*3/3 - 10. Find o such that n(o) = 0.
0, 1, 2
Suppose 3*o = 28 - 10. Let n = o - 4. Factor n*i**3 + 0*i**5 - 3*i**5 - 3*i**3 + 2*i**2 - 2*i**5 - 8*i**4.
-i**2*(i + 1)**2*(5*i - 2)
Let x(k) be the second derivative of k**3/6 - 4*k**2 - 2*k. Let j be x(11). Factor 2*y + y - j*y + 4*y**4 - 2*y**5 - 2*y**3.
-2*y**3*(y - 1)**2
Factor -4/5*q**5 + 0*q**3 + 0 + 4/5*q - 8/5*q**4 + 8/5*q**2.
-4*q*(q - 1)*(q + 1)**3/5
Let r(n) be the third derivative of -n**7/525 + n**6/60 - 3*n**5/50 + 7*n**4/60 - 2*n**3/15 - 14*n**2. Factor r(b).
-2*(b - 2)*(b - 1)**3/5
Let s be 2 + 13 - (2 + 1). Suppose 0 = -3*u + 5*k - 6, 3*k + k - s = 0. Factor 5*g + u*g + 4 - 4*g + g**2.
(g + 2)**2
Let v(k) = -k**3 + 6*k**2 - k. Let b(l) = l**3 - 7*l**2 + l. Let r(t) = -4*b(t) - 5*v(t). Factor r(h).
h*(h - 1)**2
Let f(a) = -a**3 + 15*a**2 + 14*a + 36. Let u be f(16). Let m(h) be the third derivative of 2*h**2 + 0*h + 1/150*h**5 + 1/15*h**3 + 0 - 1/30*h**u. Factor m(n).
2*(n - 1)**2/5
Let u be 4 + (58/40)/((-6)/16). Let n(h) be the first derivative of -3 + 1/10*h**4 + 0*h**2 + 0*h + u*h**3. Factor n(i).
2*i**2*(i + 1)/5
Suppose 68*g - 187 - 17 = 0. Factor 2*v**5 + 0*v + 24/5*v**4 + 0 + 4/5*v**2 + 18/5*v**g.
2*v**2*(v + 1)**2*(5*v + 2)/5
Let y(x) = -4*x**2 + 2*x - 2. Let t be 3/1*12/(-9). Let o be t/2*(-2 + 1). Let b(j) = 9*j**2 - 5*j + 5. Let l(d) = o*b(d) + 5*y(d). Factor l(s).
-2*s**2
Let y(m) = 2*m**3 + 15*m**2 + 21*m + 3. Let k(f) = -6*f**3 - 46*f**2 - 64*f - 10. Let i(n) = 3*k(n) + 10*y(n). Factor i(d).
2*d*(d + 3)**2
Let k be (-2 - 4)*4/(-6). Let -3*u + k*u + 3*u - u**2 - 3*u = 0. Calculate u.
0, 1
Let v(b) be the first derivative of -2*b**3/9 + 5*b**2/3 - 4*b - 37. Solve v(i) = 0.
2, 3
Let m(d) be the first derivative of -9*d**5/10 + 29*d**4/8 - 11*d**3/2 + 15*d**2/4 - d - 6. Factor m(c).
-(c - 1)**3*(9*c - 2)/2
Let s = 33 - 30. Let j = -16 + 18. Factor 2/11*p**s + 0 - 2/11*p**5 + 0*p**j + 0*p + 0*p**4.
-2*p**3*(p - 1)*(p + 1)/11
Let z(q) be the first derivative of -48*q**5/5 + 30*q**4 + 23*q**3 + 9*q**2/2 + 3. Determine c, given that z(c) = 0.
-1/4, 0, 3
Let q(x) be the second derivative of -x**4/6 + x**3 + 4*x**2 + 50*x. Suppose q(w) = 0. Calculate w.
-1, 4
Let u be 20/(-25)*(-5)/(-2). Let b = u + 4. Determine y, given that 0 + 0*y + 0*y**b + 2/7*y**3 = 0.
0
Let b(n) = -6*n. Let i(g) = g + 1. Let m(c) = -c**2 + 15*c + 3. Let a(z) = -3*i(z) + m(z). Let x(k) = 3*a(k) + 5*b(k). What is u in x(u) = 0?
0, 2
Suppose -288 = -15*r - r. What is x in -45*x**3 + 6 - 33/2*x**2 + 75/2*x**4 + r*x = 0?
-2/5, 1
Let x(l) = -l**3 - 9*l**2 + 9*l - 7. Let a be x(-10). Let c be a/2 + (-102)/84. Factor 4/7*p + 0*p**3 + 0 + 6/7*p**2 - c*p**4.
