c**v + 2*c**4 - 9*c**3 - 4*c + 6*c**2 + 3*c**2.
c*(c - 2)**2*(2*c - 1)
Suppose -t + 1 = -3. Suppose 0 = 2*x - 4*x + t. Suppose 2 + 6*a**3 + 2*a**3 - 4*a**2 - 4*a**5 + 0 + 0 - 4*a + x*a**4 = 0. Calculate a.
-1, 1/2, 1
Determine o so that 5*o**4 - 18*o**2 + 20*o**3 - 16*o - 12*o**2 + 11*o + 25 - 15*o = 0.
-5, -1, 1
Let q(k) = k**2 + 4*k - 17. Let n be q(-7). Factor -9*i**2 - i**3 + 0*i - 3*i - 9 - n*i**2 + 18*i**2.
-(i - 3)**2*(i + 1)
Let y = 32027/2 - 16009. Factor 25/2*c**5 - 1/2*c**2 - 15/2*c**4 - y*c**3 + 0*c + 0.
c**2*(c - 1)*(5*c + 1)**2/2
Let t(o) be the second derivative of o**9/37800 - 11*o**4/12 - 16*o. Let z(r) be the third derivative of t(r). Determine u so that z(u) = 0.
0
Let v(n) = -8*n**4 + 20*n**3 - 78*n**2 - 206*n - 124. Let k(r) = -2*r**4 + r**2 + r - 2. Let x(l) = -6*k(l) + v(l). Let x(d) = 0. Calculate d.
-7, -1, 4
Let w(k) = -19*k**3 + 4*k**2 + 10*k + 20. Let g(i) = 35*i**3 - 7*i**2 - 19*i - 38. Let z(y) = 6*g(y) + 11*w(y). Determine m, given that z(m) = 0.
-2, 2
Let k(o) = 7*o**4 - 8*o**3 + 9*o**2 - 4*o + 2. Let r(p) = -3*p**4 + p**3 - 1. Let j(u) = -k(u) - 2*r(u). Factor j(w).
-w*(w - 4)*(w - 1)**2
Let h(v) be the third derivative of -13*v**6/30 - 5*v**5/3 - 2*v**4 - 214*v**2. Determine k, given that h(k) = 0.
-1, -12/13, 0
Let t(b) be the third derivative of -b**9/20160 - b**8/8960 + b**4/4 - 2*b**2. Let x(p) be the second derivative of t(p). Factor x(w).
-3*w**3*(w + 1)/4
Let w be ((-6)/8)/((-750)/600). Factor -w*r**2 - 1/5*r**3 - 3/5*r - 1/5.
-(r + 1)**3/5
Let t(a) = a**3 - 10*a**2 - a + 13. Let n(q) = q**3 + 6*q**2 + 4*q - 6. Let y be n(-4). Let f be t(y). Find c such that 25/4*c**f - 2 - 15/2*c**2 - 9*c = 0.
-2/5, 2
Let t(b) be the second derivative of -3*b**5/130 + 8*b**4/39 - 5*b**3/39 - 96*b. Suppose t(k) = 0. What is k?
0, 1/3, 5
Let h(v) = -7 + 0*v - 10 - 3*v**2 - 13*v. Let c(f) = f**2 + 15*f + 33. Let l be c(-13). Let r(i) = 2*i**2 + 7*i + 8. Let s(a) = l*r(a) + 3*h(a). Factor s(z).
5*(z + 1)**2
Let l(z) be the first derivative of z**6/240 + z**5/20 + 3*z**4/16 + 11*z**2 - 6. Let o(u) be the second derivative of l(u). Factor o(n).
n*(n + 3)**2/2
Let c(k) be the second derivative of -k**7/7560 + k**6/3240 + k**5/270 - k**4/54 - k**3/6 + 33*k. Let h(y) be the second derivative of c(y). Factor h(s).
-(s - 2)*(s - 1)*(s + 2)/9
Let q(k) be the third derivative of k**4/12 + 5*k**3/3 + 20*k**2. Let x be q(-5). Find o such that 4/3*o + 1/3*o**4 + 0 + x*o**2 - o**3 = 0.
-1, 0, 2
Suppose f - 9 + 1 = 0. Suppose 9*w - f = 5*w. Factor 4/5*u + 2/5*u**3 + 0 - 6/5*u**w.
2*u*(u - 2)*(u - 1)/5
Let m = -9511/15 + 635. Let p(r) be the second derivative of -m*r**6 + 5*r + 3*r**4 - 10/3*r**3 - 4*r**2 + r**5 + 0. Suppose p(u) = 0. Calculate u.
-1, -2/7, 1
Let z(m) = -6*m**3 - 6*m**2 + 16*m. Let n(v) = -2*v**3 - 2*v**2 + 5*v. Let y(l) = 16*n(l) - 5*z(l). Suppose y(g) = 0. Calculate g.
