 26
Let y(d) = -2*d + 4. Let n be y(2). Let x = 20131/45315 + 1/5035. Factor n + 2/9*w**3 + x*w - 2/3*w**2.
2*w*(w - 2)*(w - 1)/9
Let z(l) = -l**5 - l**4 - l**2 + 1. Suppose 10*i - 8*i = 0. Let k(p) = 8*p**3 + 6*p**2 + 2*p**4 - 6 + i + 0*p**4 - 6*p. Let d(n) = -k(n) - 2*z(n). Factor d(u).
2*(u - 2)*(u - 1)*(u + 1)**3
Let s = 329 + -2294/7. Suppose -404*q - 2 = -405*q. Factor 6/7*b + 3/7*b**q - s.
3*(b - 1)*(b + 3)/7
Let y(i) = -i**2 + 8*i - 7. Let b be y(6). Factor -74*v**b - 18*v**2 + 41*v**5 + 37*v**5 + 48*v**3 - 26*v**4.
2*v**2*(v - 3)**2*(2*v - 1)
Let n(u) be the first derivative of -6*u**5/25 - 49*u**4/10 - 26*u**3/15 + 49*u**2/5 + 32*u/5 - 65. What is x in n(x) = 0?
-16, -1, -1/3, 1
Let x(z) be the first derivative of 0*z**2 - 2/21*z**3 + 0*z + 1/21*z**6 - 9 + 2/35*z**5 - 1/14*z**4. Factor x(l).
2*l**2*(l - 1)*(l + 1)**2/7
Let y(r) be the first derivative of 24 - 2/3*r**2 - 4/3*r - 1/9*r**3. Solve y(g) = 0 for g.
-2
Let z(o) = -o**3 + 25*o**2 + 152*o - 58. Let f be z(30). Suppose 4/3*c**f + 0*c - 2/3*c**3 + 0 = 0. What is c?
0, 2
Let i be (-17)/340*-20*(-9 + 2) - -7. Factor -3/2*g**3 + i + 9/2*g - 3*g**2.
-3*g*(g - 1)*(g + 3)/2
Suppose 1 = -5*o + 4*o + v, -5*o + v + 15 = 0. Suppose o*c = c. Factor c + 1/4*d**3 + 0*d**2 - 1/4*d**5 + 0*d**4 + 0*d.
-d**3*(d - 1)*(d + 1)/4
Let v be (-3)/(-6*(-3)/(-264)). Factor 64*p**2 - 2*p**4 - 5*p - p**5 + 22*p**4 - v*p**2 - 4*p**5 - 30*p**3.
-5*p*(p - 1)**4
Factor 30*u**2 + 59*u**5 - 65*u**3 + 42*u**5 + 40*u**4 - 106*u**5.
-5*u**2*(u - 6)*(u - 1)**2
Let k(n) be the third derivative of -n**5/30 - 19*n**4/12 - 6*n**3 - n**2 + 694*n. Factor k(h).
-2*(h + 1)*(h + 18)
Let p(f) be the second derivative of -5*f**8/224 - 3*f**7/70 + 3*f**6/80 + f**5/10 - 33*f**2/2 - 23*f. Let a(w) be the first derivative of p(w). Factor a(y).
-3*y**2*(y + 1)**2*(5*y - 4)/2
Suppose -3*c = h - 6*h - 23, -5*c - 2*h + 28 = 0. Let z(m) be the first derivative of 0*m**2 - 1/12*m**c + 0*m + 0*m**3 - 1/4*m**4 - 5 - 3/10*m**5. Factor z(k).
-k**3*(k + 1)*(k + 2)/2
Factor 0*a - 2*a**4 - 6/13*a**5 + 0*a**2 + 0 + 20/13*a**3.
-2*a**3*(a + 5)*(3*a - 2)/13
Let i(f) be the second derivative of -f**5/420 + f**4/28 - 3*f**3/14 - 19*f**2/2 + 39*f. Let y(m) be the first derivative of i(m). Factor y(j).
-(j - 3)**2/7
Let 115*t**2 + 51*t**3 - 25*t**2 - 46*t**3 - 5*t - 90 = 0. Calculate t.
-18, -1, 1
Solve 2*w**3 + 298*w**2 - 16 + 48*w + 291*w**2 - 571*w**2 + 48 = 0.
-4, -1
Let f be (6/(-5))/(3/5) - (0 + -2). Factor 2/17*m + f + 4/17*m**2 + 2/17*m**3.
2*m*(m + 1)**2/17
Let m be (-8)/((-1792)/(-1113)) - -5. Let s = m + 29/96. Factor s*x**2 + 0 + x.
x*(x + 3)/3
Let l be (127/(-45) + 3)*(-21)/(-14). Let o(a) be the first derivative of 0*a + 0*a**4 + 0*a**2 + 4/25*a**5 - 7 - l*a**3. Solve o(f) = 0 for f.
