1)
Let b(k) be the third derivative of k**8/2520 + 3*k**7/175 + 49*k**6/450 + 71*k**5/225 + 31*k**4/60 + 23*k**3/45 - k**2 - 29*k. Suppose b(a) = 0. What is a?
-23, -1
Let r(c) = c**2 + 1. Let q be r(-2). Let y(w) = w**2 - 3*w + 1. Let m be y(q). What is d in 4 + 12*d + 4 - m*d**3 - 9*d**2 - 3*d**4 + 3*d**2 = 0?
-2, -2/3, 1
Suppose -b = 5*y + 4, 5*y + 20 = -0*y - 5*b. Let u = 3358/2013 + -1/671. Suppose 2/3*a**3 + 2/3*a**5 + u*a**4 + y + 0*a + 0*a**2 = 0. What is a?
-2, -1/2, 0
Let h(q) be the first derivative of q**3/18 + 10*q**2/3 + 37*q/2 + 418. Factor h(i).
(i + 3)*(i + 37)/6
Let w = 12 + -7. Let l(d) = d**2 - 38*d - 77. Let r be l(-2). Factor -3*s**5 - r*s**5 + 8*s**4 + 2*s**w.
-4*s**4*(s - 2)
Factor 11/3*g + 13/3*g**3 + 0 + 23/3*g**2 + 1/3*g**4.
g*(g + 1)**2*(g + 11)/3
Let q(s) = 4*s**2 - 2*s + 8. Let t be q(2). Let h be (0 - (-8)/t)*5. Factor 0 - 3/7*b + 3/7*b**h.
3*b*(b - 1)/7
Let p(s) be the second derivative of 3*s**6/200 + s**5/25 - 11*s**4/120 + s**3/15 + 11*s**2/2 - 3*s. Let i(l) be the first derivative of p(l). Factor i(v).
(v + 2)*(3*v - 1)**2/5
Let f(h) = -2*h**2. Let w(c) = 7*c - 6. Let l(g) = 8*g - 7. Let r(m) = -6*l(m) + 7*w(m). Let k(y) = -f(y) + 2*r(y). Factor k(j).
2*j*(j + 1)
Let l(h) = -2*h**3 + 204*h**2 + 2*h - 201. Let x be l(102). Factor 0*r + 1/8*r**x + 0*r**2 + 0.
r**3/8
Suppose 5*x - 5*g - 405 = 0, -3*x + 231 = -0*x + 3*g. Let n = x + -155/2. Suppose 3 - n*z - 3/2*z**2 = 0. Calculate z.
-2, 1
Let h(j) = -36*j**2 + 48*j - 27. Let f(w) = w**2 - w - 5. Let c(p) = 3*f(p) - h(p). Factor c(x).
3*(x - 1)*(13*x - 4)
Let a = -2627 + 2627. Let -t**3 - 2/3*t + 5/3*t**2 + a = 0. Calculate t.
0, 2/3, 1
Let g be 28 - (13 - -31)/11. Find v, given that g + 3/2*v**2 + 12*v = 0.
-4
Suppose 27219*s - 27228*s + 36 = 0. Factor 2/3*m**s + 9/2 + 39/2*m**2 - 45/2*m - 37/6*m**3.
(m - 3)**3*(4*m - 1)/6
Let 128/11*f**2 - 4*f**4 - 236/11*f**3 - 2/11*f**5 + 58*f - 44 = 0. Calculate f.
-11, -2, 1
Let q(d) be the second derivative of -2*d**7/63 - 16*d**6/15 + 5*d**5/3 - 16*d + 1. Factor q(y).
-4*y**3*(y - 1)*(y + 25)/3
Let h be (18/(-30))/((-12)/(-40)*-1). Let p(n) be the first derivative of -2/11*n**2 - 2/11*n - h - 2/33*n**3. Factor p(v).
-2*(v + 1)**2/11
Let o(q) = -2*q**2 - q + 3. Let n(k) = k**4 - 2*k**3 + 9*k**2 + 7*k - 15. Let h(t) = n(t) + 5*o(t). Suppose h(d) = 0. What is d?
-1, 0, 1, 2
Let q(f) be the third derivative of f**7/840 + f**6/360 + 2*f**3/3 + 6*f**2. Let u(j) be the first derivative of q(j). Factor u(p).
p**2*(p + 1)
Let j = -9709/4 - -2428. Let i(b) be the first derivative of 0*b**2 + 9 + 0*b - j*b**4 + 0*b**3 - 3/5*b**5. Solve i(g) = 0.
-1, 0
Solve -34/21*u**3 + 0*u + 2/3*u**4 + 2/21*u**5 + 0 + 6/7*u**2 = 0.
