, 2/13
Let v(b) = b**2 - 3*b + 47. Let a be v(0). Let p be -48 + a + 6/4 + 0. Factor -1/2*s**4 - 3/2*s**3 - 3/2*s**2 - p*s + 0.
-s*(s + 1)**3/2
Let o(f) = 6*f**2 + 63*f. Let p be o(0). Suppose p*l + 0 - 15*l**3 + 5/2*l**4 + 45/2*l**2 = 0. What is l?
0, 3
Let g = 176 + -172. Factor -17*h**2 + 4*h**2 - 8*h + h**2 + 0*h**3 - g*h**3.
-4*h*(h + 1)*(h + 2)
Let h(m) be the second derivative of m**5/5 - 2*m**4/3 - 8*m**3/3 + 16*m**2 - 143*m. Suppose h(o) = 0. What is o?
-2, 2
Let b(w) be the first derivative of w**6/45 + 3*w**5/10 + 2*w**4/3 - 5*w**3/3 + 4. Let z(g) be the third derivative of b(g). Factor z(s).
4*(s + 4)*(2*s + 1)
Let u(k) be the first derivative of 45*k**6 + 267*k**5 + 530*k**4 + 360*k**3 - 80*k - 303. Find c, given that u(c) = 0.
-2, -2/3, -1/2, 2/9
Factor -19208/9 - 392/9*k - 2/9*k**2.
-2*(k + 98)**2/9
Let w be -17*3/(-408) + (-30)/(-16). Factor 0 - 1/4*q**3 + 0*q - 1/4*q**w.
-q**2*(q + 1)/4
Let h be -13 + (23 - 10/2). Suppose 0*f**4 - 1/5*f**h + 2/5 - 2/5*f**2 + 4/5*f**3 - 3/5*f = 0. What is f?
-2, -1, 1
What is p in -18/11 + 24/11*p**3 + 6/11*p**4 + 12/11*p**2 - 24/11*p = 0?
-3, -1, 1
Let d(n) be the second derivative of -2/3*n**2 - 1/9*n**4 + 4/9*n**3 + 2*n + 0. Factor d(v).
-4*(v - 1)**2/3
Factor 893*g - 4*g**2 - 2*g**2 + 3*g**2 - 944*g.
-3*g*(g + 17)
Suppose 3 = -4*c + 7. Let q(j) = 46*j**2 + 25*j + 4. Let m(i) = -i**2 - i. Let p(d) = c*q(d) - 3*m(d). Find x such that p(x) = 0.
-2/7
Let x(t) be the second derivative of 0 - t + 10/3*t**3 + 5/24*t**4 - 1/3*t**5 + 7*t**2 - 1/24*t**6. Let o(m) be the first derivative of x(m). Factor o(r).
-5*(r - 1)*(r + 1)*(r + 4)
Let u(y) be the first derivative of y**5/55 - 7*y**4/22 + 25*y**3/33 - 6*y**2/11 - 55. Find k such that u(k) = 0.
0, 1, 12
Suppose -i = 5*l - 6, 0 = -2*l + 4*i - 6 + 4. Let x(s) = s**3 - s**2 + s. Let y(b) = 7*b**3 + 17*b**2 + 31*b + 12. Let r(n) = l*y(n) - 3*x(n). Factor r(d).
4*(d + 1)**2*(d + 3)
Let d(y) be the second derivative of 5*y**4/48 - 75*y**3/8 + 215*y**2/4 + 228*y. Let d(p) = 0. Calculate p.
2, 43
Let g = 128243/3 - 42746. Factor 5/3*s**2 - 10/3 - g*s.
5*(s - 2)*(s + 1)/3
Let v be (-156)/48*(-18)/39. Solve 9/2 - v*k + 1/8*k**2 = 0 for k.
6
Let f(x) be the third derivative of x**8/20160 - x**7/840 + x**4/8 + 10*x**2. Let m(q) be the second derivative of f(q). Factor m(d).
d**2*(d - 9)/3
Let m(b) = -9*b**4 + 11*b**3 - 10*b**2 - 8*b. Let x = -42 - -18. Let q(v) = v**4 - v**3 + v**2 + v. Let s(l) = x*q(l) - 3*m(l). Factor s(r).
3*r**2*(r - 2)*(r - 1)
Let v(n) be the first derivative of -4/5*n**3 - 15 + 3/2*n**2 + 3/20*n**4 - 6/5*n. Let v(w) = 0. Calculate w.
1, 2
Suppose 0 = -109*m + 122*m - 52. Let j(k) be the third derivative of 1/735*k**7 + 4*k**2 + 1/84*k**m - 1/210*k**5 - 1/420*k**6 + 0*k**3 + 0 + 0*k. Factor j(v).
