79*q - 2. Factor a(c).
2*(c - 5)*(c - 3)*(c - 1)
Let d(p) = -p**3 - p**2 + 1. Suppose t - 4 + 2 = 0. Let a(h) = 5*h**3 - 3 + 2*h**2 + 0*h**3 - 1 + h**t. Let c(u) = a(u) + 4*d(u). Factor c(z).
z**2*(z - 1)
Let s(m) be the first derivative of -5*m**6/6 - 3*m**5 - 5*m**4/2 + 36. Factor s(z).
-5*z**3*(z + 1)*(z + 2)
Let n(y) be the first derivative of 1/4*y**3 + 2 + 5/8*y**2 - 1/2*y. Factor n(a).
(a + 2)*(3*a - 1)/4
Suppose -23*w - 9*w = 61*w - 465. Factor 0*c**4 + 0*c + 0 + 2/9*c**3 + 0*c**2 - 2/9*c**w.
-2*c**3*(c - 1)*(c + 1)/9
Suppose 2*i + 2*y - 20 + 6 = 0, i = 5*y - 17. Let v(l) = 19*l**2 + 159*l - 43. Let m(k) = 10*k**2 + 79*k - 21. Let q(t) = i*v(t) - 5*m(t). Factor q(r).
(r + 12)*(7*r - 2)
Let s(i) be the third derivative of -i**8/252 + 2*i**7/21 - 5*i**6/6 + 25*i**5/9 + 4*i**2 - 17*i. What is n in s(n) = 0?
0, 5
Let n be (132/(-24) - -7)*((-8)/(-6))/1. Suppose -9/2*x + 3/2*x**3 - 3*x**n + 0 = 0. Calculate x.
-1, 0, 3
Let w(l) = l**2 - 36*l - 91. Let o(k) = 4*k**2 - 180*k - 456. Let s(j) = -3*o(j) + 16*w(j). Factor s(d).
4*(d - 11)*(d + 2)
Let x = -146/27 + 1184/189. Solve 0*t**2 + 0 - 2/7*t**5 + x*t**4 + 0*t - 4/7*t**3 = 0 for t.
0, 1, 2
Let a(q) be the first derivative of q**3/6 - 41*q**2/2 + 1681*q/2 + 153. Factor a(u).
(u - 41)**2/2
Let 0*j + 0*j**3 + 0 + 0*j**2 + 10*j**4 - 1/3*j**5 = 0. What is j?
0, 30
Let s(z) = 16*z**3 + 95*z**2 - 237*z - 54. Let d(t) = -24*t**3 - 143*t**2 + 355*t + 82. Let u(j) = -5*d(j) - 7*s(j). Factor u(v).
2*(v - 2)*(v + 8)*(4*v + 1)
Let x(c) be the third derivative of -1/315*c**7 + 0*c**3 - c**2 - 1/60*c**6 + 0*c**4 + 1/168*c**8 + 0 + 0*c + 1/90*c**5. Find v, given that x(v) = 0.
-1, 0, 1/3, 1
What is s in -5 - 12*s**2 - 6517*s**4 + 6519*s**4 - 1 - 16*s = 0?
-1, 3
Suppose 0 = 4*a - 6 - 6. Suppose 4*d + a = -4*h - 1, -3*h + 5*d + 29 = 0. Let 2*g**2 - 2*g + 2 + 2*g**h - 9 + 5 = 0. Calculate g.
-1, 1
Let v(z) = 2*z**4 - 2*z**2 - 2. Let b(f) = -8*f**4 + 9*f**2 + 9. Let p = -22 - -20. Let j = 11 + -20. Let o(t) = j*v(t) + p*b(t). Solve o(x) = 0.
0
Let c be 46/48 + 273/728. Factor -2/3*q + 2/3*q**5 - 4/3*q**2 + 0*q**3 + 0 + c*q**4.
2*q*(q - 1)*(q + 1)**3/3
Let b(p) be the second derivative of 0*p**2 + 4/345*p**6 + 1/483*p**7 + 8*p + 1/69*p**3 + 0 + 2/69*p**4 + 3/115*p**5. Determine u so that b(u) = 0.
-1, 0
Let g(f) be the first derivative of 0*f**4 + 0*f + 0*f**3 + 5 - 3*f**2 + 1/160*f**6 - 1/80*f**5. Let x(b) be the second derivative of g(b). Factor x(t).
3*t**2*(t - 1)/4
Let h(j) = 13*j + 32. Let r be h(-3). Let n(o) = -2*o - 14. Let u be n(r). Let 2/5*q**4 + 0*q + u*q**2 - 1/5*q**5 - 1/5*q**3 + 0 = 0. What is q?
0, 1
Let h be (0 - 1)/((-6)/90). Find a, given that -9*a**5 - h*a**3 + 25*a**4 - 41*a**2 - 4*a**2 + 4*a**5 = 0.
