et y be -10 + 7 - (-1 + 8 + -3). Let u be (-9)/y + -1 - (-2)/(-56). Factor 0 - 1/4*m**2 + 1/4*m**3 + 1/4*m**4 - u*m.
m*(m - 1)*(m + 1)**2/4
Let i(g) be the first derivative of g**6/40 - 2*g**5/15 + g**4/6 + 13*g**2/2 + 28. Let o(s) be the second derivative of i(s). Factor o(d).
d*(d - 2)*(3*d - 2)
Let r(c) be the first derivative of 5*c**3/3 - 15*c**2 - 80*c - 67. Factor r(d).
5*(d - 8)*(d + 2)
Let y = -231 + 233. Let j(f) be the third derivative of 0 - 1/8*f**4 + 0*f + 1/20*f**5 - f**3 - f**y. Factor j(o).
3*(o - 2)*(o + 1)
Determine a, given that 5*a**2 + a**2 - 27*a**2 - 6*a + 10*a**3 - 7*a**2 = 0.
-1/5, 0, 3
Suppose p = 4*w - 9 - 4, -3*w - 3*p = 9. Determine i, given that 0 + 10/3*i**3 - w*i**2 - 2/3*i**4 - 6*i = 0.
-1, 0, 3
Let w(n) = -n**3 + 4*n + 1. Let k be w(2). Let h be 0*(-3 + 20/6)*k. Factor 0*c + 2/7*c**5 + h*c**2 + 0 + 0*c**4 - 2/7*c**3.
2*c**3*(c - 1)*(c + 1)/7
Let j(u) = -u**2 + 43*u - 222. Let k be j(6). Factor 1/4 - 1/4*m**2 + k*m.
-(m - 1)*(m + 1)/4
Let p(d) = d + 1. Suppose 0 = -4*z + 20 - 8. Let l(s) = 4*s**3 + 48*s**2 + 195*s + 259. Let j(y) = z*p(y) - l(y). Solve j(r) = 0.
-4
Determine s so that -72*s**2 + 150*s + 287*s**2 + 42*s**4 - 47*s**4 + 13*s**3 + 47*s**3 = 0.
-2, -1, 0, 15
Let l(m) be the first derivative of m**4/16 + 2*m**3/3 + 13*m**2/8 + 3*m/2 - 64. Factor l(n).
(n + 1)**2*(n + 6)/4
Suppose -5*q + 80 = -82 + 147. What is b in -2/5*b**q + 2/5*b - 2/5*b**2 + 2/5 = 0?
-1, 1
What is c in 41*c - 6*c - 139*c**2 + 134*c**2 = 0?
0, 7
Let a(u) be the first derivative of -3 + 0*u**2 + 0*u**3 + 0*u + 0*u**4 + 7/15*u**6 - 4/25*u**5. Factor a(q).
2*q**4*(7*q - 2)/5
Let x = 32 - 27. Let q(r) = r**5 + r**4 + r**3 - r**2 - r. Let a(l) = 6*l**5 + 5*l**4 + 3*l**3 - 5*l**2 - 4*l. Let k(h) = x*q(h) - a(h). Solve k(s) = 0 for s.
-1, 0, 1
Suppose 2*o = -20 - 14. Let a(x) = 20*x**3 + 14*x - 17. Let z = -17 - -11. Let g(f) = -7*f**3 - 5*f + 6. Let q(u) = o*g(u) + z*a(u). Find n such that q(n) = 0.
-1, 0, 1
Suppose -2*s - 2 + 0 = 0. Let y(r) = -r + 2. Let t be y(6). Let l(u) = -u**2 - u. Let z(c) = 8*c**2 + 12*c. Let k(n) = s*z(n) + t*l(n). Factor k(o).
-4*o*(o + 2)
Let l(r) be the second derivative of -r**5/25 + 37*r**4/15 - 646*r**3/15 - 722*r**2/5 - 2*r + 85. Factor l(k).
-4*(k - 19)**2*(k + 1)/5
Let p(a) = -a**2 + 3*a**2 + 4*a - 4*a - a**3 - a. Let l be p(1). Solve -4*i**3 + 10/3*i**2 + l + 2/3*i = 0 for i.
-1/6, 0, 1
Let w = -6488/77 + 930/11. Factor w*q**2 - 6/7*q + 0.
2*q*(q - 3)/7
Let h = 358 + -1073/3. Let l(z) be the first derivative of 2 + h*z**2 + 0*z - 1/9*z**3. Solve l(p) = 0 for p.
0, 2
Let h be 5/15 - (-3)/(-9). Factor 4*i**2 - 6*i - 6*i + i - 3 + h.
