 5*r**3 - 5*r**2 - 9*r - 4. Let x(m) = 5*m**3 - 5*m**2 - 10*m - 5. Let o(b) = -5*d(b) + 4*x(b). Solve o(h) = 0.
-1, 0, 1
Let z = -476/15 + 100/3. Let c be 67/15 - (-1)/3. Solve c*v - 2*v**3 + z + 6/5*v**2 = 0.
-1, -2/5, 2
Let z(w) = -w**2 - 2*w + 3. Let l(h) = 2*h**2 + 5*h - 7. Let p(i) = -2*l(i) - 5*z(i). Let c(f) = f**2 - 4. Let q(g) = c(g) - 4*p(g). Factor q(s).
-3*s**2
Suppose 5 - 1 = 4*u. Factor 2 - 2*j - j**2 - 1 - u.
-j*(j + 2)
Factor 0*u**2 + 12*u + 2*u**4 + 4*u**2 - 8 + 4*u**4 - 2*u**4 - 12*u**3.
4*(u - 2)*(u - 1)**2*(u + 1)
Let j(q) be the third derivative of q**9/10080 + q**8/4480 - q**7/1680 - q**6/480 - q**4/4 - 6*q**2. Let k(h) be the second derivative of j(h). Solve k(r) = 0.
-1, 0, 1
Factor 5/3*o**3 + 0 - 10/3*o**2 - 5*o.
5*o*(o - 3)*(o + 1)/3
Solve 2/11*l**5 + 0*l + 2/11*l**4 - 2/11*l**2 + 0 - 2/11*l**3 = 0.
-1, 0, 1
Let j(l) = -l**2 + 8*l - 10. Let r be j(6). Let w(i) be the first derivative of 2/3*i**3 - 3*i**r + 3 + 4*i. Let w(x) = 0. Calculate x.
1, 2
Find r, given that 4*r**2 + r**3 + r**2 - 2*r**2 = 0.
-3, 0
Let j = 11 + -8. Let t(h) be the first derivative of 1/5*h**2 + 1 + 0*h + 2/25*h**5 + 3/10*h**4 + 2/5*h**j. What is c in t(c) = 0?
-1, 0
Suppose -4*o + 4*l + 104 = 0, -8 = -o - 4*l - l. Factor -o*d**3 + 22*d**2 + 5*d**3 - 6*d + 2*d.
-2*d*(d - 1)*(9*d - 2)
Let d(a) = 6*a**4 + 5*a**3 - 31*a**2 + 43*a - 13. Let p(j) = 3*j**4 + 3*j**3 - 15*j**2 + 21*j - 6. Let u(r) = 3*d(r) - 5*p(r). Let u(g) = 0. Calculate g.
-3, 1
Suppose 2 + 4 = 2*f, -4*f = -3*t. Let m(k) be the first derivative of -28*k**2 + 4 + 16/3*k - 343/6*k**t + 196/3*k**3. Determine r, given that m(r) = 0.
2/7
What is v in -3/5*v + 6/5*v**4 + 9/5*v**5 + 6/5 - 36/5*v**2 - 6*v**3 = 0?
-1, 1/3, 2
Suppose 12*r = -3*j + 10*r - 2, -5*j + r = -1. Solve 0*u + j - 2/3*u**3 - 1/3*u**2 - 1/3*u**4 = 0.
-1, 0
Let a be 2/(-4) - (5 - (-102)/(-12)). Factor 0 - 4/3*m**2 - 2/3*m**a - 2/3*m.
-2*m*(m + 1)**2/3
Suppose -f = -2*f - 5*d - 13, 4*f - 5*d - 23 = 0. Let b = 2 + f. Factor 3*u**2 + 3*u + 0*u**4 - 3*u**3 - 3*u**b + 0*u**4.
-3*u*(u - 1)*(u + 1)**2
Let i = 2382/865 + 8/173. What is l in -i*l**2 + 0 - 4/5*l - 6/5*l**4 - 16/5*l**3 = 0?
-1, -2/3, 0
Let q = 1639 + -14771/9. Let t = q + 85/18. Determine y so that 1/2*y**2 + 3/2*y**4 - 1/2*y + 0 + t*y**3 = 0.
-1, 0, 1/3
Factor 157*p**4 - 24 + 180*p - 12*p**4 + 2*p**4 - 481*p**2 + 115*p**2 + 63*p**3.
3*(p - 1)*(p + 2)*(7*p - 2)**2
Let h = 3 + -3. Suppose u - 5*u + 8 = h. Solve -d + u*d**2 - 2*d + d = 0.
0, 1
Let k(x) = x**3 + 5. Let f be k(0). Let l(m) = -10*m**2 + 32*m - 10. Let z(p) = -4*p**2 + 13*p - 4. Let h(b) = f*l(b) - 12*z(b). Factor h(s).
-2*(s - 1)**2
Suppose 5*w = 4*y - 3 + 7, 4*w + 4*y + 4 = 0. Let j(z) be the second derivative of w - 4/21*z**3 - 4/7*z**2 - 2*z - 1/42*z**4. Determine f, given that j(f) = 0.