-1, 0, 3
Suppose 0 = 2*o + 2*s - 34, -13 = -2*o - s + 18. Let z be -2 - (o/(-8) - 1). Factor 0*v - z*v**3 + 0 + 3/2*v**2.
-3*v**2*(v - 2)/4
Let a(j) be the first derivative of -j**7/1155 + j**5/330 + 5*j**2 + 13. Let w(c) be the second derivative of a(c). Factor w(p).
-2*p**2*(p - 1)*(p + 1)/11
Suppose i + h - 19 = -0*h, 2*i - 26 = 4*h. Suppose -5*y + i + 8 = 3*f, 4*y = -5*f + 33. Suppose -4/3 - 3*b**5 - 5*b**4 + 5*b**y + 0*b + 5/3*b**3 = 0. What is b?
-1, 2/3
Let d(z) be the second derivative of 1/12*z**4 - 30*z + 0*z**2 + 1/84*z**7 - 1/30*z**6 + 0 + 0*z**3 - 1/40*z**5. Solve d(r) = 0.
-1, 0, 1, 2
Let w(r) be the second derivative of r**6/240 - 3*r**5/80 + 5*r**4/96 + 18*r. Factor w(s).
s**2*(s - 5)*(s - 1)/8
Let q be 4/(-10) - (-252)/30. Let c(x) = -3*x - 18 + 8 + x**2 + q. Let v(p) = 5*p**2 - 13*p - 9. Let b(f) = -9*c(f) + 2*v(f). Suppose b(k) = 0. Calculate k.
-1, 0
Let u be 3 - (-7)/((-7)/(-8)). Solve -60*q**2 - 11*q**3 + 24*q + u*q**4 + 15*q**5 + 28*q**4 + 0*q**5 - 7*q**3 = 0 for q.
-2, 0, 2/5, 1
Let o(m) be the second derivative of -m**6/90 - 11*m**5/60 - 5*m**4/12 + 3*m**3/2 - 2*m + 202. Factor o(s).
-s*(s - 1)*(s + 3)*(s + 9)/3
Suppose l = 5*h - 3*h, 0 = 3*l + 4*h - 40. Let n = -8 + l. Factor -4*s**3 + 0*s**3 + 4*s + 0*s + n*s.
-4*s*(s - 1)*(s + 1)
Let d(w) be the second derivative of -w**4/9 + 26*w**3/9 + 28*w**2/3 + 325*w. Factor d(s).
-4*(s - 14)*(s + 1)/3
Let h(b) be the third derivative of -b**6/120 - b**5/12 - 7*b**4/24 - b**3/2 + 162*b**2. Factor h(q).
-(q + 1)**2*(q + 3)
Let q(m) = -13*m**2 - 14*m + 2. Let x(s) = -53*s**2 - 53*s + 7. Let c(d) = 18*q(d) - 4*x(d). Factor c(l).
-2*(l + 2)*(11*l - 2)
Let w(l) be the second derivative of l**10/7560 - l**9/3780 - l**8/1680 + l**7/630 - l**4/3 + 14*l. Let r(u) be the third derivative of w(u). Solve r(g) = 0.
-1, 0, 1
Suppose -3*q - 752 = -8*q + j, 5*q + 3*j - 764 = 0. Let k = -449/3 + q. Factor 2/3*i**2 + k - 2*i.
2*(i - 2)*(i - 1)/3
Let n(w) be the second derivative of -w**5/5 - 2*w**4/3 + 2*w**3/3 + 4*w**2 + w - 5. Factor n(l).
-4*(l - 1)*(l + 1)*(l + 2)
Let w(q) = q**3 - q**2 + q. Let m be 2/1*3/2. Let l(n) = 5*n**3 + n**2 + n - 4. Let u(x) = m*w(x) - l(x). Find t, given that u(t) = 0.
-2, -1, 1
Let s(z) be the third derivative of 0*z**4 - 15*z**2 + 0 + 0*z + 0*z**5 - 5/112*z**8 - 2/21*z**7 + 0*z**3 + 1/6*z**6. Factor s(c).
-5*c**3*(c + 2)*(3*c - 2)
Let p = 3361/24 - 140. Let y(m) be the third derivative of 3/16*m**4 - 4*m**2 + 1/6*m**3 + p*m**5 - 3/80*m**6 + 0*m + 0 - 1/60*m**7. What is r in y(r) = 0?
-1, -2/7, 1
Let k(w) = 4*w**5 - 10*w**4 + 136*w**3 - 216*w**2 + 86*w. Let t(i) = -i**5 + 2*i**4 - 27*i**3 + 43*i**2 - 17*i. Let y(z) = -3*k(z) - 14*t(z). Factor y(b).
