 such that l*v**2 - 4*v**2 + 4*v**5 - 3*v**3 - 3*v**4 + 7*v**2 - v**5 = 0.
-1, 0, 1
Suppose 73 = 59*l - 4 - 41. Suppose -98/3 - 2/3*g**l - 28/3*g = 0. Calculate g.
-7
Let j(p) be the first derivative of 3*p + 25/4*p**4 + 3/2*p**2 - 3 + 5*p**3. Let t(r) be the first derivative of j(r). Factor t(g).
3*(5*g + 1)**2
Let y(s) be the first derivative of 3/2*s + 3 - 1/2*s**3 + 0*s**2. Factor y(x).
-3*(x - 1)*(x + 1)/2
Factor 4/5*i + 2/5*i**2 + 2/5.
2*(i + 1)**2/5
Let u(v) be the third derivative of v**6/1140 + v**5/57 - 11*v**4/228 - 115*v**2. Let u(o) = 0. What is o?
-11, 0, 1
Let h(c) = c**2 - 34*c + 58. Let k be h(31). Let g be 1444/56 - (-10)/k. Factor 3 - 57/2*p + g*p**2.
3*(p - 1)*(17*p - 2)/2
Let y(b) be the third derivative of -b**5/360 + 29*b**4/72 + 2*b**2 + 196*b. Solve y(l) = 0.
0, 58
Let a(u) = 5*u**5 + 57*u**4 + 8*u**3 - 90*u**2 - u + 39. Let g(z) = z**5 + 2*z**4 + z**3 - 1. Let k(d) = a(d) - 6*g(d). Determine h so that k(h) = 0.
-1, 1, 45
Suppose -d + 3 = -7. Solve 223*l - 5*l**2 - 7 - 3 - 198*l - d*l**3 = 0.
-2, 1/2, 1
Let 171*w - 40*w**3 + 15*w**4 - 108 + 9*w**2 - 20*w**2 - 26*w**3 + 117*w - 10*w**2 = 0. What is w?
-2, 2/5, 3
Let k = 14 - 11. Suppose 2*x - 7 = -k. Suppose -2*m**4 + 2*m - 2*m**3 - 3*m**2 + 8*m**x - 3*m**2 = 0. Calculate m.
-1, 0, 1
Let w(u) = -6*u**3 + 13*u**2 + 57*u + 77. Let g(q) = -7*q**3 + 13*q**2 + 58*q + 80. Let z(y) = -7*g(y) + 8*w(y). Factor z(r).
(r + 2)*(r + 4)*(r + 7)
Suppose 24*u - 22*u = 6. Find m such that 20*m - 71*m**2 + 48*m**u + 32*m - 8*m**2 - 12 - 9*m**4 = 0.
2/3, 1, 3
Let u = -6562 + 137804/21. Factor -6/7*x - u*x**3 - 8/21 - 4/7*x**2.
-2*(x + 1)**2*(x + 4)/21
Let v = 11239/3620 + 69/724. Solve 8/5 - 2/5*d**3 - v*d + 2*d**2 = 0 for d.
1, 2
Solve -16*b**4 - 4 + 4*b**2 + 11*b + 12*b**4 + 4 - 16*b**3 + 5*b = 0.
-4, -1, 0, 1
Let g(s) = -43*s**2 + 85*s - 27 - 55*s**2 + 22*s**3 - 9*s**4 + 11*s**3 + 26*s**2. Let n(z) = z**4 - z**3 - z - 1. Let j(t) = g(t) + 5*n(t). Factor j(r).
-4*(r - 2)**3*(r - 1)
Let w = 5/96 - -619/96. Let o(q) = -q**3 + 33*q**2 + 3*q - 98. Let j be o(33). Factor 11/2*l - j + 2*l**3 - w*l**2.
(l - 2)*(l - 1)*(4*l - 1)/2
Let o = 14 + -17. Let n be o + 3 + 2 + 0. Factor 17 + 12*g + 4 - 4 - 5 + 3*g**n.
3*(g + 2)**2
Let l(c) be the second derivative of -7*c**5/10 + 5*c**4 - 29*c**3/3 + 6*c**2 - 8*c. Find t such that l(t) = 0.
2/7, 1, 3
Let s(d) be the second derivative of -d**6/30 - d**5/5 + d**4/12 + 2*d**3/3 - 50*d. Suppose s(j) = 0. Calculate j.
-4, -1, 0, 1
Let g(f) = 11*f**2 + 44*f - 3. Let j(p) = 130*p**2 + 525*p - 35. Let r(x) = 35*g(x) - 3*j(x). Suppose r(m) = 0. Calculate m.
-7, 0
Let v(n) be the second derivative of -n**6/6 + 5*n**5/4 - 5*n**4/2 - 10*n**3/3 + 20*n**2 - 2*n - 4. Suppose v(w) = 0. What is w?
