2 + 0*y + 1/5*y**5 + 1/2*y**4 + 1/3*y**3 - 11. Determine h so that c(h) = 0.
-1, 0
Let d = 128/31 + -3041/744. Let v(m) be the second derivative of 0 - 1/40*m**5 + 1/12*m**3 - 12*m - 1/4*m**2 + d*m**4. Factor v(r).
-(r - 1)**2*(r + 1)/2
Let t(y) be the second derivative of -1/12*y**4 + 2/3*y**3 + 6*y**2 + 0 - 38*y. Let t(n) = 0. Calculate n.
-2, 6
Let h(g) be the second derivative of -g**7/231 + g**6/165 + g**5/22 - g**4/66 - 8*g**3/33 - 4*g**2/11 - 319*g. Factor h(b).
-2*(b - 2)**2*(b + 1)**3/11
Let j = -62 + 64. Let d(c) = -c**5 + c**4 - c**3 - c**2. Let p(m) = -17*m**5 + 89*m**4 - 98*m**3 - 67*m**2 - 9*m. Let i(s) = j*d(s) - 2*p(s). Factor i(l).
2*l*(l - 3)**2*(4*l + 1)**2
Let a(o) = 4*o + 52. Let f be a(-10). Factor 3*v**3 - v**2 - 4*v**3 - 12 + f.
-v**2*(v + 1)
Suppose 7*q = 38 + 130. Factor -28 + q*l + 15*l**2 + 12*l**2 + 25.
3*(l + 1)*(9*l - 1)
Let j be 4/(24/6) - -1. Let f(p) be the first derivative of -2/11*p - 5 - 2/33*p**3 + 2/11*p**j. Suppose f(l) = 0. Calculate l.
1
Let k(w) be the second derivative of w**5/30 + w**4 + 20*w**3/3 + 56*w**2/3 + 339*w. Let k(b) = 0. Calculate b.
-14, -2
Let v(q) be the second derivative of -q**6/120 + q**5/80 + q**4/24 - 2*q - 40. Factor v(f).
-f**2*(f - 2)*(f + 1)/4
Suppose -56 - 7 = 9*l. Let n be ((-29)/l + -3)/(12/14). Factor -32/3*p - 28/3*p**2 - n*p**3 + 64/3.
-4*(p - 1)*(p + 4)**2/3
Suppose -2*m - 113 = -z, -z - 217 = 3*m + m. Let j = m + 55. Factor 2/3*b**2 + 0*b - 1/3*b**3 + j.
-b**2*(b - 2)/3
Let f(j) be the second derivative of -j**5/120 + j**4/8 - j**3/2 + 15*j. Solve f(x) = 0.
0, 3, 6
Suppose -21*w = -20*w - 3. Let -7 + 4*o**2 - 2*o**3 - 4*o + 6*o**w + 3 = 0. What is o?
-1, 1
Let d = -97 + 110. Suppose -d*j + 32 = -5*j. Factor 4/5*u**3 - 2/5 + 0*u**2 - 4/5*u + 2/5*u**j.
2*(u - 1)*(u + 1)**3/5
Let u(p) be the second derivative of p**7/210 - p**6/90 - p**3 + 11*p. Let v(l) be the second derivative of u(l). Let v(k) = 0. Calculate k.
0, 1
Suppose -b**2 - 13*b + 9*b + 12 + 5*b = 0. What is b?
-3, 4
Let j = 66 + -72. Let k be (j/28)/((-6)/8). Suppose 0 - k*l - 2/7*l**2 = 0. Calculate l.
-1, 0
Let 0 + 2/3*m**2 + 0*m**3 + 4/9*m - 2/9*m**4 = 0. Calculate m.
-1, 0, 2
Let v(x) be the first derivative of -x**6/12 + 7*x**5/20 - x**4/2 + x**3/6 + x**2/4 - x/4 - 86. Factor v(z).
-(z - 1)**4*(2*z + 1)/4
Let o be (0 - -8) + (1 - 0). Let f be (6/12)/((-2)/(-456)). Let 2 - f*h**4 - o*h**2 + 117*h**4 - 2 + 6*h = 0. Calculate h.
-2, 0, 1
Let v(g) = -g - 5. Let a = 4 + -9. Let j be v(a). Factor 9*b**2 - b**5 + b**3 + j*b**4 - 8*b**2 - b**4.
-b**2*(b - 1)*(b + 1)**2
Let u(l) be the second derivative of -l**7/133 - 4*l**6/285 + 4*l**5/95 + 3*l**4/19 + 11*l**3/57 + 2*l**2/19 + 33*l + 2. Solve u(b) = 0 for b.