-1, 0, 1
Let q = 106 - 100. Let w(b) be the third derivative of 9/280*b**q + 0*b**3 + 3/245*b**7 + 0*b - 7*b**2 + 0 + 0*b**4 + 0*b**5 + 1/784*b**8. Solve w(o) = 0 for o.
-3, 0
Suppose 3*x - a + 3 = 6*x, 5*a = x - 17. Suppose -22 = -2*f - x*f - t, -2*t - 16 = -4*f. Solve 18/7*b**3 + 0*b + 2/7*b**f + 0 + 12/7*b**4 + 0*b**2 = 0.
-3, 0
Let b = -11 - -20. Let m = -49 + 50. Factor -2*c - m + 1 - b*c**2 + 11*c**2.
2*c*(c - 1)
Find f such that 2/15*f**3 - 14/15*f + 0*f**2 + 4/5 = 0.
-3, 1, 2
Suppose 290*a - 8 = 288*a. Let v(h) be the second derivative of 0 + 0*h**3 + 0*h**2 + 5*h + 1/30*h**a. Suppose v(o) = 0. What is o?
0
Let h(z) be the first derivative of z**4/30 + 4*z**3/45 - 11*z**2/15 - 8*z/5 - 177. Let h(j) = 0. What is j?
-4, -1, 3
Suppose 0 = -3*j - 3*o + 6, -1 = 3*j - 4*o - 14. Suppose -4*w = d + 3*d - 4, -3*d = 2*w. Factor w*t**4 + 6*t**2 + 2*t**2 - j*t**2 + t**4 - t - 8*t**3.
t*(t - 1)*(2*t - 1)**2
Let s(q) be the second derivative of -1/4*q**4 + 1/20*q**5 + 1/30*q**6 - 1/6*q**3 + 13*q + 0 + q**2. Factor s(b).
(b - 1)**2*(b + 1)*(b + 2)
Let x(l) be the first derivative of -2*l**5/5 - 6*l**4 + 2*l**3/3 + 12*l**2 - 84. Factor x(y).
-2*y*(y - 1)*(y + 1)*(y + 12)
Let i(p) = -7*p**5 + 5*p**4 + 13*p**3 - 32*p**2 + 3*p + 3. Let m(z) = 6*z**5 - 6*z**4 - 14*z**3 + 32*z**2 - 2*z - 2. Let j(f) = 2*i(f) + 3*m(f). Factor j(b).
4*b**2*(b - 2)**2*(b + 2)
Let j = -39 + 41. Let -20*t**3 + 17*t**3 + 6*t**4 - j*t**5 - t**5 = 0. What is t?
0, 1
Let o(l) = 55*l**3 + 40*l**2 - 25*l - 5. Let v(q) = -27*q**3 - 19*q**2 + 12*q + 2. Let a(w) = 2*o(w) + 5*v(w). Determine b, given that a(b) = 0.
-1, 0, 2/5
Let b(q) = 3*q**2 - 28*q - 63. Let o be b(-2). Factor 0*j**2 + o*j**4 + 10/3*j**3 + 5/3*j**5 + 0 + 0*j.
5*j**3*(j + 1)*(j + 2)/3
Let l(z) be the second derivative of -1/15*z**4 + 4/5*z**2 - 12*z + 0 + 2/15*z**3. Factor l(c).
-4*(c - 2)*(c + 1)/5
Suppose 2/5*l**2 - 46/5*l + 84/5 = 0. What is l?
2, 21
Let d(k) be the third derivative of 9*k**8/448 + 9*k**7/40 - 87*k**6/160 - 377*k**5/240 - 23*k**4/16 - 2*k**3/3 + 2*k**2 + 116*k. Factor d(y).
(y - 2)*(y + 8)*(3*y + 1)**3/4
Let p(i) = -i**2 - 2. Let k(l) = 5*l**3 + 7*l**2 - 5*l - 16. Let d(j) = -k(j) + 3*p(j). Let d(n) = 0. Calculate n.
-2, -1, 1
Suppose -i**3 + 60 + 4*i**3 + i**3 + 0*i**3 + 66*i**2 + 123*i - i**3 = 0. Calculate i.
-20, -1
Let n(a) be the second derivative of a**4/4 - 14*a**3 + 294*a**2 - 42*a. Factor n(k).
3*(k - 14)**2
Let r be (2/(-1) + 4)/1. Let j = -2 + r. Factor j*t - 3/2 + 3/2*t**2.
3*(t - 1)*(t + 1)/2
Let p = -38 - -42. Factor -57 - 5*u + p*u**3 + 33 + u + 26 - 2*u**4.
-2*(u - 1)**3*(u + 1)
Let j(o) be the first derivative of -o**5/15 + o**4/6 + 4*o**3/3 - 5*o**2/2 - 12. Let x(b) be the second derivative of j(b). Factor x(h).