-1, 2
Let x(b) be the first derivative of -1/25*b**5 + 2/15*b**3 + 1/30*b**6 - 1/5*b + 1/10*b**2 - 1/10*b**4 - 14. Factor x(y).
(y - 1)**3*(y + 1)**2/5
Let v(g) = 16*g. Let k be v(-1). Let s = k + 26. Solve -119*n**2 - 12 - 38*n**3 + 18*n**3 - 29*n**3 - s*n + 90*n = 0 for n.
-3, 2/7
Let d(k) be the third derivative of k**6/1800 - k**5/120 + k**4/30 + 5*k**3 + 29*k**2. Let c(u) be the first derivative of d(u). Let c(w) = 0. What is w?
1, 4
Let r(v) be the first derivative of -v**3/3 - 7*v**2/2 - 12*v - 84. Factor r(k).
-(k + 3)*(k + 4)
Let g(q) = q**2 - 6*q - 135. Let j be g(-9). Factor j + 0*l - 2/5*l**3 - 2/5*l**4 + 0*l**2.
-2*l**3*(l + 1)/5
Suppose 6*b - 20*b = -28. Let t(h) be the first derivative of 2/3*h**3 - 2/3*h**b + 0*h - 1/6*h**4 + 1. Let t(x) = 0. Calculate x.
0, 1, 2
Suppose -12 = 3*f - 48. Suppose -4*x = -2*l - f, 2*l + 3 + 5 = 2*x. Factor 0 + 1/5*b**x - 1/5*b.
b*(b - 1)/5
Let q be 8 - 12 - 1*(-8 - -4). Factor 0 + 1/4*x**4 + q*x + 2*x**3 + 4*x**2.
x**2*(x + 4)**2/4
Let z = 1192 - 1190. Factor 18/5*q**4 + 0 - z*q**2 - 2/5*q - 6/5*q**3.
2*q*(q - 1)*(3*q + 1)**2/5
Let t be (-4 + -3 - -3) + (14 - -10). Suppose 5*p - j - 2*j = 15, t = 2*p - 4*j. Let -6/7*b**2 + 2/7*b - 2/7*b**4 + 6/7*b**3 + p = 0. What is b?
0, 1
Let q(h) = -h**3 - 4*h**2 + h + 23. Let f be q(-7). Let v = 163 - f. Factor 2/3*w**4 + v*w**3 - 1/3*w - 2/3*w**2 + 1/3*w**5 + 0.
w*(w - 1)*(w + 1)**3/3
Let c(r) = 3 - r + 2 + 4 - 5. Let z be c(-4). Find y such that -10*y - z*y**3 + 13*y + 4*y**4 - 3*y + 4*y**2 = 0.
0, 1
Let r(g) = 2*g**2 + g. Let s(j) = 9*j**2 + 3. Let z(y) = 4*r(y) - s(y). Factor z(q).
-(q - 3)*(q - 1)
Let v(h) be the first derivative of h**9/1008 - h**8/280 - 3*h**7/280 + 16*h**3/3 - 10. Let w(l) be the third derivative of v(l). Find d, given that w(d) = 0.
-1, 0, 3
Suppose -8/15 - 4802/15*t**2 + 392/15*t = 0. Calculate t.
2/49
Suppose -11*n = -15*n - 24. Let f(k) = -k**3 - 7*k**2 - 9*k - 13. Let o be f(n). Factor 1/2*a**2 - 1/4 - 1/4*a**o + 1/2*a**3 - 1/4*a - 1/4*a**4.
-(a - 1)**2*(a + 1)**3/4
Let p(a) be the second derivative of 0*a**3 + 0 + 18*a + 0*a**4 + 1/225*a**6 + 0*a**2 + 1/50*a**5. Factor p(d).
2*d**3*(d + 3)/15
Let z(k) = -k**3 - k**2 + 2*k + 1. Let g(n) = -5*n**4 + 20*n**3 + 110*n**2 + 55*n - 205. Let u(s) = g(s) + 25*z(s). Factor u(l).
-5*(l - 4)*(l - 1)*(l + 3)**2
Let w(d) = 5*d**2 + 31*d - 43. Let o(p) be the third derivative of p**5/30 + 5*p**4/12 - 7*p**3/3 - 11*p**2. Let n(u) = -7*o(u) + 2*w(u). Factor n(k).
-4*(k - 1)*(k + 3)
Suppose -3 = 3*f + 3, -4 = 2*v + 2*f. Suppose -d - 2*l + 10 = v, 2*d + 16 = 4*l + 4. Factor -3/2*i - 3/4 - 3/4*i**d.
-3*(i + 1)**2/4
Let z be 20 + (-4 - -8) + 0. Solve 16*q**3 - 27 + 13*q**3 - 47*q**3 + z*q**2 + 18*q + 3*q**4 = 0.
