or 114*a - 104*a - 2*a**3 + 7*a**3 + 15*a**2.
5*a*(a + 1)*(a + 2)
Suppose -24*n - 18*n - n**2 + 62*n - 23*n + 4*n**2 = 0. What is n?
0, 1
Let w = -23 + 23. Suppose w = -2*b + 8*b. Determine m, given that 6 + 8*m**3 + 4*m**5 + 4*m**2 - 8*m**4 + b*m**4 - 10*m - 2 - 2*m**5 = 0.
-1, 1, 2
Let p be 64/28 - 8/28. Factor 3*j**3 + 6*j**p - 7*j - j + 2*j - 9*j**2.
3*j*(j - 2)*(j + 1)
Let m be (-1)/(-2)*(38 - 8). Let g = m - 10. Factor -4*q**4 + q**5 + q**3 - 4*q**4 + 3*q**g + 3*q**3.
4*q**3*(q - 1)**2
Let f(t) be the first derivative of 10/9*t**2 + 1/9*t**4 + 16/27*t**3 - 11 + 8/9*t. Solve f(n) = 0.
-2, -1
Suppose 0 = -3*z + 3. Let p be (-2 - -1)/(24/(-48)). Factor -z + k**p + 2*k - 2 + 3.
k*(k + 2)
Let q(c) be the third derivative of 32/15*c**6 - c**2 + 47/15*c**5 - 2/3*c**4 + 5*c + 32/105*c**7 + 0 - 2*c**3. What is x in q(x) = 0?
-3, -1, -1/4, 1/4
Suppose -4 = 2*x - 4*x. Suppose 0*n + 4*n + 5*n = 0. Factor 0*h**4 + n*h**x - 1/5*h**3 + 0 + 1/5*h**5 + 0*h.
h**3*(h - 1)*(h + 1)/5
Let 375/4*i + 625/4 + 75/4*i**2 + 5/4*i**3 = 0. What is i?
-5
Find y, given that -500*y - 79*y - 1190 - 138*y - y**2 + 112*y - 4*y**2 = 0.
-119, -2
Let d(j) be the second derivative of j**6/15 - j**5/5 - j**4/2 + 4*j**3/3 + 4*j**2 + 24*j. Suppose d(m) = 0. Calculate m.
-1, 2
Let v(d) = -172*d + 4818. Let j be v(28). Determine g, given that 0 + 8/3*g**5 + 18*g**4 + 14*g**j + 106/3*g**3 - 6*g = 0.
-3, -1, 0, 1/4
Let k = 4 - 1. Let v(u) = -12*u**5 + 14*u**4 - 6*u**2 - 4. Let x(s) = -11*s**5 + 14*s**4 - s**3 - 5*s**2 - 3. Let f(j) = k*v(j) - 4*x(j). Factor f(b).
2*b**2*(b - 1)**2*(4*b + 1)
Let w = 27/70 - 6/35. Let a(h) be the first derivative of 1/14*h**6 + 0*h**5 + w*h**2 - 3/14*h**4 + 10 + 0*h**3 + 0*h. Find b, given that a(b) = 0.
-1, 0, 1
Factor 134*h + 13*h**2 - 15*h**4 - 267*h + 133*h + 7*h**2 + 5*h**5.
5*h**2*(h - 2)**2*(h + 1)
Let n(t) be the third derivative of t**5/90 - 2*t**4/9 - t**3 + 2*t**2 - 88*t. Let n(a) = 0. What is a?
-1, 9
Let p(s) be the second derivative of -s**7/280 + s**5/80 + 2*s**2 + 20*s. Let m(k) be the first derivative of p(k). Factor m(a).
-3*a**2*(a - 1)*(a + 1)/4
Let z = -726567/10780 - 1/2156. Let w = -67 - z. Factor -2/15*b**4 - w*b**2 + 2/5*b**3 + 2/15*b + 0.
-2*b*(b - 1)**3/15
Let -4*r - 2/11*r**3 + 26/11*r**2 + 0 = 0. What is r?
0, 2, 11
Let q = 451/3 + -150. Let i(p) be the second derivative of 8*p**2 - q*p**4 - 12*p + 0*p**3 + 0. Determine n so that i(n) = 0.
-2, 2
Let o(a) = 9*a**4 + 22*a**3 - 29*a**2 - 11*a - 2. Let q(y) = -5*y**4 - 12*y**3 + 16*y**2 + 6*y + 1. Let j(l) = 6*o(l) + 11*q(l). Determine h so that j(h) = 0.
-1, 1
Let w(q) be the first derivative of 52 + 1/7*q**2 + 8/21*q - 2/63*q**3. Factor w(c).