-2*p*(p - 2)*(p + 1)**2/7
Let k(m) be the second derivative of 1/30*m**5 - 3*m - 1/6*m**2 + 0 + 0*m**4 + 1/90*m**6 - 1/9*m**3. Let k(t) = 0. What is t?
-1, 1
Let c(k) be the third derivative of -k**7/1155 - k**6/330 - k**5/330 - 4*k**2. Suppose c(d) = 0. Calculate d.
-1, 0
Let f(m) be the second derivative of -m**5/110 - m**4/33 + m. Find n, given that f(n) = 0.
-2, 0
Let o(d) = 10*d + 9. Let m be o(4). Factor -65*g**2 - 52*g + 37*g**2 - 8 - m*g**2 - 48*g**3 - 15*g**2.
-4*(g + 1)*(3*g + 2)*(4*g + 1)
Suppose -26*o**4 - 6*o**3 + 19*o**4 + 3*o**5 + 10*o**4 = 0. What is o?
-2, 0, 1
Let l(c) = 5*c**3 + 55*c**2 + 124*c - 184. Let r(v) = 5*v**3 + 55*v**2 + 123*v - 183. Let p(k) = 3*l(k) - 4*r(k). Find m such that p(m) = 0.
-6, 1
Suppose 0 = 2*z - 5*z - 15. Let v = z + 7. Factor -2*o**v + 0*o**2 + 0*o + 2*o.
-2*o*(o - 1)
Suppose a + 3*r = 20, -a + 6*a - 30 = -r. Let b(u) = u - 3. Let t be b(a). Suppose 0*i - 2*i**3 + 2*i + t + 0*i**2 - 2*i**2 = 0. Calculate i.
-1, 1
Let 4/9*n**3 + 0 - 2/9*n**4 + 0*n - 2/9*n**2 = 0. What is n?
0, 1
Suppose 4*u - d - 7 = 0, 0 = 6*u - 8*u - 5*d + 9. Factor 2/7*h**u - 2/7 - 2/7*h**3 + 2/7*h.
-2*(h - 1)**2*(h + 1)/7
Factor 0*n + 1/4*n**2 - 1/4.
(n - 1)*(n + 1)/4
Let x(v) be the third derivative of v**8/224 - 3*v**7/140 + v**6/40 + v**5/20 - 3*v**4/16 + v**3/4 - 6*v**2. Factor x(r).
3*(r - 1)**4*(r + 1)/2
Suppose 10 = -2*f + 7*f. Factor 0 - 1/4*i - 3/4*i**f - 3/4*i**3 - 1/4*i**4.
-i*(i + 1)**3/4
Factor 2/7*d**2 - 18/7 + 18/7*d - 2/7*d**3.
-2*(d - 3)*(d - 1)*(d + 3)/7
Let z(f) be the third derivative of 0 + 7*f**2 - 1/24*f**6 - 1/420*f**7 - 3/10*f**5 - 9/4*f**3 - 9/8*f**4 + 0*f. Determine o so that z(o) = 0.
-3, -1
Let z(f) be the second derivative of -f**7/28 - 7*f**6/60 - f**5/12 + f**4/12 + f**3/12 - f**2/12 - 2*f - 18. Factor z(p).
-(p + 1)**3*(3*p - 1)**2/6
Let d(i) be the first derivative of 10 + i + 1/3*i**3 - i**2. Factor d(v).
(v - 1)**2
Factor -9 - 4*o**2 + 12 - 3 + 8*o.
-4*o*(o - 2)
Let p = 5 - 14. Let m(t) = t**2 + 2*t + 1. Let f(x) = 4*x + 0*x + 0*x + 2*x**2 + 2. Let w(q) = p*m(q) + 4*f(q). Find o such that w(o) = 0.
-1
Let u(z) = z - 3. Let h be u(3). Let d be h + (4 - (0 - -1)). Solve -2*b**2 - 3*b**d + 2*b**3 + 0*b**3 = 0.
-2, 0
Let v(w) be the first derivative of 8*w**6/105 + 6*w**5/35 + 3*w**4/28 + w**3/42 - 2*w + 4. Let m(b) be the first derivative of v(b). Factor m(j).
j*(j + 1)*(4*j + 1)**2/7
Let y(l) be the first derivative of -2*l**6 + 32*l**5/5 - 4*l**4 - 8*l**3 + 14*l**2 - 8*l + 30. Determine m so that y(m) = 0.
-1, 2/3, 1
Let f(c) be the first derivative of 0*c + 7/150*c**5 - 3/2*c**2 + 1/30*c**4 + 1/75*c**6 - 1/15*c**3 + 3. Let r(k) be the second derivative of f(k). Factor r(d).
2*(d + 1)**2*(4*d - 1)/5
Let r(y) be the second derivative of y**7/840 - y**6/120 + y**5/40 - y**4/24 - y**3/2 - 6*y. Let m(a) be the second derivative of r(a). Factor m(i).
