s(h) be the third derivative of -9*h**8/1120 - 11*h**7/350 - 19*h**6/600 + h**5/50 + 3*h**4/80 - h**3/30 + 19*h**2 + 2. Suppose s(x) = 0. Calculate x.
-1, 2/9, 1/3
Find p such that 4/3*p**3 - 2/9*p + 0*p**2 + 16/9*p**4 + 2/3*p**5 + 0 = 0.
-1, 0, 1/3
Let b be (1 - -1) + -1 + 4. Factor -b*k**2 + 6*k + 3*k**2 + 10 - 2.
-2*(k - 4)*(k + 1)
Let j(t) be the second derivative of -t**4/18 - t**3/9 + 2*t**2 - 2*t + 13. Determine q so that j(q) = 0.
-3, 2
Let r = 122 + -110. Find q such that -54*q**2 - 218 - r*q**3 - q**4 - 108*q - 132 + 269 = 0.
-3
Let u(s) be the second derivative of 1/6*s**6 + 0*s**2 + 0*s**3 + 1/2*s**5 + 0 - 5/4*s**4 + 6*s. Suppose u(t) = 0. Calculate t.
-3, 0, 1
Let p(w) be the first derivative of -2*w**2 + 0*w + 4/3*w**3 - 2. Factor p(a).
4*a*(a - 1)
Let u be (-265)/(-245) - 1 - 0. Let d = 18/49 - u. Factor -2/7 + 4/7*b - d*b**2.
-2*(b - 1)**2/7
Let b(a) = -5*a**4 + 4*a**4 + 2*a + 6*a**4 - 2*a**3 + a**2 + 2*a. Let v(l) = -6*l**4 + 3*l**3 - l**2 - 5*l. Let t(r) = 5*b(r) + 4*v(r). Factor t(w).
w**2*(w + 1)**2
Let x(k) be the second derivative of 4*k**5/105 + 19*k**4/42 - 10*k**3/21 - 3*k**2 + 10*k. Let q(v) be the first derivative of x(v). Solve q(i) = 0.
-5, 1/4
Factor 25 + 274*l + 59*l + 51 - 6*l**2 + 81 + 11.
-3*(l - 56)*(2*l + 1)
Let i = -23 - -77/3. Suppose 0 = -3*b + 12, 3*r - 5*b + 3 = -2*b. Factor -4*g + 0*g**2 - i + 4/3*g**r.
4*(g - 2)*(g + 1)**2/3
Let v be (-14)/8*(-21 - 11). Suppose v = 2*j + 12*j. Factor -18/5*y**5 + 0*y**2 + 24/5*y**j + 0 + 0*y - 8/5*y**3.
-2*y**3*(3*y - 2)**2/5
Let l(z) = 13*z**3 - 33*z**2 + 36*z - 7. Let n(r) = -3*r**3 + 8*r**2 - 9*r + 2. Let b(f) = 2*l(f) + 9*n(f). Find p such that b(p) = 0.
1, 4
Let v be (-7 + -4 + 3)/(-2). Let a(p) = -5*p**2 - 24*p. Let k(g) = 55*g**2 + 195*g + 96*g - 26*g. Let u(m) = v*k(m) + 45*a(m). Find f, given that u(f) = 0.
-4, 0
Let t(z) = 15*z**4 + 30*z**3 - 33*z**2 - 15*z + 3. Let f(y) = 30*y**4 + 62*y**3 - 66*y**2 - 31*y + 5. Let l(n) = 3*f(n) - 5*t(n). Determine c so that l(c) = 0.
-3, -2/5, 0, 1
Solve -2549*c**2 - 204*c**3 + 1757*c**2 + 159*c + 12*c**4 + 825*c**3 = 0 for c.
-53, 0, 1/4, 1
Let u(t) = 8*t - 5 + 24*t**2 - 27*t**4 - 8*t**3 - 8*t**2 + 11*t**2 + 6. Let a(c) = c**4 - c**2 + 1. Let j(d) = a(d) - u(d). Factor j(y).
4*y*(y - 1)*(y + 1)*(7*y + 2)
Suppose -540 = 46*t - 52*t. Let v be -5*(-4 + t/25). Factor -y + 1/3*y**v + 2/3.
(y - 2)*(y - 1)/3
Let f(g) be the second derivative of -5*g**7/42 - 3*g**6/10 + 7*g**5/20 + 3*g**4/4 - g**3/3 - 200*g. Let f(u) = 0. What is u?
-2, -1, 0, 1/5, 1
Let k be -9*(4/4)/(-3). Suppose 6 = k*v - v. Suppose v*u - 3*u - 3*u - 3*u**2 = 0. What is u?
-1, 0
Suppose 4*z = 3*n + 7, -5*n + 7 = z - 4*n. Factor -6*j + 0*j + 2*j**2 - 15*j**3 - 3*j**5 + 19*j**2 - 12*j**3 + 15*j**z.