-2*(c - 4)*(c + 1)/21
Let n(z) = 5*z - 20. Let t be n(7). Let b be 8/20*t/12. Factor y + 1/2*y**2 + b.
(y + 1)**2/2
Let m(f) = f**2 + f + 2*f**3 + f**3 - f**3 + 2*f**2 - 9. Let g(y) = -8*y**3 - 13*y**2 - 3*y + 35. Let u(z) = 6*g(z) + 22*m(z). Factor u(l).
-4*(l - 1)*(l + 1)*(l + 3)
Let t(j) be the first derivative of -3*j**5/35 - 9*j**4/7 - 46*j**3/7 - 90*j**2/7 - 75*j/7 + 361. Let t(f) = 0. Calculate f.
-5, -1
Let l(f) be the second derivative of 18*f + 1/27*f**6 - 5/54*f**4 + 0*f**2 + 1/45*f**5 - 2 - 2/27*f**3. Find t, given that l(t) = 0.
-1, -2/5, 0, 1
Let c(s) be the third derivative of s**10/907200 + s**9/362880 + s**5/6 + 12*s**2. Let v(u) be the third derivative of c(u). Factor v(d).
d**3*(d + 1)/6
Factor -17 + 2*d**2 + 0 - d**2 - 26*d + 10*d.
(d - 17)*(d + 1)
Let f(j) be the second derivative of j**9/6048 + j**8/3360 - 10*j**3/3 + 3*j + 7. Let u(a) be the second derivative of f(a). Find d such that u(d) = 0.
-1, 0
Let f be (-9)/21 - (-115)/105. Let m(h) be the first derivative of -5 + f*h - 2/3*h**3 - 2/3*h**2. Find j such that m(j) = 0.
-1, 1/3
Let g(j) be the first derivative of -j**6/2 - 3*j**5/5 + 45*j**4/2 - 74*j**3 + 201*j**2/2 - 63*j - 227. Find f, given that g(f) = 0.
-7, 1, 3
Suppose -4*y - 5 = -5*y. Suppose y*c - 32 = c. Factor -4*g**3 + 136 - 4*g + c*g**2 - 136.
-4*g*(g - 1)**2
Let m(h) be the second derivative of h**8/1176 + 4*h**7/735 + h**6/84 + h**5/105 - 25*h**2/2 - 17*h. Let r(g) be the first derivative of m(g). Factor r(z).
2*z**2*(z + 1)**2*(z + 2)/7
Let r = -15 + 23. Suppose -6 = i - r. Factor y**3 - 9*y**i + 17*y - 16 - 20*y + 27*y.
(y - 4)**2*(y - 1)
Suppose 9 = 2*f - 7. Determine a so that 29*a**4 + 20*a + 15*a**4 - f + 108*a**2 + 122*a**3 + 2*a**3 = 0.
-1, 2/11
Suppose k - 5*r = -3*r + 8, 5*k - 2*r - 16 = 0. Factor -2*h**2 - 2 - 1 + k - 6*h - 3.
-2*(h + 1)*(h + 2)
Let r(f) = -13*f - 8. Let u be r(12). Let v = 1812/11 + u. Factor 4/11 - 2/11*o**3 + v*o**2 - 10/11*o.
-2*(o - 2)*(o - 1)**2/11
Suppose 0 = -2*z - 5*q + 34, 0*z - q = 4*z - 32. Let m be 99/21 + 2/z. Let -34*d**5 + 92*d**3 - 24*d**4 - 8 - 28*d + 8*d**2 + 2*d**m - 8*d = 0. Calculate d.
-2, -1/2, -1/4, 1
Let u(x) be the first derivative of 0*x + 1/2*x**2 + 17 + 1/4*x**4 + 2/3*x**3. Factor u(o).
o*(o + 1)**2
Let a(d) be the second derivative of 1/50*d**6 + 0 - 13*d + 7/60*d**4 - 1/15*d**3 + 0*d**2 - 2/25*d**5. Let a(c) = 0. Calculate c.
0, 2/3, 1
Let v(q) be the second derivative of q**8/5880 - q**7/2940 - q**6/252 - q**5/140 + 5*q**3/6 - 3*q. Let x(g) be the second derivative of v(g). Factor x(o).
2*o*(o - 3)*(o + 1)**2/7
Let c(t) = -t**2 + 5*t - 3. Let q be c(3). Factor 15*p**2 + 15*p - 25*p**3 + 55*p**3 + 5 - 25*p**q.
5*(p + 1)**3
Let h(j) = 6*j**3 + 71*j**2 + 76*j + 23. Let y(d) = -6*d**3 - 72*d**2 - 74*d - 24. Let r(o) = 4*h(o) + 3*y(o). Factor r(x).