(i - 3)*(4*i + 1)
Let w(k) be the first derivative of 2*k**2 - 7/20*k**5 - 2/3*k**3 + 4*k - k**4 + 22 - 1/24*k**6. What is v in w(v) = 0?
-2, 1
Let q = -162007/7 - -23144. Factor q*c**3 + 12/7*c**2 + 45/7*c + 50/7.
(c + 2)*(c + 5)**2/7
Let t(n) = n**3 + 8*n**2 - 13*n + 1. Let l be t(-9). Let a = -37 + l. Solve -3/7*w**2 + 0 + a*w = 0 for w.
0
Suppose 0 = 5*u + 3*n - 5*n + 498, 5*u - 5*n + 510 = 0. Let d = -96 - u. Let -4*h**3 - 3*h**d + 1/2 - 3/2*h**4 + 0*h = 0. Calculate h.
-1, 1/3
Let k = -256 + 258. Let l(m) be the second derivative of -2/9*m**3 + 0*m**k + 0 - 2*m + 1/18*m**4. Factor l(j).
2*j*(j - 2)/3
Let r(n) be the second derivative of 0 + 0*n**3 + 24*n + 0*n**2 - 1/120*n**6 + 0*n**4 - 1/40*n**5. What is h in r(h) = 0?
-2, 0
Let 100564 + 216337 + 3*w**2 - 66338 + 1471*w + 263*w = 0. Calculate w.
-289
Let a(z) be the third derivative of -z**6/120 + z**5/6 - 25*z**4/24 + 3*z**2 - 21. Factor a(v).
-v*(v - 5)**2
Let c be ((-24)/20)/((-3)/24). Suppose 48/5*v**2 - c*v**3 + 3/5*v - 3/5 = 0. Calculate v.
-1/4, 1/4, 1
Let b(o) = -6*o**2 + 87*o - 6. Let n(g) = -13*g**2 + 173*g - 14. Let q(u) = -7*b(u) + 3*n(u). Factor q(t).
3*t*(t - 30)
Let g(x) = 7*x**4 + 5*x**3 - 18*x**2 - 23*x + 24. Let v(a) = 3*a**4 + 2*a**3 - 9*a**2 - 10*a + 12. Let t(n) = -2*g(n) + 5*v(n). Determine q so that t(q) = 0.
-2, 1, 3
Let b(q) be the second derivative of 1/15*q**6 + 13/6*q**4 - 4*q**3 - 3/5*q**5 + 11*q + 4*q**2 + 0. Suppose b(a) = 0. What is a?
1, 2
Let f = -19762 + 19764. What is k in -10/7*k**3 - 38/7*k**f + 8/7*k**4 - 2*k + 6/7 = 0?
-1, 1/4, 3
Let f(m) = -4*m**3 + m**2 + 3*m + 2. Let o be f(-1). Suppose -113*j**o + 8*j**3 + 12*j**3 + 109*j**4 + 24*j**2 = 0. What is j?
-1, 0, 6
Suppose -3*a + s + 8 + 5 = 0, -a + 2*s + 11 = 0. Factor -b**3 + 6*b**4 - 8 - 10*b**a - b**4 + b**4 + 12*b - b**5 + 2*b**2.
-(b - 2)**3*(b - 1)*(b + 1)
Let k(y) be the second derivative of -y**8/30240 + y**7/11340 + y**6/3240 - y**5/540 - y**4/3 + 7*y. Let h(m) be the third derivative of k(m). Factor h(c).
-2*(c - 1)**2*(c + 1)/9
Let a = 4148/279 - 144/31. Determine j so that -8/9*j + 8/3*j**5 + 104/9*j**3 + 0 - a*j**4 - 28/9*j**2 = 0.
-1/6, 0, 1, 2
Let d(z) be the second derivative of z**8/560 - z**6/120 - 5*z**3/3 - 12*z. Let c(l) be the second derivative of d(l). Factor c(p).
3*p**2*(p - 1)*(p + 1)
Let o(j) be the third derivative of j**6/120 + 73*j**5/5 + 10658*j**4 + 12448544*j**3/3 + 928*j**2. Determine y so that o(y) = 0.
-292
Let o(q) be the second derivative of q**6/180 - q**5/15 - 2*q**3/3 - 11*q. Let n(d) be the second derivative of o(d). Let n(b) = 0. What is b?
0, 4
Let c = 180 + -176. Let f be c/(-6)*6/(-22). Factor 2/11*b**2 + f - 4/11*b.
2*(b - 1)**2/11
Let y(u) be the third derivative of u**6/280 - u**5/140 - 2*u**4/7 + 8*u**3/7 + 524*u**2. Factor y(v).
3*(v - 4)*(v - 1)*(v + 4)/7
Suppose -3*d + 29 = 4*s, -2*s = -3*s - d + 8. Suppose 3*a - 31 = s. Factor -6 - a*k**2 + 1 - 3 + 20*k.