-3*j*(j - 2)*(j - 1)**3
Let j(a) be the first derivative of 2/21*a**3 - 2/7*a - 1/14*a**4 + 1/7*a**2 - 5. Find k such that j(k) = 0.
-1, 1
Let h(p) be the third derivative of p**5/240 - p**4/12 + 7*p**3/24 + 17*p**2 - 11. Determine n so that h(n) = 0.
1, 7
Let a be (3 - 35/12)*(-254 + 262). Factor -2*i**3 + 0*i - 2/3*i**5 + 0 - 2*i**4 - a*i**2.
-2*i**2*(i + 1)**3/3
Let n = 7079/10 + -704. Let u = -12/5 + n. Factor u*d**2 + 2/3 + 2*d.
(3*d + 2)**2/6
Suppose 2*b - a + 11 = -0*b, -5*b - 35 = -5*a. Let r be 11/(-44) - ((-3)/b)/(-3). Factor 11/3*c**4 + 5*c**3 + r + 2/3*c + 3*c**2 + c**5.
c*(c + 1)**3*(3*c + 2)/3
Let w(n) = -n**3 - 5*n**2 + 3. Let o be w(-5). Let a be (-1)/(-1*o/6). Factor 6*c**4 - 2*c + a*c**3 - 3*c**2 - c**2 - 2*c**2 + 0*c**2.
2*c*(c - 1)*(c + 1)*(3*c + 1)
Suppose 2*n - n - 3 = 0. Let a = -9866/3 + 3289. Solve a*m - 1/3*m**2 + 0 - 1/3*m**n + 1/3*m**4 = 0 for m.
-1, 0, 1
Let g = 2 - 2. Let a = -23703 - -23708. Solve 0*o + 1/2*o**2 + 3/4*o**a + 3/4*o**3 - 2*o**4 + g = 0 for o.
-1/3, 0, 1, 2
Let g = -6 - -7. Let p(c) = -c**3 + 1. Let i(n) = 2*n**3 + 4*n**2 + 4*n - 10. Let r(h) = g*i(h) + 6*p(h). Factor r(s).
-4*(s - 1)**2*(s + 1)
Factor 6/7*d**3 + 0 + 0*d**2 - 6/7*d.
6*d*(d - 1)*(d + 1)/7
Let g = -346/77 - -62/11. Let l(f) be the first derivative of g*f**5 - 6/7*f - 17/14*f**4 + 1 + 17/7*f**2 - 34/21*f**3. What is w in l(w) = 0?
-1, 1/4, 3/5, 1
Let w(g) be the first derivative of -4*g**3/21 + 46*g**2/7 - 72*g + 630. Factor w(c).
-4*(c - 14)*(c - 9)/7
Let o(w) = -1. Let n(x) = 2*x**3 + 354*x**2 + 20886*x + 410769. Let v(c) = 2*n(c) + 22*o(c). Factor v(j).
4*(j + 59)**3
Let q be 60/(-48) + 1 - (-214)/840. Let s(o) be the third derivative of 0*o**3 + 1/84*o**4 + 0 + 11*o**2 - q*o**5 + 0*o. Determine v so that s(v) = 0.
0, 1
Let y be (-780)/(-351)*(-3)/(-25). Factor 2/15*k - 2/15*k**3 - y*k**2 + 4/15.
-2*(k - 1)*(k + 1)*(k + 2)/15
Let b be ((-2)/6)/((-2)/12). Solve 4*d**b + d - 5*d**2 + d**3 - d = 0.
0, 1
Let b be 118/38 - 96/912. Let r(a) be the first derivative of 0*a + 1/9*a**b - 1/6*a**2 + 6. Factor r(m).
m*(m - 1)/3
Determine t, given that -51/4*t - 3/4*t**3 + 6 + 15/2*t**2 = 0.
1, 8
Solve -10*l**4 + 6*l - 6*l + 13*l**5 - 9*l**5 - 56*l**3 - 10*l**4 = 0 for l.
-2, 0, 7
Let x = 746 - 1489/2. Let y(s) = s**3 - 5*s**2 + 5*s - 1. Let o be y(4). Factor -3/2*k - x*k**2 + 3/2*k**o + 3/2.
3*(k - 1)**2*(k + 1)/2
Find u, given that -1129*u**2 - 2 + u**4 - 5*u + 1130*u**2 - 3*u**5 + u**5 + 7*u**3 = 0.
-1, -1/2, 1, 2
Let u(o) be the third derivative of o**6/40 + 3*o**5/10 - o**4/8 - 3*o**3 - 161*o**2. Suppose u(k) = 0. What is k?
-6, -1, 1
Let x(p) be the third derivative of p**8/112 - p**7/14 + 9*p**6/40 - 7*p**5/20 + p**4/4 + 93*p**2. Factor x(j).