-9, 0, 1
Let u be (-56)/(-90) + 4/(-18). Let w be (-44)/11*(-7 + 2)/25. Find v such that -v + 3/5*v**3 + u - w*v**2 = 0.
-1, 1/3, 2
Let p be 6/(-5)*1*(-130)/78. Let i = -44/27 - -1084/135. Determine q so that -i + 16/5*q - 2/5*q**p = 0.
4
Let j be (-24)/(-14) - (-18)/63. Let -6*i**j + 5*i**2 + 5*i**2 = 0. Calculate i.
0
Factor -53824 - 486*x**3 - 62976*x**2 - 450*x**3 - 108576*x - 4*x**4 + 7292*x**2.
-4*(x + 1)**2*(x + 116)**2
Let v = -352 - -1058/3. Let i(r) be the first derivative of 4/3*r - 2 + v*r**2 + 1/9*r**3. Factor i(s).
(s + 2)**2/3
Let u = -469/1230 - -17/41. Let m(l) be the second derivative of -1/10*l**2 - u*l**3 + 1/30*l**4 + 1/50*l**5 - 1/210*l**7 + 0 - 7*l - 1/150*l**6. Factor m(y).
-(y - 1)**2*(y + 1)**3/5
Let p(u) be the first derivative of -u**4/4 + 17*u**3/9 + 9*u**2 + 16*u/3 + 130. Factor p(h).
-(h - 8)*(h + 2)*(3*h + 1)/3
Let v(k) be the first derivative of -k**4/72 + k**3/36 + 3*k + 1. Let w(h) be the first derivative of v(h). Factor w(g).
-g*(g - 1)/6
Factor -68*g - 220*g + 6036 + 22*g**2 - g**3 + 11*g**2 - 5780.
-(g - 16)**2*(g - 1)
Let o be ((-6)/2)/(3/(-14)). Let d = o - 9. Determine r so that -24*r**3 - 14*r**5 - 74*r**4 + 8*r - 2*r**4 - 26*r**d + 20*r**2 = 0.
-1, -2/5, 0, 1/2
Let k(f) be the third derivative of f**8/33600 - f**7/2800 + 7*f**5/60 + 4*f**2. Let n(q) be the third derivative of k(q). Find r such that n(r) = 0.
0, 3
Let c(q) = 6*q**2 - 46*q + 54. Let l(y) = -y**2 + 9*y - 11. Let x(p) = -3*c(p) - 14*l(p). Factor x(a).
-4*(a - 2)*(a - 1)
Let l(j) be the second derivative of -j**7/84 + 17*j**6/20 - 78*j**5/5 - 169*j**4/6 - 15*j. Factor l(c).
-c**2*(c - 26)**2*(c + 1)/2
Let j(p) be the third derivative of -289*p**6/160 + 493*p**5/80 - 15*p**4/2 + 9*p**3/2 - 10*p**2 + 2*p. Factor j(l).
-3*(l - 1)*(17*l - 6)**2/4
Let y(g) be the third derivative of g**6/540 - 53*g**5/270 + 154*g**4/27 + 784*g**3/9 - 291*g**2. Solve y(x) = 0.
-3, 28
Suppose z = 3 - 1. Suppose 0 = -u - 2*w + 4, -2*u + z*w = u - 4. Factor 11*f + u*f - 4*f**2 - f.
-4*f*(f - 3)
Let t(s) be the third derivative of s**6/24 - s**5/12 - 5*s**4/24 + 5*s**3/6 + 4*s**2 - 2. Find a, given that t(a) = 0.
-1, 1
Let x(v) be the second derivative of -v**5/20 + 131*v. Factor x(z).
-z**3
Factor -30*t**3 + 2*t - 26*t**4 + 38*t**4 - 26*t**4 - 10*t - 2*t**5 - 26*t**2.
-2*t*(t + 1)**3*(t + 4)
Let v = 80641/80 - 1008. Let d(f) be the third derivative of 7/120*f**5 + v*f**6 + 1/12*f**3 - 4*f**2 + 5/48*f**4 + 0*f + 0. Factor d(c).
(c + 1)**2*(3*c + 1)/2
Let i(j) be the second derivative of j**6/10 + 12*j**5/5 + 23*j**4/2 - 72*j**3 + 243*j**2/2 - 40*j - 1. Factor i(y).
3*(y - 1)**2*(y + 9)**2
Let m(s) = -s**3 + 66*s**2 + 717*s + 1153. Let n(i) = 68*i**2 + 716*i + 1154. Let t(u) = 2*m(u) - 3*n(u). Factor t(k).
-2*(k + 2)*(k + 17)**2
Let k(w) = 0 + 0*w - 3 + w - 2. Let q be k(7). Suppose 4*y + q*y**2 + y**3 - 2*y**3 - y**3 = 0. Calculate y.