2*b*(b - 2)*(b - 1)**2*(b + 5)
Let p be (2/12)/((-105)/27 + 4). Find s, given that -4*s**3 - s - 7/2*s**2 - p*s**4 + 0 = 0.
-1, -2/3, 0
Let j(a) be the third derivative of a**6/105 + 143*a**5/105 + 60*a**4 - 864*a**3/7 + 562*a**2. Factor j(u).
4*(u + 36)**2*(2*u - 1)/7
Factor -1915 + 1915 - 16*w + 16*w**2 - 4*w**3.
-4*w*(w - 2)**2
Let v(r) be the third derivative of -r**7/420 - r**6/30 - 7*r**5/120 - 6*r**2 - 15. What is n in v(n) = 0?
-7, -1, 0
Let p = -10/9 - -289/252. Let b(h) be the second derivative of 3/4*h**3 + 3/4*h**2 + 1/4*h**4 - p*h**7 - 3/20*h**5 - 3/20*h**6 + 0 + 3*h. Solve b(v) = 0.
-1, 1
Suppose -34*z = 6*z - 240. Suppose 2*d = 10 - z. Factor 1/2*w**d + w + 0.
w*(w + 2)/2
Suppose -5*y + 3 = 3*z - 6*z, -2*y + 22 = 4*z. Let q = -491/2 - -268. What is m in q*m**3 - 45/2*m**z + 0 - 5*m**2 + 0*m = 0?
0, 1/3, 2/3
Let u(d) = -d**2 - 7*d + 7. Let y(c) be the first derivative of 9 - c + 1/2*c**2. Let i(k) = -2*u(k) - 22*y(k). Factor i(m).
2*(m - 2)**2
Let r(i) be the first derivative of -i**4/16 + 3*i**2/8 - i/2 + 18. Factor r(s).
-(s - 1)**2*(s + 2)/4
Let y = 322/5 - 64. Let z(h) = -14*h + 212. Let x be z(15). Determine b so that y + 2/5*b**x + 4/5*b = 0.
-1
Let z(a) = -a**3 + 2 + 3*a - a + a. Let h be z(-2). Solve 0 - f**5 - f**h + 0 + 0*f**5 = 0 for f.
-1, 0
Let q be (0 - 0) + 15 + 3. Suppose -5*v + q = -2. Suppose -z**3 + 5*z**3 - z**2 + z**5 - 5*z**3 + z**v = 0. What is z?
-1, 0, 1
Let z(q) be the second derivative of q**7/3 + 2*q**6/15 - 49*q**5/10 - 28*q**4/3 - 4*q**3 + 73*q. Solve z(b) = 0 for b.
-2, -1, -2/7, 0, 3
Let q(c) = c**4 - 2*c**3 + c**2 + c + 1. Let i(s) = 4*s**4 - 23*s**3 - 4*s**2 + 14*s + 6. Let y(p) = -i(p) + 6*q(p). Factor y(o).
o*(o + 2)*(o + 4)*(2*o - 1)
Let w(a) be the first derivative of -5*a**4/4 + 70*a**3/3 - 218. Suppose w(k) = 0. Calculate k.
0, 14
Let q(v) = v**2 - 49*v + 182. Let o be q(45). Let p(u) be the second derivative of 0 - 1/60*u**5 + u - 1/12*u**4 - 1/6*u**o - 1/6*u**3. Factor p(s).
-(s + 1)**3/3
Let f(g) be the first derivative of 0*g + 1/3*g**2 + 32 + 1/36*g**6 + 1/15*g**5 - 1/8*g**4 - 2/9*g**3. Find o such that f(o) = 0.
-2, 0, 1
Let y be (-2)/1 + 26 + 21/(-1). Factor 0 + 1/2*p**2 - 1/4*p**4 + 1/4*p**y + 0*p.
-p**2*(p - 2)*(p + 1)/4
Let w be -3 - 4*44/(-48). Solve 4/3*b**3 - 2/3*b + 0*b**2 - w*b**5 + 0 + 0*b**4 = 0.
-1, 0, 1
Suppose -19*c + 0*c + 228 = 0. Suppose -3*k + c = k. Factor 0 + 0*r**2 + 2/11*r**k + 4/11*r**4 + 2/11*r**5 + 0*r.
2*r**3*(r + 1)**2/11
Let m(j) be the second derivative of j**7/189 + j**6/27 + 4*j**5/45 + 2*j**4/27 + j - 151. Factor m(k).
2*k**2*(k + 1)*(k + 2)**2/9
Let k = -24994 + 24996. Suppose 2/17*q**3 + 22/17*q + 14/17*q**k + 10/17 = 0. Calculate q.
-5, -1
Let a(i) = -i**2 + 472*i - 52900. Let z(d) = 2*d**2 - 946*d + 105800. Let q(j) = -13*a(j) - 6*z(j). Factor q(w).
(w - 230)**2
Suppose