3*j*(j - 2)*(j - 1)**3
Let -11*a + 1/2*a**2 + 20 = 0. What is a?
2, 20
Suppose 0 = -3*u - 2*o - 10, -5*o - 25 = u - 2*u. Suppose 6*v - 7*v + 3 = u. Factor -v*l**4 + l**4 - 7*l + 3*l**3 + 3*l + 4*l**2 + 0*l**4 - l**5.
-l*(l - 1)**2*(l + 2)**2
Let q(o) = -12*o - 7. Let i(t) = -13*t - 8. Let r(d) = -4*i(d) + 5*q(d). Let f(b) = b**2 + 7*b + 2. Let l(m) = -5*f(m) - 4*r(m). Factor l(s).
-(s + 1)*(5*s - 2)
Suppose -y - 2*y + 24 = -3*l, -4*y = 5*l + 67. Let s = 15 + l. Factor -4*p**3 - 2*p**s - p**3 + 5*p**4 + 2*p**3.
3*p**3*(p - 1)
Let c(w) = 12*w**5 - 198*w**4 - 142*w**3 + 34*w**2 - 34*w. Let m(x) = x**5 - 18*x**4 - 13*x**3 + 3*x**2 - 3*x. Let l(j) = -6*c(j) + 68*m(j). Factor l(u).
-4*u**3*(u + 1)*(u + 8)
Let u = 26 - 24. Find q such that -u*q + q**4 - 2*q**3 + 7*q**3 - 9*q**3 + 5*q**2 = 0.
0, 1, 2
Let x(q) = -8*q + 51. Let j be x(6). Suppose -m + 3 = 9*n - 10*n, 0 = -m + 3. Factor 8/7*o**2 + 4/7*o + n + 4/7*o**j.
4*o*(o + 1)**2/7
Let c = 5461/105 + -52. Let g(j) be the second derivative of -1/30*j**4 - 1/25*j**6 + 0*j**3 - 9*j - 3/50*j**5 - c*j**7 + 0*j**2 + 0. Factor g(k).
-2*k**2*(k + 1)**3/5
Let x(s) be the first derivative of 4*s**2 + s**2 - 6*s**2 - 4*s**2 - 5*s**3 + 5*s + 4. Solve x(a) = 0.
-1, 1/3
Factor 0 + 4/3*a**4 + 4*a - 4*a**3 - 4/3*a**2.
4*a*(a - 3)*(a - 1)*(a + 1)/3
Let c(j) = 5*j**4 + 5*j**3 - 10*j**2 + 5*j. Let a(t) = -t**3 + t**2 - t. Suppose 2*u + 5 = -5. Let m(r) = u*a(r) - c(r). Solve m(b) = 0 for b.
-1, 0, 1
Suppose 5*a - a + 4 = 0. Let o(s) = -12*s**2 + 26*s - 5. Let i = 4 - 3. Let n(r) = -r + 1. Let q(t) = a*n(t) + i*o(t). Suppose q(k) = 0. What is k?
1/4, 2
Suppose -7982 = 9*b - 8000. Let k(y) be the first derivative of 0*y**b + 0*y - 10 - 1/16*y**4 - 1/20*y**5 + 0*y**3. Factor k(m).
-m**3*(m + 1)/4
Let w(z) be the second derivative of 7*z**4/6 - 4*z**3/3 + 4*z**2/7 - 2*z - 6. Factor w(c).
2*(7*c - 2)**2/7
Let f(p) be the second derivative of p**4/6 - 16*p**3/3 + 5*p - 9. Factor f(t).
2*t*(t - 16)
Let w(a) be the first derivative of 6 - 17/4*a**2 + 17/6*a**3 - 7/8*a**4 + 1/10*a**5 + 3*a. Find i, given that w(i) = 0.
1, 2, 3
Let x(d) be the first derivative of 5*d**6/6 - 6*d**5 + 5*d**4/4 + 40*d**3 + 40*d**2 - 470. Determine k, given that x(k) = 0.
-1, 0, 4
Let g(j) be the first derivative of -2*j**5/25 + 9*j**4/10 + 4*j**3/3 + 389. Let g(c) = 0. Calculate c.
-1, 0, 10
Let w = -279 + 281. What is t in 8/5 + 0*t - 2/5*t**w = 0?
-2, 2
Let p(o) be the second derivative of -o**8/6720 - o**7/630 - o**6/144 - o**5/60 - 3*o**4/2 + 14*o. Let j(i) be the third derivative of p(i). Factor j(l).
-(l + 1)**2*(l + 2)
Let q(z) be the first derivative of 11*z**6/15 + 26*z**5/25 + z**4/5 - 81. Determine w so that q(w) = 0.
-1, -2/11, 0
Let o = -49 - -46. Let u be -1*o/(-9)*0. Factor u*y**2 + 0 + 3/5*y**3 - 12/5*y**4 + 