-1, 0
Suppose -65 = -27*m + 16. Let g(h) be the first derivative of 4/5*h**5 + 2*h**2 + 4 + 0*h + 4*h**m + 3*h**4. Let g(f) = 0. Calculate f.
-1, 0
Let w(j) be the second derivative of 6*j**2 + 3/40*j**5 + 3*j**3 - 13*j + 0 + 3/4*j**4. Solve w(q) = 0 for q.
-2
Find n, given that -6/5*n**4 + 0 + 2/5*n**3 + 2/5*n + 6/5*n**2 - 4/5*n**5 = 0.
-1, -1/2, 0, 1
Let r(k) = k**3 - 25*k**2 - 25*k - 28. Let z be r(26). Let a be 9/6 + z + 2. Factor a - 3*x + 3/2*x**2.
3*(x - 1)**2/2
Let k(v) be the third derivative of 2*v**7/525 - 11*v**6/150 + 7*v**5/15 - 5*v**4/6 - 892*v**2. Solve k(n) = 0 for n.
0, 1, 5
Suppose -b + 4*q = 3*b + 20, 0 = 5*b - 2*q + 13. Let n be ((-256)/(-200))/(b*(-6)/45). Factor -14*d**2 + n*d - 8/5.
-2*(5*d - 2)*(7*d - 2)/5
Suppose -r + 21 = 6*r. Determine n so that -r*n**5 + 6*n**5 + 0*n**5 + 0*n**5 = 0.
0
Let p(j) = j**2 + 1. Let v(s) = 9*s**2 + 9*s - 36. Let h(u) = -u**3 - 18*u**2 - 18*u + 71. Let m(q) = 3*h(q) + 5*v(q). Let d(t) = -m(t) + 6*p(t). Factor d(z).
3*(z - 1)*(z + 3)**2
Let s(u) be the first derivative of 3*u**5/5 - 15*u**4/4 + 8*u**3 - 6*u**2 + 121. Factor s(g).
3*g*(g - 2)**2*(g - 1)
Suppose -3*t + 6*f = 3*f + 18, -3*t + f = 12. Let z(b) = b**2 + 2*b - 1. Let x be z(t). Factor 0 + 1/9*h**x - 2/9*h.
h*(h - 2)/9
Solve -168*w**3 - 70*w**4 + 1940*w**2 + 26*w**4 - 1908*w**2 = 0 for w.
-4, 0, 2/11
Let d(h) = 6*h**4 - 37*h**3 - 50*h**2 + 96*h - 10. Let p(r) = -5*r**4 + 38*r**3 + 49*r**2 - 94*r + 8. Let g(w) = -4*d(w) - 5*p(w). What is z in g(z) = 0?
-2, 0, 1, 43
Let b(u) = -24*u**4 + 21*u**3 - 24*u**2. Let t(k) = -13*k**4 + 10*k**3 - 12*k**2. Let d(z) = -5*b(z) + 9*t(z). Solve d(r) = 0 for r.
0, 1, 4
Let y be (-2)/(-5) + 33/5. Suppose 0 = -5*m + 3 + y. What is z in -3*z**2 + z + 0*z**3 + z**3 + 6*z**2 - 5*z**m = 0?
0, 1
Let r(g) be the second derivative of -g**6/6 + 11*g**5/4 - 75*g**4/4 + 135*g**3/2 - 135*g**2 - 258*g. Factor r(l).
-5*(l - 3)**3*(l - 2)
Factor 128/5*w**3 + 16/5*w**2 + 0 + 308/5*w**4 + 0*w + 196/5*w**5.
4*w**2*(w + 1)*(7*w + 2)**2/5
Suppose -8 + 385*p**2 - 58*p - 56 + 14*p - 18*p - 383*p**2 = 0. What is p?
-1, 32
Let h be (0 + 24/28)/((-36)/(-1848)*11). Factor -8/3*n**3 - 8*n**2 + 0*n + 0 - 2/9*n**h.
-2*n**2*(n + 6)**2/9
Let k(m) = 3*m + 11. Let b(y) = 4*y + 12. Let g(q) = -2*b(q) + 3*k(q). Let d be g(-5). Factor -22 + 4*h + 22 + d*h**2.
4*h*(h + 1)
Suppose -1/4*t**2 + 3/4*t - 1/2 = 0. What is t?
1, 2
Suppose 2*l + 2*s - 30 = 0, 0*s - 27 = -2*l - s. Let n(d) be the first derivative of 49/2*d**4 + 28*d**3 + 6 + l*d**2 + 16/7*d. Factor n(w).
2*(7*w + 2)**3/7
Let c(d) = 8*d**3 - 163*d**2 + 792*d + 963. Let q(m) = 20*m**3 - 408*m**2 + 1980*m + 2408. Let z(t) = -12*c(t) + 5*q(t). Find n, given that z(n) = 0.
