1)*(u + 1)**3/2
Suppose -10 - 8 = -3*d. Let v be d/(-60) + (-47)/(-70). Factor v*l + 0 + 4/7*l**2.
4*l*(l + 1)/7
Suppose -2*g = -3*y + 8, -5*g + 32 = 3*y + 10. Factor -3*h - h**g + 9 + 4*h + 5*h - 2.
-(h - 7)*(h + 1)
Let m(x) be the first derivative of 2*x**5 - 5*x**4/4 - 40*x**3/3 + 10*x**2 + 66. Let m(a) = 0. Calculate a.
-2, 0, 1/2, 2
Let a be 17 - ((-12)/(-8))/((-1)/2). Let b(i) = -i**3 - i**2. Let p(j) = -5*j**3 - 6*j**2 - j. Let n(d) = a*b(d) - 5*p(d). Factor n(u).
5*u*(u + 1)**2
Let w be -4*(-15)/12 + 0. Factor 6*o**4 + 7*o**4 - 3*o**5 - 45*o**3 + w*o**4 + 27*o**2 + 3*o**4.
-3*o**2*(o - 3)**2*(o - 1)
Let c be (-25)/(-2) + (-3)/6. Find g such that c + 59*g - 4*g**2 - 31*g - 36*g = 0.
-3, 1
Let q(d) be the second derivative of 5*d**4/12 - 5*d**3 + 25*d**2/2 + 279*d. Factor q(w).
5*(w - 5)*(w - 1)
Let i(k) be the third derivative of k**7/168 - k**6/36 - k**5/6 + k**4/6 - 4*k**2. Let l(t) be the second derivative of i(t). Solve l(z) = 0.
-2/3, 2
Let l(f) = -f**2 + f - 1. Let o(v) = -6*v**2 + 51*v + 30. Let w(y) = -9*l(y) + o(y). Suppose w(i) = 0. Calculate i.
-13, -1
Let m(q) be the second derivative of 1/20*q**4 + 0 + 16*q + 1/100*q**5 + 0*q**3 - 2/5*q**2. Factor m(r).
(r - 1)*(r + 2)**2/5
Find x such that 4*x**3 - 3*x**3 - 3*x**3 - 6*x**2 + 20*x = 0.
-5, 0, 2
Factor 0 + 9522/7*d + 2/7*d**3 + 276/7*d**2.
2*d*(d + 69)**2/7
Let a(u) = 4*u + 104. Let w be a(0). Let x = w - 102. What is h in -2/5*h + 3/5*h**x + 0 - 1/5*h**3 = 0?
0, 1, 2
Let b(x) be the second derivative of -x**4/4 - 13*x**3 + 81*x**2/2 - 2*x. Factor b(s).
-3*(s - 1)*(s + 27)
Let f(o) be the third derivative of 3*o**8/392 + o**7/35 + o**6/42 - o**5/35 - o**4/28 + o**3/21 + 72*o**2. Factor f(g).
2*(g + 1)**3*(3*g - 1)**2/7
Let t = -3959 - -11878/3. Factor t*h**3 - h**2 + 1 - 1/3*h.
(h - 3)*(h - 1)*(h + 1)/3
Let z(x) be the first derivative of 26 - 2/7*x**2 + 2/21*x**3 + 0*x. Let z(m) = 0. Calculate m.
0, 2
Let -32/3*w - 10*w**2 + 0 + 2/3*w**3 = 0. What is w?
-1, 0, 16
Let a(b) = 9*b**3 + 9*b**2 + 11*b + 6. Let u(f) = f**3 + f + 1. Suppose 0 = 11*r - 10*r. Suppose 3*x = -r*x + 15. Let y(s) = x*u(s) - a(s). Factor y(m).
-(m + 1)**2*(4*m + 1)
Let s(p) = -21*p**2 + 11*p + 13. Let k(h) = -10*h**2 + 6*h + 6. Let y = 32 + -26. Let u(w) = y*s(w) - 13*k(w). What is c in u(c) = 0?
0, 3
Let w(i) be the second derivative of -80/33*i**3 - 34*i - 9/55*i**6 - 24/11*i**4 - 16/11*i**2 - 54/55*i**5 + 0. Let w(r) = 0. What is r?
-2, -2/3
Suppose 99 - 4 = 40*k + 15. Factor 1/6*x**5 - 4/3*x + 2/3*x**k + x**3 - 5/6*x**4 + 0.
x*(x - 2)**3*(x + 1)/6
Let a(k) be the second derivative of 3/100*k**5 + 0 + 0*k**2 - 16*k + 0*k**3 - 1/30*k**4 - 1/150*k**6. Find r such that a(r) = 0.