2*v*(v - 1)**2*(v + 1)/7
Let r(z) = 14*z**2 - 52*z + 6. Let k(v) = 5*v**2 - 17*v + 2. Let b = 54 + -49. Let s(a) = b*r(a) - 16*k(a). Factor s(d).
-2*(d - 1)*(5*d - 1)
Suppose 74*v - 5*d - 12 = 73*v, -v = d. Determine o so that 0 - 2/5*o + 2/15*o**v = 0.
0, 3
Let s be 12/6 + 5*7. Factor 25*g + 15*g**3 + s - 61*g - 49 - 9*g**2.
3*(g - 2)*(g + 1)*(5*g + 2)
Let i(k) be the first derivative of 1/6*k**4 - k**2 - 1/20*k**5 + 1/6*k**3 + 2*k + 3. Let t(m) be the first derivative of i(m). Factor t(o).
-(o - 2)*(o - 1)*(o + 1)
Let u(q) be the third derivative of 2/135*q**5 + 35*q**2 - 1/36*q**4 - 1/540*q**6 + 0*q + 0*q**3 + 0. Factor u(s).
-2*s*(s - 3)*(s - 1)/9
Suppose 2 = r + 3 - 2. Let r + 1/2*h**2 - 5/2*h + h**3 = 0. Calculate h.
-2, 1/2, 1
Let r be (-4)/(-8)*((-6)/(-2) + 1). Find x such that 10/3*x**r + 4/3 + 22/3*x = 0.
-2, -1/5
Let h(l) = l**3 - 2*l**2 + l + 1. Let x be h(1). Suppose -27 = -5*q + 4*k - 3, -x = k. Solve 0*f**5 - 176*f**4 - q*f**5 + 184*f**4 - 4*f**3 = 0 for f.
0, 1
Solve -878/5*q + 42/5*q**2 - 84/5 = 0.
-2/21, 21
Let w(b) = 6*b**2 + 130*b + 40. Let d(q) = -4*q**2 - 130*q - 41. Let t(x) = 4*d(x) + 5*w(x). Factor t(f).
2*(f + 9)*(7*f + 2)
Let o(a) be the second derivative of a**5/20 - 7*a**4/6 + 41*a**3/6 + 28*a**2 + 227*a. Solve o(l) = 0 for l.
-1, 7, 8
Let u(v) be the second derivative of v**4/78 + 12*v**3/13 + 35*v**2/13 + 11*v - 18. Factor u(h).
2*(h + 1)*(h + 35)/13
Let w(v) be the third derivative of -v**7/30 + 17*v**6/120 + v**5/60 - 17*v**4/24 + v**3 + 149*v**2. Suppose w(y) = 0. Calculate y.
-1, 3/7, 1, 2
Determine y, given that -16/7*y**4 + 0*y**3 - 4/7*y**5 + 0 + 64/7*y**2 + 64/7*y = 0.
-2, 0, 2
Let m(u) = -3*u - 62. Let a be m(-25). Suppose -16*k = -a*k. Factor 0 + 3*r**4 + 15/4*r**3 + 3/4*r**2 + k*r.
3*r**2*(r + 1)*(4*r + 1)/4
Suppose -5*f**4 + 10*f**4 + 10*f**3 - 3004*f**2 + 50*f + 2939*f**2 = 0. Calculate f.
-5, 0, 1, 2
Let q(g) = 460*g**2 - 155*g - 1980. Let a(b) = -21*b**2 + 7*b + 90. Let x(d) = -45*a(d) - 2*q(d). Find l such that x(l) = 0.
-9/5, 2
Let j be (4/(-2) - -2)*2/(-10). Let k(r) be the second derivative of -3/40*r**5 + 3/4*r**2 + j - 7*r - 1/8*r**4 + 1/4*r**3. Suppose k(q) = 0. What is q?
-1, 1
Suppose 4*x - 2*r - 122 = -4*r, 0 = -5*r + 5. Let o be (-297)/(-132)*8/x. Factor 3/5*c**4 + 0 + o*c**2 - 6/5*c**3 + 0*c.
3*c**2*(c - 1)**2/5
Let m(n) be the first derivative of -56/15*n**3 + 8/5*n + 24 + n**4 + 14/5*n**2. Solve m(l) = 0 for l.
-1/5, 1, 2
Let k(q) = -q**3 - 2*q**2 - 2. Let x be k(-3). Suppose 0 = 2*m - x*m + 10. Factor m*l**2 + 0*l**2 + l**2.
3*l**2
Let z(y) be the second derivative of -y**7/105 + 7*y**6/75 - 3*y**5/25 + 3*y + 33. Factor z(l).