-1, -1/3, 2
Suppose m + 7 = -6*y + y, -y = 1. Let c be (2/m)/((-1)/4). Factor 0*t**4 + t**c - 5*t**3 + 2*t**2 + 5*t**3 - 3*t**3.
t**2*(t - 2)*(t - 1)
Let n(b) be the first derivative of 2/15*b**3 + 0*b + 5 + 2/5*b**2. Factor n(a).
2*a*(a + 2)/5
Factor x**2 - 52*x - 5*x**2 + 1548 - 1596.
-4*(x + 1)*(x + 12)
Let w(k) be the second derivative of 1/180*k**5 + 0*k**2 + 2*k + 1/24*k**4 + 0 - 1/1080*k**6 + 2/3*k**3. Let p(y) be the second derivative of w(y). Factor p(c).
-(c - 3)*(c + 1)/3
Let m(a) be the third derivative of 1/120*a**5 - 1/12*a**3 - 22*a**2 + 0 + 0*a + 0*a**4. Determine r so that m(r) = 0.
-1, 1
Let g be (12/(-14))/((-92)/322). Factor -3*a**3 + 3/2 - 3/2*a**4 + g*a + 0*a**2.
-3*(a - 1)*(a + 1)**3/2
Let n(k) = -4*k + 13. Let z be n(4). Let y be z*(-20)/12*3/12. Solve -y*f**2 - 2*f - 3/4 = 0 for f.
-1, -3/5
Let a(i) = 4*i**5 - 2*i**4 + i**3 - 2*i**2 - 2*i - 2. Let m(q) = 11*q**5 - 5*q**4 + 2*q**3 - 6*q**2 - 5*q - 5. Let g(n) = -8*a(n) + 3*m(n). Factor g(k).
(k - 1)**2*(k + 1)**3
Let l(g) be the third derivative of g**7/525 + 7*g**6/300 - g**5/150 - 7*g**4/60 - 20*g**2 + 2*g. Find y, given that l(y) = 0.
-7, -1, 0, 1
Let q = 29 - 27. Let d be (q - -2)/(-8)*-6. Find c, given that 3 - d*c + 18*c**3 - 3*c**2 - 33*c**3 + 18*c**3 = 0.
-1, 1
Suppose -46 - 24*a**2 - 2 + 154*a - 94*a + 3*a**3 = 0. What is a?
2, 4
Let b be (48/(-21))/((-6)/21). Suppose 3*v + 20 = b*v. Factor v*q**2 + 3*q + 2 + 2*q**2 - 4*q**2 - 7*q.
2*(q - 1)**2
Suppose p + 7*b = 2*b - 5, -4 = -p + 4*b. Suppose p = -8*h + 4*h + 3*h. Factor -1/2*u - 7/4*u**2 + 7/4*u**4 + 1/2*u**3 + h.
u*(u - 1)*(u + 1)*(7*u + 2)/4
Factor -9*b - 18*b**3 - 4*b**5 - 59651*b**4 + 5*b**3 + 30*b**2 + 59631*b**4.
-b*(b + 3)**2*(2*b - 1)**2
Let j(i) = -10*i**2 + 8*i - 4. Let w(p) be the second derivative of -3*p**4/2 + 8*p**3/3 - 9*p**2/2 + 7*p. Let k(f) = 11*j(f) - 6*w(f). Factor k(u).
-2*(u - 1)*(u + 5)
Let c(y) be the first derivative of y**4/38 - 98*y**3/57 - 208*y**2/19 - 424*y/19 + 38. Factor c(r).
2*(r - 53)*(r + 2)**2/19
Let f = 26 + 102. Factor -125*h + f*h + 3*h**5 - 6*h**3 + 0*h**3.
3*h*(h - 1)**2*(h + 1)**2
Let p(k) = -k**2 - 15*k - 30. Let c be p(-18). Let v be (-14)/6*96/c. Determine u so that -v*u + 0 + 8/3*u**2 + 2*u**3 + 2/3*u**5 - 8/3*u**4 = 0.
-1, 0, 1, 2
Let k(x) be the third derivative of x**6/960 + 17*x**5/40 + 289*x**4/4 + 19652*x**3/3 + 348*x**2 - 2. Factor k(b).
(b + 68)**3/8
Let r(z) = 7*z**3 - 11*z**2 + 54*z - 80. Let t(d) = 3*d**3 + d**2 - d. Let a(u) = r(u) - 2*t(u). Factor a(j).
(j - 5)*(j - 4)**2
Let j(w) = w + 3. Let m be j(4). Suppose -5*x = -u - 5, -2*x + m + 7 = 2*u. Solve -3/2*s - 1 - 1/2*s**x = 0.
-2, -1
Let b = -5767/3 + 1923. Find w such that 0 - 1/3*w**3 - b*w**2 - 1/3*w = 0.
-1, 0
Let r = 3/142 + -793/10650. Let b = 178/525 + r. Factor b*o**2 + 6/7*o**3 + 0 + 2/7*o**5 + 0*o + 6/7*o**4.