0, 1, 2
Let d be 104/520 + 19/(-5)*-1. Let r(l) be the second derivative of -9*l + 0 + 0*l**2 - 1/110*l**5 - 1/22*l**d - 2/33*l**3. Solve r(v) = 0 for v.
-2, -1, 0
Let a(j) = 2*j**2 + 238*j - 1240. Let u be a(-124). Find x such that u - 3/2*x**2 + 3*x = 0.
0, 2
Suppose 6*n = 4*n + 6. Suppose -5*q + 5*m + 8 = n, 0 = -2*m + 2. Factor 1/3*t**3 + 0 - 1/3*t**4 - 1/3*t**5 + 0*t + 1/3*t**q.
-t**2*(t - 1)*(t + 1)**2/3
Let w = -49/15 + 199/60. Let n(z) be the second derivative of -w*z**4 - 1/5*z**3 - 3/10*z**2 - 9*z + 0. Factor n(s).
-3*(s + 1)**2/5
Let y = -11875 - -106877/9. Solve y*s**2 + 16/9*s + 32/9 = 0.
-4
Factor 6/7*g**3 - 2/7*g**5 + 0 + 0*g**4 + 0*g + 4/7*g**2.
-2*g**2*(g - 2)*(g + 1)**2/7
Let d(w) be the first derivative of w**4/8 + w**3/3 - 31*w**2/4 + 14*w + 394. Let d(p) = 0. Calculate p.
-7, 1, 4
Let o(f) be the second derivative of 1/60*f**4 + 1/5*f**2 - 10*f - 1/10*f**3 + 0. Suppose o(i) = 0. What is i?
1, 2
Let l = -18943 + 18946. Suppose 18/11*g**2 - 16/11 - 4/11*g**l + 4/11*g - 2/11*g**4 = 0. What is g?
-4, -1, 1, 2
Let f = -33 - -36. Solve 25*b**2 + 29*b + 20 + 5*b + 6*b + 5*b**f = 0 for b.
-2, -1
Let d(f) = -4*f**4 + 14*f**3 + 24*f**2 - 55*f. Let k(y) = y**4 - 5*y**3 - 8*y**2 + 18*y. Let p(r) = -2*d(r) - 7*k(r). Determine b, given that p(b) = 0.
-4, 0, 1
Let q(x) be the third derivative of x**6/40 - 9*x**5/20 + 27*x**4/8 - 27*x**3/2 - 113*x**2. Factor q(c).
3*(c - 3)**3
Suppose -5*k + 14 = -3*o, -4*o - 4*k + 16 = -2*k. Suppose -3*c + 8 + 10 = 3*d, d = o*c - 6. Factor 0 + 2/3*r - 1/3*r**d.
-r*(r - 2)/3
Let j(n) be the second derivative of n**4/114 + 32*n**3/57 - 33*n**2/19 + 7*n + 2. Factor j(p).
2*(p - 1)*(p + 33)/19
Let u(c) = 91*c + 1559. Let y be u(-17). Factor 0 + y*n - 3/2*n**2.
-3*n*(n - 8)/2
Let x be ((-24)/(-18))/(4/(-18)). Let m(p) = -45*p**3 - 30*p**2 + 19*p + 16. Let o(d) = d - 1. Let f(q) = x*o(q) - m(q). Factor f(b).
5*(b + 1)*(3*b - 2)*(3*b + 1)
Let y be (17/(-782)*4)/((-1)/3). Suppose 2/23 - 8/23*w**4 - 10/23*w + y*w**2 + 10/23*w**3 = 0. Calculate w.
-1, 1/4, 1
Let y be (3*12/(-4) - -5) + 7. Let p(t) be the second derivative of 1/3*t**4 - 9*t + 0 - 1/10*t**5 - 1/3*t**y + 0*t**2. Factor p(i).
-2*i*(i - 1)**2
Let p(r) = r**2 - 128*r - 2027. Let v(k) = 128*k + 2034. Let d(w) = -2*p(w) - 3*v(w). Let d(c) = 0. Calculate c.
-32
What is o in -45*o**2 - 20*o**4 - 13*o**4 - 9415*o**5 + 9418*o**5 + 150*o**2 + 69*o**3 = 0?
-1, 0, 5, 7
Factor -1408*g + 319*g**3 + 283*g**3 - 15*g**4 - 218*g**3 - 242 - 3*g**4 - 1916*g**2.
-2*(g - 11)**2*(3*g + 1)**2
Let c(s) be the third derivative of -2*s**7/735 - 4*s**6/105 - 17*s**5/105 - 5*s**4/21 + 286*s**2. Factor c(g).
-4*g*(g + 1)*(g + 2)*(g + 5)/7
Factor 0 - 4/3*v**2 - 16/9*v - 2/9*v**3.
-2*v*(v + 2)*(v + 4)/9
Let z be (-1 + (-3)/9)*-3. Suppose -z*t**2 + 12*t**3 - 11*t**3 + 5*t - 2 + 3 - 3 = 0. Calculate t.