-1, 0, 2
Let b(y) be the second derivative of -y**6/3420 + y**5/1140 - 3*y**3/2 - y. Let j(n) be the second derivative of b(n). Factor j(k).
-2*k*(k - 1)/19
Let o(w) be the second derivative of -w**7/105 + 2*w**6/75 - w - 17. Solve o(m) = 0 for m.
0, 2
Let u = -2/1735 + 3636/144005. Let n = u - -986/415. Factor -2/5*b - 8/5*b**4 + 0 - n*b**3 - 2/5*b**5 - 8/5*b**2.
-2*b*(b + 1)**4/5
Let w = 640/39 + 64/13. Let n = w - 21. Factor 2*t + 3 + n*t**2.
(t + 3)**2/3
Let z(v) = -2*v**4 - 10*v**3 + 21*v**2 + 13*v - 25. Let y(c) = 3*c**4 + 21*c**3 - 42*c**2 - 26*c + 49. Let s(r) = 6*y(r) + 10*z(r). Solve s(o) = 0.
-1, 1, 2, 11
Let t = 6/2131 - -57513/8524. Factor 3/2 - 15/4*z**3 - t*z + 9*z**2.
-3*(z - 1)**2*(5*z - 2)/4
Let u(r) = r + 20. Let b be u(-17). Factor -i**b + 23*i + 26*i - 5 - 60*i - 7*i**2.
-(i + 1)**2*(i + 5)
Let i = -1728 + 209087/121. Let k = 118/363 - i. Factor 0*x + 0 + k*x**5 - 4/3*x**2 + x**4 + 0*x**3.
x**2*(x - 1)*(x + 2)**2/3
Let c(g) be the second derivative of -9*g**7/98 - 87*g**6/70 - 66*g**5/35 + 142*g**4/7 - 264*g**3/7 + 216*g**2/7 + 402*g. Solve c(z) = 0.
-6, 2/3, 1
Factor -6*r**2 + 3*r**2 - 5*r**2 - 33*r**5 + 38*r**5 + 10*r**3 + 0*r**2 + 23*r**4.
r**2*(r + 1)*(r + 4)*(5*r - 2)
Suppose -3*x + 7 = 1. Let b be (x - 3) + 3/1. Let 2*f - 5*f + 5 - 1 - 3*f**b + 3*f**3 - 1 = 0. What is f?
-1, 1
Let d(a) be the second derivative of a**5/10 - 7*a**4/6 + 11*a**3/3 - 5*a**2 - 35*a. Suppose d(y) = 0. What is y?
1, 5
Suppose 4317*m - 4324*m = -14. Suppose 1/4*f**m + 0*f - 1 = 0. What is f?
-2, 2
Let k(m) be the second derivative of m**6/420 - m**5/105 - m**4/84 + 2*m**3/21 - 4*m**2 - 9*m. Let z(l) be the first derivative of k(l). Factor z(p).
2*(p - 2)*(p - 1)*(p + 1)/7
Suppose 0 = 2*n + 2*n. Find f such that 4*f - 3*f**3 + 5*f + 3*f**2 - 3*f + n*f**3 = 0.
-1, 0, 2
Let x be 4 - 0*3/12. Let y(a) = -1. Let i(w) = w**2 + 2*w + 2. Let h(u) = x*y(u) + 2*i(u). Suppose h(q) = 0. Calculate q.
-2, 0
Let -4220*o + 7*o**2 + 1985*o + 1785*o + 128 = 0. Calculate o.
2/7, 64
Let l = -50 + 168. Let j be l/42 - 1/6*-2. Factor -4/7 + j*m**2 + 18/7*m.
2*(m + 1)*(11*m - 2)/7
Let u(p) = 2 - 8*p - 216*p**3 - 6*p + 7*p**4 + 224*p**3 + 3*p**2. Let v(o) = 13*o**4 + 15*o**3 + 5*o**2 - 27*o + 3. Let z(g) = 11*u(g) - 6*v(g). Factor z(h).
-(h - 2)*(h + 1)**2*(h + 2)
Factor 27*d**2 + 64 + 18*d**3 - 132*d + 45*d**2 + 20*d**3 - 42*d**3.
-4*(d - 16)*(d - 1)**2
Suppose -137*c + 141*c + 4 = 0. Let s be c/(-5) + 299/805. Determine z so that -169/7*z**2 - s + 52/7*z = 0.
2/13
Let u = 17/11 - 52/55. Let q(x) be the first derivative of 0*x + 3 + 3/8*x**2 - x**3 + u*x**5 - 3/16*x**4. Determine f, given that q(f) = 0.
-1, 0, 1/4, 1
Let j be (