2*o**2*(o + 1)**3/7
Factor 0*i + 0 - 2/3*i**2 + 13/3*i**3.
i**2*(13*i - 2)/3
Factor -3/5*i + 6/5*i**3 + 6/5*i**2 - 3/5 - 3/5*i**5 - 3/5*i**4.
-3*(i - 1)**2*(i + 1)**3/5
Factor 155 + 222*n + 4898*n + 5*n**3 - 320*n**2 - 155.
5*n*(n - 32)**2
Suppose -3*g = 3*u - 33, 5 = 2*u - g - 8. What is v in 2*v**3 + 8*v + 7*v**2 + 2*v**4 + u*v**3 + 9*v**2 = 0?
-2, -1, 0
Let i be 6/(-9) + (-172)/(-6). Let t = 27 - i. Let a(s) = -3*s**2 - 3*s - 12. Let r(y) = -y + 1. Let q(u) = t*a(u) - 6*r(u). Suppose q(d) = 0. Calculate d.
-2, -1
Let a(u) be the second derivative of -2*u**6/15 - 2*u**5 - 17*u**4/3 - 16*u**3/3 + 3*u + 9. Factor a(y).
-4*y*(y + 1)**2*(y + 8)
Let f be (-7 - 1908/(-132)) + (3 - 17)/2. Factor -3/11*u**2 - 1/11*u**5 - f*u**4 - 7/11*u**3 + 0 + 0*u.
-u**2*(u + 1)**2*(u + 3)/11
Let d = -106963/9 + 11885. Factor 0 - 2/9*i + 0*i**2 + d*i**3.
2*i*(i - 1)*(i + 1)/9
Let q = -279 - -279. Let k(l) be the first derivative of -1 + 2/15*l**3 + 1/5*l**2 + q*l. Let k(s) = 0. What is s?
-1, 0
Let b(c) be the second derivative of c**4/12 - c**2/2 + c + 5. Suppose b(k) = 0. What is k?
-1, 1
Let w be 24/40 - (-224)/10. Factor 4*h**2 - 15*h**4 - 3*h**3 + w*h**3 + 4*h**3 + 51*h**4.
4*h**2*(3*h + 1)**2
Let j(s) be the first derivative of 0*s**2 - 1/22*s**4 + 0*s + 2/55*s**5 - 2/33*s**3 + 1/33*s**6 + 21. Find p such that j(p) = 0.
-1, 0, 1
Let z = 54846/5 + -10969. Let z*a**3 + 4/5*a**2 + a + 2/5 = 0. Calculate a.
-2, -1
Suppose 32 + 16*k - 6*k**2 + 4*k**4 + 2*k**2 - k**2 - 4*k**3 - 19*k**2 = 0. Calculate k.
-2, -1, 2
Let p(q) be the first derivative of -q**3/4 + 45*q**2/4 - 675*q/4 - 23. Factor p(r).
-3*(r - 15)**2/4
Let i be (24/72)/(3 - (-4)/(-2)). Find r such that 0*r**2 + 0*r + i*r**4 + 0*r**3 + 0 = 0.
0
Let o(s) be the first derivative of 4*s + 8 - 1/3*s**2 - 2/9*s**3. Factor o(f).
-2*(f - 2)*(f + 3)/3
Let d(w) be the third derivative of -w**6/20 + w**5/20 + w**4 + 5*w**3/2 + 12*w**2. Factor d(a).
-3*(a + 1)**2*(2*a - 5)
Let d(i) be the third derivative of i**8/336 - 13*i**7/210 + 41*i**6/120 - 47*i**5/60 + 3*i**4/4 + 3*i**2 - 10*i. Suppose d(v) = 0. Calculate v.
0, 1, 2, 9
Suppose -5*m + 1 = -3*l, -3*m + 7*m - l = 5. Let 20*u**m - 5*u + 3*u - 2*u = 0. What is u?
0, 1/5
Let t(h) be the second derivative of -h**7/189 - h**6/27 - h**5/30 + h**4/6 - 37*h - 1. Factor t(q).
-2*q**2*(q - 1)*(q + 3)**2/9
Let a(q) be the third derivative of q**6/180 - q**5/18 + q**4/18 + 8*q**3/9 - q**2 - 4*q. What is i in a(i) = 0?
-1, 2, 4
Let g = 65 + -67. Let b be (g/(-12))/(2/21*7). Find s such that -3/4*s**3 + 0 + 1/4*s + b*s**2 - 1/4*s**4 + 1/2*s**5 = 0.
-1, -1/2, 0, 1
Let p(d) be the first derivative of -2*d + 1/20*d**4 - 5 - 1/10*d**2 + 2/3*d**3. Find z, given that p(z) = 0.
-1