2*(x + 1)*(x + 10)*(3*x + 1)
Let q(m) = m**2 + m - 1. Let z be q(1). Factor 3*r**2 - 4*r**3 + z + r - 2*r**4 + 3*r - 2*r**4.
-(r - 1)*(r + 1)*(2*r + 1)**2
Let y = 8/13 + -27/65. Let k(n) be the third derivative of -1/25*n**5 + y*n**4 + 1/300*n**6 - 8/15*n**3 + 0 + n**2 + 0*n. Factor k(r).
2*(r - 2)**3/5
Let w = 6 - 7. Let n be -3*w*(-2 - -3). Factor 3*u**n + 0 + 0 - 2*u - u**3.
2*u*(u - 1)*(u + 1)
Let n(m) = m**4 + m - 1. Let r(w) = -12*w**4 - 4*w**3 - 4*w**2 - 12*w + 16. Let q(g) = -16*n(g) - r(g). Factor q(u).
-4*u*(u - 1)**2*(u + 1)
Let o(r) be the third derivative of -1/180*r**5 - 1/18*r**4 + 5*r**2 + 0 + 0*r + 0*r**3. Factor o(s).
-s*(s + 4)/3
Let n(x) = 35 - 15 - 4*x**2 - 5*x - 18 + x**3. Let t be n(5). Factor t*h**2 - h**2 + 3*h**2 + 12*h.
4*h*(h + 3)
Let w(s) be the second derivative of -11*s**4/3 - 2*s**3/3 + 24*s**2 - 406*s. Find q, given that w(q) = 0.
-12/11, 1
Let j(n) = -2*n**2 - 5*n + 5. Let v be j(-3). Let m be (16/(7 + -11))/(v/(-1)). Let 6/5 - 3/5*g + 3/5*g**3 - 6/5*g**m = 0. Calculate g.
-1, 1, 2
Let v = -8 + -6. Let d(m) = 5*m**2 + 6*m + 7. Let x(u) = -u**2 - 1 - u**2 + 5*u**2 - 4*u**2. Let z(i) = v*x(i) - 2*d(i). Determine n, given that z(n) = 0.
0, 3
Let f(t) = 4*t**4 + 16*t**3 - 4. Let z(c) = c**3 + c. Suppose -3*h + 2*h = -8. Let d(j) = h*z(j) - f(j). Suppose d(p) = 0. Calculate p.
-1, 1
Factor 255*f**2 - 578*f + 0 + 1/4*f**4 + 33/2*f**3.
f*(f - 2)*(f + 34)**2/4
Let g(r) be the second derivative of r**7/336 + r**6/60 + 3*r**5/80 + r**4/24 + r**3/48 + 19*r. Factor g(z).
z*(z + 1)**4/8
Let g(u) be the third derivative of -u**5/240 - 43*u**4/96 - 7*u**3/4 - 646*u**2. Determine q so that g(q) = 0.
-42, -1
Factor 49*k**3 - 21*k**4 + 6*k**2 - 52*k**3 - 6*k**2 - 18*k**5.
-3*k**3*(k + 1)*(6*k + 1)
Let n = -103 + -184. Let l be n/35 - -6 - -3. Factor -8/5 - l*k**3 - 4*k - 16/5*k**2.
-4*(k + 1)**2*(k + 2)/5
Let k be -4 + 42/4 + -5. Factor 0 + k*y - 3/2*y**2.
-3*y*(y - 1)/2
Let z = 9697/7 + -48422/35. Factor -6/5*c**4 + z*c**3 + 0 + 0*c**2 + 0*c + 1/5*c**5.
c**3*(c - 3)**2/5
Let k(c) be the first derivative of c**3/6 - 55*c**2/2 + 3025*c/2 + 420. Factor k(q).
(q - 55)**2/2
Let h(b) be the third derivative of -7*b**2 + 2/15*b**3 - 1/20*b**4 + 0*b - 1/75*b**5 + 0. Factor h(j).
-2*(j + 2)*(2*j - 1)/5
Let j(z) be the first derivative of z**6/2 - 63*z**5/5 + 441*z**4/4 - 343*z**3 - 50. Let j(c) = 0. What is c?
0, 7
Let k = 163891/6505 - -7/1301. Factor 147/5*s**2 + k*s + 27/5.
3*(7*s + 3)**2/5
Let c = -10715 + 10715. What is p in 0*p + 8/13*p**4 - 2/13*p**5 + 4/13*p**2 + c - 10/13*p**3 = 0?
0, 1, 2
Let z(v) be the second derivative of -6*v**2 + 19*v - 1/4*v**4 + 0 + 2*v**3. Factor z(w).
-3*(w - 2)**2
Let b be (628/(-32) - 0)/(9/12). Let t = -74/3 - b. Let -t*u**2 - 5/2*u**3 + u + 0 = 0