-4*(k - 1)*(3*k - 2)
Let q(x) = 2*x**3 + x**2. Let c(v) = 34*v**3 + 243*v**2 - 344*v + 64. Let u(w) = -c(w) - q(w). Factor u(f).
-4*(f - 1)*(f + 8)*(9*f - 2)
Factor -219/2*k**2 - 1944 + 2052*k + 3/2*k**3.
3*(k - 36)**2*(k - 1)/2
Let j(z) be the third derivative of -z**10/226800 + z**9/45360 - z**8/30240 + z**5/20 + 9*z**2. Let x(i) be the third derivative of j(i). What is n in x(n) = 0?
0, 1
Let f(a) be the third derivative of a**9/20160 - a**8/4480 - a**7/3360 + a**6/480 + a**4/12 - 7*a**2. Let r(m) be the second derivative of f(m). Factor r(y).
3*y*(y - 2)*(y - 1)*(y + 1)/4
Let l be 0 + -4 + 9 + -4. Let i be (14/(-6) - -4)*l. Suppose -i*b - 1/3 - 10/3*b**3 - 10/3*b**2 - 1/3*b**5 - 5/3*b**4 = 0. What is b?
-1
Suppose -10*n - 2 = -9*n. Let p be ((-72)/20)/(n/5). Factor -3*m**2 + p*m**2 - 3*m**2.
3*m**2
Let k(x) = 4*x + 45. Let n be k(-11). Let v(q) be the first derivative of -8*q**2 + 2/3*q**3 + 3/2*q**4 - n + 8*q. Factor v(j).
2*(j - 1)*(j + 2)*(3*j - 2)
Let r be 3 + 0 + (-78)/(-6). Solve -3*d + 55*d**2 - 59*d**2 + 3*d + r = 0.
-2, 2
Let p = -1664 - -6657/4. Solve -1/2*g**2 + 1/2*g**4 + p*g - 1/4*g**5 + 0*g**3 + 0 = 0 for g.
-1, 0, 1
Let v(p) be the first derivative of p**3/6 - 4*p**2 + 32*p - 82. Suppose v(b) = 0. Calculate b.
8
Solve 2242/7*p**2 + 8/7*p**5 - 298/7*p**4 + 2658/7*p**3 - 722/7*p + 0 = 0 for p.
-1, 0, 1/4, 19
Let x(k) = 18*k**5 - 19*k**4 + k**3 - 5*k + 5. Let m(i) = 27*i**5 - 28*i**4 + i**3 - 8*i + 8. Suppose d - 14 + 6 = 0. Let v(r) = d*x(r) - 5*m(r). Factor v(w).
3*w**3*(w - 1)*(3*w - 1)
Let u = 8291 - 8288. Let 15*q**u + 25/2*q + 1/2*q**5 - 5*q**4 - 20*q**2 - 3 = 0. What is q?
1, 6
Let f be 16/224 - 276/(-56). Let a(z) be the third derivative of 5/6*z**4 - 10/3*z**3 - 3*z**2 + 0 - 1/12*z**6 - 1/42*z**7 + 0*z + 1/4*z**f. Factor a(m).
-5*(m - 1)**2*(m + 2)**2
Let b(f) be the second derivative of -f**5/10 - 17*f**4/6 + 37*f**3/3 - 19*f**2 - 367*f. Find i, given that b(i) = 0.
-19, 1
Let b(q) = 8*q**2 + 33*q + 3. Let p(m) = 13*m**2 + 65*m + 5. Let t(h) = -5*b(h) + 3*p(h). Factor t(x).
-x*(x - 30)
Let u(q) be the second derivative of -q**5/5 + q**4/3 - 8*q + 5. Determine w so that u(w) = 0.
0, 1
Suppose -4*u = -2*u - 10, -y = -4*u + 17. What is w in -9*w**4 + 5*w**5 - w**4 + 10*w**2 - 11*w**3 + 6*w**y = 0?
-1, 0, 1, 2
Let q = -1/3532 - -3537/17660. Let -q*g**5 - 17/5*g**3 - 17/5*g**2 - 6/5*g + 0 - 7/5*g**4 = 0. What is g?
-3, -2, -1, 0
Factor -1/2*k**2 + 1/2*k**4 + 0*k + 0*k**3 + 0.
k**2*(k - 1)*(k + 1)/2
Let p(u) = 68*u**2 + 144*u - 296. Let m(d) = 14*d**2 + 29*d - 59. Let t(z) = 24*m(z) - 5*p(z). Factor t(h).
-4*(h - 2)*(h + 8)
Let d(v) be the second derivative of v**7/84 + v**6/12 + v**5/5 + v**4/6 + 38