-2
Let g(s) be the second derivative of 0*s**3 + 0*s**2 + 0 + 1/6*s**4 - 4*s. Factor g(v).
2*v**2
Let w(v) be the second derivative of v**5/30 + v**4/6 - v**3 + v**2/2 + v. Let a(q) be the first derivative of w(q). Suppose a(c) = 0. Calculate c.
-3, 1
Let x(o) be the first derivative of o**4/4 + 2*o**3/3 + 5. Factor x(d).
d**2*(d + 2)
Let l(r) = 2*r. Let k be l(1). Let j = 588 + -586. Factor 2/3*y + 0 + 2/3*y**4 + j*y**k + 2*y**3.
2*y*(y + 1)**3/3
Let i(n) be the third derivative of n**5/5 + 4*n**4/3 + 8*n**3/3 + 15*n**2. Factor i(q).
4*(q + 2)*(3*q + 2)
Let m(w) = 4*w - 11. Let f be m(6). Factor -2*o**2 - 2*o + f*o**4 + 2*o**3 - 11*o**4 + 0*o**2.
2*o*(o - 1)*(o + 1)**2
Let v be (19/6)/(6/(-9)). Let r = v + 21/4. Factor 0*t**2 - 1/2*t**3 + 0 + r*t.
-t*(t - 1)*(t + 1)/2
Let s(n) be the second derivative of 2*n**7/315 - n**6/360 + 3*n**2/2 - 3*n. Let c(o) be the first derivative of s(o). Determine q so that c(q) = 0.
0, 1/4
Let w(f) be the third derivative of f**7/840 - f**6/240 - f**5/240 + f**4/48 + 7*f**2. Factor w(v).
v*(v - 2)*(v - 1)*(v + 1)/4
Let l = -4 + 5. Let n be 5/l - (2 + 1). Factor b**n + b**2 - 3*b**2 + b**4.
b**2*(b - 1)*(b + 1)
Let x(s) = -4*s**3 + 1. Let j be x(-1). Suppose -j*o = 3*h + 4, 8*o = 3*o - 10. Factor -1/3*n - 23/3*n**h - 20/3*n**3 + 2/3.
-(n + 1)*(4*n - 1)*(5*n + 2)/3
Let n(c) = -15*c**3 + 39*c**2 + 30*c - 18. Let p(j) = j**3 - j**2 + 1. Let x(f) = -n(f) - 18*p(f). Factor x(u).
-3*u*(u + 2)*(u + 5)
Let j = -14 + 10. Let x be 10/(-15)*18/j. Factor -3*c**2 - 2*c + 3*c**2 + x*c**2 + 1 - 2*c**2.
(c - 1)**2
Let j(w) be the second derivative of -9/20*w**5 + 0 - 1/6*w**3 - 1/2*w**4 + 3*w + 0*w**2. Factor j(u).
-u*(3*u + 1)**2
Let k(y) = -y**3 - y**2 - y - 3. Let r be k(0). Let b(v) = -2*v. Let g be b(r). Factor i**2 + 3*i**2 + 4*i - i**2 - g*i.
i*(3*i - 2)
Let a(g) be the first derivative of 0*g - 2/9*g**2 + 2/27*g**3 + 1. Factor a(s).
2*s*(s - 2)/9
Let w(t) be the second derivative of t**6/285 - t**5/190 - t**4/114 + t**3/57 - 5*t. Find n such that w(n) = 0.
-1, 0, 1
Let t(g) be the third derivative of g**9/1512 - g**7/210 + g**5/60 + g**3/2 + 2*g**2. Let p(b) be the first derivative of t(b). Find n, given that p(n) = 0.
-1, 0, 1
Let u(t) be the second derivative of -t**8/2520 - t**7/540 - t**6/540 + t**5/180 - t**4/2 - 8*t. Let m(n) be the third derivative of u(n). Factor m(q).
-2*(q + 1)**2*(4*q - 1)/3
Let s = -2 + 4. Let h(g) be the first derivative of -1/9*g**3 - 1/3*g**s - 1/3*g - 1. Suppose h(a) = 0. Calculate a.
-1
Let w(p) be the third derivative of p**7/1260 - p**6/540 - p**5/90 - p**3/6 - 7*p**2. Let o(x) be the first derivative of w(x). Factor o(s).
2*s*(s - 2)*(s + 1)/3
Let o = -1087 - -1087. Determine w so that -1/3*w**5 + o*w**2 - w**3 + 0 + 0*w + 4/3*w**4 = 0.
0, 1, 3
Let z(q) be the second derivative of 0 + 11/10*q**4 + 27/10*q**2 - 12/5*q**3 - 3*q - 6/25*q**5 + 1/50*q**6. Factor z(a).
3*(a - 3)**2*(a - 1)**2/5
Let h(t) be the second derivative of t**6/135 - t**5/