-4*(h - 2)*(h + 1)
Let v(p) be the second derivative of -p**4/8 - 7*p**3/2 - 18*p**2 - 283*p. Factor v(g).
-3*(g + 2)*(g + 12)/2
Let g(b) = 3*b**2 - 262*b + 264. Let p(w) = -8*w**2 + 656*w - 660. Let o(k) = -12*g(k) - 5*p(k). Let o(v) = 0. Calculate v.
1, 33
Let f(w) be the third derivative of 0*w - 5/6*w**4 - 13*w**2 - 4/15*w**5 + 0*w**3 + 0 + 1/30*w**6. Factor f(y).
4*y*(y - 5)*(y + 1)
Let d = -6/2441 - -4912/12205. Factor -162/5 - d*q**2 + 36/5*q.
-2*(q - 9)**2/5
Let y(q) = -q**3 - q**2 + 2*q + 2. Let p be y(-2). Let h = p + 3. Find x, given that 3*x**5 - 49*x**2 + 47*x**2 + 4*x + 4*x**5 + 2*x**4 - h*x**5 - 6*x**3 = 0.
-2, -1, 0, 1
Let s(w) = -4*w**3 - 6*w**2 - 2*w - 6. Let y(n) = -9*n**3 - 13*n**2 - 4*n - 13. Suppose -4*f - 19 = 5. Let k(a) = f*y(a) + 13*s(a). Solve k(d) = 0 for d.
-1, 0, 1
Let r(u) = 106*u - 7526. Let g be r(71). Find w, given that g*w - 12/5*w**3 - 2/15*w**4 + 0 - 54/5*w**2 = 0.
-9, 0
Let r be (-2)/26*(48 - 50). Determine d so that 14/13*d**2 + r*d**3 + 0*d + 0 = 0.
-7, 0
Let m be (-2)/(-1*4)*276/46. Let h(a) be the third derivative of 0*a**4 + 0*a + 0*a**m - 1/30*a**6 - 2*a**2 - 1/30*a**5 + 0. Solve h(s) = 0.
-1/2, 0
Solve -3*y**3 - 14*y**2 + 444 - 465 + 39*y - y**2 = 0.
-7, 1
Factor 21/4 + 21/2*f**3 - 27/4*f**4 - 45/4*f + 3/2*f**2 + 3/4*f**5.
3*(f - 7)*(f - 1)**3*(f + 1)/4
Let u(p) = -p**2 - 11*p - 25. Let s be u(-6). Let j = 4 + -1. Factor -4*v**2 - 3*v + 4*v**4 + v - v**j + v**3 + 2*v**s.
2*v*(v - 1)*(v + 1)**3
Suppose 2/3*t**2 + 20 - 22/3*t = 0. What is t?
5, 6
Let w be 8/6 - (-4)/6. Suppose -y + 0 = -w. Factor 6*i + 0*i**2 - y*i**2 - i**2.
-3*i*(i - 2)
Let s be 36/(-126) - (-4)/14. Solve s*g - 9*g + 3*g**3 - 12*g**2 + 6 + 4 + 44 = 0 for g.
-2, 3
Let d be (-1)/((-66)/134) - (-4 - -5). Let n = -4/11 + d. Suppose 1/3*b**2 - 2/3*b**3 + n*b + 0 - 1/3*b**4 = 0. Calculate b.
-2, -1, 0, 1
Factor 0 + 1/3*y**2 + 7/3*y**3 - 1/3*y**4 - 7/3*y.
-y*(y - 7)*(y - 1)*(y + 1)/3
Let b(v) be the first derivative of -2/7*v - 5/7*v**2 - 4/21*v**3 + v**4 - 3/7*v**6 - 8 + 6/35*v**5. Suppose b(s) = 0. What is s?
-1, -1/3, 1
Let g = 326 + -323. Let z be (-1 - 1) + 7 + -2. Factor -8*l**z + 2*l**2 + 0*l**2 + 9*l**g - 3*l.
l*(l - 1)*(l + 3)
Suppose 2*s - 34 = -28. Let b(f) be the second derivative of -13*f + 1/2*f**2 + 0 + 1/6*f**s + 1/48*f**4. What is x in b(x) = 0?
-2
Suppose 320/7*v**2 + 60/7*v**5 - 64/7 - 76/7*v**4 + 0*v - 240/7*v**3 = 0. What is v?
-2, -2/5, 2/3, 1, 2
Let u(l) be the second derivative of -2/5*l**6 - 4*l**4 + 0*l**2 + 51/20*l**5 + 8*l + 0 + 3/2*l**3. Find y, given that u(y) = 0.
0, 1/4, 1, 3
Let b(c) = c**3 + 10*c**2 + 6*c. Let n(o) = -2*o**3 - 20*o**2 - 11*o. Let a(k) = 7*b(k) + 3*n(k). Determine l so that a(l) = 0.
-9, -1, 0
Let w = -64 - -64. Suppose w = -4*v