(i - 1)**3
Let u(o) be the first derivative of -1/10*o**2 + 2/5*o - 1/15*o**3 - 6. Determine n so that u(n) = 0.
-2, 1
Suppose -7 = -3*n + 8. Factor -20*o**4 + 59*o - 18 + 60*o**3 + 2*o**4 - 92*o**2 + 2*o**n + 7*o.
2*(o - 3)**2*(o - 1)**3
Let q(j) be the third derivative of j**6/1080 - j**5/360 - j**4/36 + j**3/6 - 7*j**2. Let l(i) be the first derivative of q(i). Factor l(o).
(o - 2)*(o + 1)/3
Suppose n - 5 = -2. Let m = 6 - n. Factor 5*y**3 + 2*y + 4 - 2*y**2 + y**m - 8*y - 2*y**4.
-2*(y - 2)*(y - 1)**2*(y + 1)
Let w(n) = n**2 + 6*n + 5. Let g be w(-6). Find l, given that g*l + 2*l**3 + 1 + 3*l**3 - 4*l**2 - 4*l**3 - 3 = 0.
1, 2
Let m = -6 - -8. Let v = 1648/5 + -328. Factor v*l**m - 2*l - 2/5*l**3 + 4/5.
-2*(l - 2)*(l - 1)**2/5
Let z(h) be the third derivative of h**7/21 + h**6/30 - h**5/6 - h**4/6 + 9*h**2. Suppose z(p) = 0. Calculate p.
-1, -2/5, 0, 1
Let v(i) be the first derivative of 0*i**3 + 1 + 1/6*i**6 - 1/5*i**5 + 0*i + 0*i**4 + 0*i**2. Let v(q) = 0. Calculate q.
0, 1
Let g = -12/17 - -191/102. Let v = g - -1/6. Factor 2/3*y**2 + 0 - v*y.
2*y*(y - 2)/3
Let v(i) be the third derivative of i**5/10 + i**4/8 - 14*i**2. Factor v(p).
3*p*(2*p + 1)
Let v(k) be the second derivative of -3*k + 63/10*k**5 - 13/12*k**4 - 2*k**2 - 27/10*k**6 + 0 - 14/3*k**3. Determine w so that v(w) = 0.
-2/9, 1
Let g(q) = -q**3 - 3*q - 2. Let x(z) = -4*z**3 + z**2 - 9*z - 7. Let v(c) = -14*g(c) + 4*x(c). What is w in v(w) = 0?
-1, 0, 3
Let t(x) be the second derivative of -x**8/26880 + x**7/3360 - x**5/120 + x**4/3 + 6*x. Let j(h) be the third derivative of t(h). Find c, given that j(c) = 0.
-1, 2
Let z(l) = 5*l**3 - 8*l**2 - 3*l + 2. Let y(o) = o. Suppose 5*p + 4*w - 36 = 0, -p + 3*p = -2*w + 16. Let k(a) = p*y(a) + z(a). Factor k(g).
(g - 1)**2*(5*g + 2)
Find j such that -1/3*j**5 + 25/3*j**2 - 16/3*j - 19/3*j**3 + 4/3 + 7/3*j**4 = 0.
1, 2
Let f(t) be the second derivative of -t**4/72 + t**3/36 - 2*t. Factor f(h).
-h*(h - 1)/6
Suppose 2*w + 22 = 3*w + 4*k, 2*k = -4*w + 32. Suppose -2*z = z - w. Factor -d - d + 1 + 2*d**5 - d**5 + 2*d**2 - d - 3*d**4 + z*d**3.
(d - 1)**4*(d + 1)
Determine t, given that -6*t**2 + 3*t**3 - 231*t + 231*t = 0.
0, 2
Let p(z) = 3*z**4 + 3*z**2 + 2*z + 4. Let r be (-16)/(-8)*(1 - 3). Let j(d) = -d**3 + d**2 + d + 1. Let y(i) = r*j(i) + p(i). Factor y(c).
c*(c + 1)**2*(3*c - 2)
Let u(w) be the first derivative of -4*w**5/5 - 2*w**4 + 4*w**3 + 8*w**2 - 16*w + 13. Factor u(m).
-4*(m - 1)**2*(m + 2)**2
Let d(b) = -2*b**4 - 5*b**3 + 3*b**2 + 2*b - 7. Let a(g) = g**4 + 5*g**3 - 3*g**2 - 3*g + 6. Let v(i) = -3*a(i) - 2*d(i). Factor v(x).
(x - 4)*(x - 1)**2*(x + 1)
What is g in -5 + 4 + 0 - 4*g - 3*g - 9*g**3 + 17*g**2 = 0?
-1/9, 1
Let n = 541/7 + -77. Factor