-1, 11
Factor -22*a**2 + 5*a**3 - 20*a**2 + 0*a**3 + 32*a**2 - 15*a.
5*a*(a - 3)*(a + 1)
Let q be (-20)/(-7) + (-3)/(-21). Factor q*t**2 + 8 - 5 - 3.
3*t**2
Let p(b) = 3*b**2 - b. Let v(l) = -5*l**2 - 31*l - 128. Let g(k) = p(k) + v(k). Suppose g(o) = 0. What is o?
-8
Suppose 24*d + 16*d**2 - 1 + 0*d**2 + 23 + 2*d**2 - 16*d**2 = 0. Calculate d.
-11, -1
Let c(m) = 3*m**2 - 44*m - 61. Let w be c(16). Let f(d) be the first derivative of 0*d + 4/21*d**w - 5 + 0*d**2. Find u, given that f(u) = 0.
0
Let z(w) = -w**3 + 12*w**2 + w - 6. Let v be z(12). Suppose 3*g = v*g - 6. Factor 6*p**3 - g*p**2 + 2*p**5 - 3*p - 6*p - 6*p**4 + 9*p.
2*p**2*(p - 1)**3
Determine v, given that 0*v + 0 - 4/7*v**2 + 4/7*v**3 + 4/7*v**4 - 4/7*v**5 = 0.
-1, 0, 1
Suppose 14*i - 18*i + 3*r = 1, 4*i = r + 5. Determine u, given that -i*u + 12/5 + 2/5*u**2 = 0.
2, 3
Suppose 2*p - 21 = -5*o, -807*p + 4*o - 3 = -804*p. Factor -10/3*y + 5*y**2 - 5/3*y**p + 0.
-5*y*(y - 2)*(y - 1)/3
Let u(m) = -m**3 - m + 1. Let x(g) = -8*g + 6*g**2 - 10*g**2 - 7 + 19*g + 8*g**3. Let q(s) = -21*u(s) - 3*x(s). Find r, given that q(r) = 0.
0, 2
Let o(m) be the third derivative of m**6/270 - m**5/45 - m**4/6 + 5*m**3/6 - 11*m**2. Let t(a) be the first derivative of o(a). Factor t(f).
4*(f - 3)*(f + 1)/3
Let c(r) be the third derivative of r**5/36 - 85*r**4/72 - 70*r**3/3 + r**2 + 22*r. Factor c(h).
5*(h - 21)*(h + 4)/3
Let k(w) be the second derivative of 0 + 3*w + 0*w**4 - 1/60*w**5 + w**3 + 0*w**2 - 1/360*w**6. Let v(o) be the second derivative of k(o). Solve v(l) = 0.
-2, 0
Factor -15/8*f + 3/8*f**2 + 0.
3*f*(f - 5)/8
Suppose 0 = -17*j - j + 54. Factor -32*f + 2 - 5 - 14*f**2 - 21 - 7*f**j + 5*f**3.
-2*(f + 2)**2*(f + 3)
Let h(y) be the second derivative of 2*y**5/75 + 41*y**4/90 + 94*y**3/45 + 7*y**2/5 + 52*y. Determine g, given that h(g) = 0.
-7, -3, -1/4
Factor -10*h**2 + 9 - 35*h**2 - 40*h**3 + 81*h + 43*h**3 - 48.
3*(h - 13)*(h - 1)**2
Suppose -261*t - 372*t = -849 - 2316. Factor 0*m + 0 + 6/7*m**4 - 12/7*m**3 + 3/7*m**t - 24/7*m**2.
3*m**2*(m - 2)*(m + 2)**2/7
Let n be (-2 - (-5 + 0))*49/(-3). Let l = n - -51. Factor 1/4*x**5 - 1/4*x**3 - 1/4*x**4 + 1/4*x**l + 0 + 0*x.
x**2*(x - 1)**2*(x + 1)/4
Factor 3/4*m**3 + 57/4*m**2 + 105/4*m + 51/4.
3*(m + 1)**2*(m + 17)/4
Let i = 6167/5 + -1233. Factor 0 - 6/5*b**2 + i*b + 4/5*b**3.
2*b*(b - 1)*(2*b - 1)/5
Suppose 0 + 16/3*l**2 - 8/3*l - 10/3*l**3 + 2/3*l**4 = 0. What is l?
0, 1, 2
Let t(u) = -20*u - 6. Let f be t(-1). Let x(o) = -o**3 + 15*o**2 - 18*o + 59. Let k be x(f). Let 0*i**4 + 0*i**2 - 3/4*i**5 + 0*i + 0 + 3/4*i**k = 0. What is i?
-1, 0, 1
Let n(q) be the third derivative of -2/15*q**3 + 0 + q**2 + 1/100*q**6 + 1/150*