-2*l**3*(l - 6)*(l - 1)/5
Let a(k) be the first derivative of 2*k**3/33 - 10*k**2/11 - 2*k - 89. Factor a(g).
2*(g - 11)*(g + 1)/11
Let n be 19/5 - 11/(-55). What is l in n*l**2 - 2 + 38*l - 3*l**2 - 37*l = 0?
-2, 1
Let u = -476 + 9523/20. Let g(j) be the second derivative of 1/2*j**3 + 1/2*j**4 + u*j**5 + 2*j + 0 + 0*j**2. Factor g(o).
3*o*(o + 1)**2
Let t(q) = 10*q**2 + 55*q - 80. Let s(p) = 11*p**2 + 53*p - 82. Let r(k) = 5*s(k) - 6*t(k). Let r(n) = 0. Calculate n.
-14, 1
Let x(h) be the second derivative of h**4/42 + 64*h**3/21 + 1024*h**2/7 - 58*h. Factor x(r).
2*(r + 32)**2/7
Let c(n) be the first derivative of -5*n**4/8 - 5*n**3/3 - 5*n**2/4 - 117. Suppose c(b) = 0. What is b?
-1, 0
Let r(y) = y**3 + y**2 - 2. Let h be r(-2). Let m = h - -7. Determine c so that 21*c**3 + 4 + m + 9 + 15*c**2 - 2 - 48*c = 0.
-2, 2/7, 1
Let h be ((-7262)/(-5))/(3/(-585)*-14044). Let f = 2/10533 + h. Let -77/6*r**2 - f*r**3 + 20/3*r - 2/3 = 0. Calculate r.
-1, 2/11
Factor -1331*x - 14641/4 - 11*x**3 - 1/4*x**4 - 363/2*x**2.
-(x + 11)**4/4
Let x(g) = -99*g + 108*g + g**3 + 2 + 10*g**2 + 0*g**3. Let s be x(-9). Factor -1/3*z - 1/6*z**4 + 0 + 1/2*z**s + 0*z**3.
-z*(z - 1)**2*(z + 2)/6
Let u(o) be the third derivative of 13*o**2 + 3/7*o**5 + 0 + 9/7*o**4 + 0*o + 1/735*o**7 - 72/7*o**3 + 17/420*o**6. Factor u(c).
2*(c - 1)*(c + 6)**3/7
Let p(n) = n**2. Let f = -34 - -31. Let t(i) = -i**4 - i**3 - 2*i**2 + i. Let l(k) = f*p(k) - t(k). Find a such that l(a) = 0.
-1, 0, 1
Let l(h) be the third derivative of 1/12*h**3 + 1/120*h**5 + 1/24*h**4 + 0 + 14*h**2 + 0*h. Factor l(a).
(a + 1)**2/2
Let o(m) be the second derivative of -m**5/4 - 5*m**4/3 - 25*m**3/6 - 5*m**2 - 11*m + 6. Find u, given that o(u) = 0.
-2, -1
Let n(p) = 5*p - 9. Let y be 3 - -2 - (-5 + 2). Let v be n(y). Factor -36 - v*b + 11*b + b**3 - 28*b**2 - 40*b - 5*b**3.
-4*(b + 1)*(b + 3)**2
Let h be 108/(-30)*(-3)/(12/10). Factor -14*b**3 + 13*b**3 - 7*b - b**2 + h*b.
-b*(b - 1)*(b + 2)
Let g(p) be the first derivative of -p**6/90 - 9*p + 1. Let y(d) be the first derivative of g(d). Determine c, given that y(c) = 0.
0
Let j(v) be the second derivative of 2*v + 0 - 1/6*v**4 + 0*v**2 + 1/3*v**3. Factor j(n).
-2*n*(n - 1)
Let u(i) be the second derivative of -i**5/90 + 7*i**4/54 - 2*i**3/9 + i. Factor u(b).
-2*b*(b - 6)*(b - 1)/9
Let y(q) be the second derivative of -q**5/120 - 55*q**4/24 - 747*q**3/4 + 6889*q**2/12 - 588*q. Factor y(b).
-(b - 1)*(b + 83)**2/6
Factor -77*c**2 + 28220*c - 55*c**2 + 478*c**2 + 86*c**2 + 236*c**2 + 4*c**3 + 27556.
4*(c + 1)*(c + 83)**2
Let x(a) be the second derivative of a**4/72 - 5*a**3/6 + 8*a - 5. Find m, given that x(m) = 0.
0, 30
Let s(a) = 2*a**3 - 7*a**2 - a. Let k(w) be the second derivative of 0*w**2 + 1/12*w**4 + 1/6*w**3 + 0 - 10*w. Let b(q) = -3*k(q) - s(q). Factor b(m).
-2*m*(m -