-1, 1, 3
Suppose -13*w - 22 = -256. Let y(j) be the first derivative of w*j - 5 - 5*j**3 + 39/2*j**2. Solve y(f) = 0.
-2/5, 3
Let g(k) = -k**2 - 81*k + 524. Let b be g(6). Determine m so that 9/4*m**b + 27/4*m + 15/4 - 3/4*m**3 = 0.
-1, 5
Let a(v) be the second derivative of -v**4/6 - 4*v**3 + 2*v - 7. Factor a(c).
-2*c*(c + 12)
Let b = 2 + 19. Suppose -b*h + 14*h = -21. Determine q, given that -2/5*q + 2/5*q**h + 2/5 - 2/5*q**2 = 0.
-1, 1
Let b(w) be the third derivative of -w**8/17640 - w**7/4410 + w**6/1260 - 3*w**3/2 + w**2. Let i(k) be the first derivative of b(k). Factor i(x).
-2*x**2*(x - 1)*(x + 3)/21
Let m(b) = 13*b**3 + 5*b**2. Let c(f) be the first derivative of f**4/4 + f**3/3 + 10. Let d(g) = 3*c(g) - m(g). Solve d(q) = 0 for q.
-1/5, 0
Let w be ((-3)/(-10*12/8))/(21/175). Factor 4/3*u**3 - 2/3 + 11/3*u**2 + w*u.
(u + 1)*(u + 2)*(4*u - 1)/3
Suppose 0*i - 12 = -2*i. Suppose 2*h = i*h - 16. Find g such that 11*g**2 + h - 4*g - 2 + 0*g - 9*g**2 = 0.
1
Suppose 48 = u + 50. Let v be ((-40)/100)/(1/(1 + u)). Factor v*n**2 - 2/5*n + 0.
2*n*(n - 1)/5
Let x = 135 + -133. Let m = 209/70 - 27/10. Factor -6/7*p - m*p**3 - 10/7*p**x + 18/7.
-2*(p - 1)*(p + 3)**2/7
Factor 10*t**2 - 8*t**4 + 7*t - 5 - 12*t + 10*t**3 + 2*t**4 - 5*t**5 + t**4.
-5*(t - 1)**2*(t + 1)**3
Let o(r) be the first derivative of -2*r**3/45 - 86*r**2/15 - 567. Factor o(j).
-2*j*(j + 86)/15
Factor 0 + 1/4*d**2 + 31/4*d.
d*(d + 31)/4
Suppose 1 = -3*b - 2, 3*b + 9 = 2*f. Factor 12*m**3 - 8*m**f + 1 - 12*m**2 - 1.
4*m**2*(m - 3)
Let d(j) be the third derivative of -j**5/140 - j**4/7 - 6*j**3/7 + 34*j**2 - 1. Factor d(h).
-3*(h + 2)*(h + 6)/7
Let n(t) be the first derivative of 6/5*t**3 - 3/4*t**4 + 6/5*t**2 + 3/25*t**5 - 8 - 24/5*t. Solve n(k) = 0 for k.
-1, 2
Let i = -65450 + 65454. Suppose -3*h - 2*h = 0. Factor 16/5*w**i + 4/5*w**5 + 0 + 8/5*w**2 + h*w + 4*w**3.
4*w**2*(w + 1)**2*(w + 2)/5
Suppose -2*z + 56 = -6*z. Let a = -11 - z. Factor a*u + 30*u**2 + 0*u - 9*u**5 + 33*u**4 + 1 - 46*u**3 - 12*u.
-(u - 1)**3*(3*u - 1)**2
Let v = 953 - 950. Suppose -2*p = -27 + 27. Factor -5/2*n**v - n**4 + p - 1/2*n - 2*n**2.
-n*(n + 1)**2*(2*n + 1)/2
Let n(x) = -2*x**3 + 22*x**2 + 47*x - 271. Let k be n(12). Determine q, given that -242/7*q**k + 0 - 88/7*q**4 + 234/7*q**3 + 88/7*q**2 + 8/7*q = 0.
-1, -2/11, 0, 1
Suppose 213 = 2*s - 9. Suppose -2*m - 103 = -s. Determine o, given that 0*o**2 + 0 + 1/5*o**m - 2/5*o**3 + 0*o = 0.
0, 2
Let w(y) = -4*y**3 + 38*y**2 - 160*y + 128. Let k(x) = x**3 - 2*x**2. Let p(q) = 2*k(q) + w(q). Determine o so that p(o) = 0.
1, 8
Suppose 27 = -5*w - q, 2*w - 9 = -4*q - 27. Let k be (-3 - w)/(3/6). Factor -2/5*n**2 + 0 + 0*n + 2*n**3 - 8/5*n**k.
-2*n**2*(n - 1)*(4*n - 1)/5
Let c(m) be the first derivative of 1/4*m**4 + 0*m + 0*m**2 - m