1, 2
Let p be 1488/(-465)*(-10)/4. Let k(o) be the second derivative of -p*o + 0 + 1/6*o**2 - 1/9*o**3 + 1/36*o**4. Factor k(y).
(y - 1)**2/3
Suppose 3*d - 5*i + 17 = 2*d, 0 = -i + 4. Suppose -34*l**2 + 2 - 12*l - 192*l**d + 182*l**3 - 2 = 0. What is l?
-3, -2/5, 0
Factor 1/5*y**3 + 6/5*y**2 + y + 0.
y*(y + 1)*(y + 5)/5
Let a = 34350/111553 + -2/8581. Determine t, given that -a*t + 2/13*t**2 + 2/13 = 0.
1
Let j = -33 - -33. Solve -13 + j - 3*k**2 + 0 + 12*k + 1 = 0 for k.
2
Let c(f) = 6*f**2 - 8*f + 8. Let l(o) = -5*o**2 + 8*o - 8. Let m(y) = 3*c(y) + 4*l(y). Factor m(q).
-2*(q - 2)**2
Let y(p) be the first derivative of 4*p**2 + 1/6*p**4 + 4/3*p**3 + p - 2. Let f(r) be the first derivative of y(r). Factor f(a).
2*(a + 2)**2
Suppose -2*p + 11 = 7. Let -8*v**2 + 11 - 4*v + p*v**3 + 14*v - 15 = 0. What is v?
1, 2
Factor -4*f - 4*f**4 - 2*f + 29617*f**2 - 10*f - 29569*f**2 - 4*f**3 - 64.
-4*(f - 2)**2*(f + 1)*(f + 4)
Let r be 37/60 - 18/(-135). Let l = -63/71 - -2847/568. Find a, given that 39/8*a**2 - r - l*a = 0.
-2/13, 1
Let s be (33/(-4) + 8/32)/2. Let m be 16/5 + s/2. Solve -3/5*n**2 + 0 - m*n = 0 for n.
-2, 0
Factor -24/7*j - 1/7*j**2 - 23/7.
-(j + 1)*(j + 23)/7
Let f be (-1)/(-18) + (-58)/(-36). Let -f*y**4 + 0 + 2/3*y**2 - y**3 + 0*y = 0. Calculate y.
-1, 0, 2/5
Let m = 17421 - 191625/11. Factor 4/11 - 2/11*z**3 + 0*z**2 + m*z.
-2*(z - 2)*(z + 1)**2/11
What is g in g**4 + 9*g**4 - 20*g**4 - 5*g**5 + 20*g**3 + 10*g**2 - 15*g = 0?
-3, -1, 0, 1
Suppose 4*p = -s + 23, 4*p + 3 - 21 = -2*s. Let q be ((-2)/11)/(-1) + -7 + p. Factor 2/11*v**4 + 2/11*v - 2/11*v**3 + 0 - q*v**2.
2*v*(v - 1)**2*(v + 1)/11
Factor s**4 - 3 - 27/4*s**3 - 8*s + 57/4*s**2.
(s - 3)*(s - 2)**2*(4*s + 1)/4
Determine x so that 8/3*x - 1/6*x**2 + 6 = 0.
-2, 18
Let i(h) be the second derivative of -4*h**3 + 2 + 24*h**2 + 11*h + 1/4*h**4. Solve i(u) = 0.
4
Suppose -104 + 253*j**2 + 356*j - 105*j**2 - 120*j**2 = 0. Calculate j.
-13, 2/7
Factor 3/7*g**4 + 144/7*g**2 + 0 + 192/7*g - 45/7*g**3.
3*g*(g - 8)**2*(g + 1)/7
Let y(o) = -2*o**2 + 97*o - 228. Let j be y(46). Factor 6/19*a - 4/19 - 2/19*a**j.
-2*(a - 2)*(a - 1)/19
Factor -86/7*w**2 + 0 - 6*w - 4/7*w**3.
-2*w*(w + 21)*(2*w + 1)/7
Suppose 5 + 1 = 2*q. Factor -q*f + f - f - 4 + 5*f + 2*f**2.
2*(f - 1)*(f + 2)
Let t(v) be the first derivative of 2*v**3/3 - 170*v**2 + 14450*v - 635. Factor t(p).
2*(p - 85)**2
Suppose -232 + 182 = -10*o. Let w(a) be the third derivative of 0*a**o + 0*a - 1/24*a**4 + 6*a**2 + 0 + 1/120*a**6 + 0*a**3. What is m in w(m) = 0?
-1, 0, 1
Factor 0 - 3/4*m**4 - 3/4*m**3 + 3/4*m + 3/4*m**2.
-3*m*(m - 1)*(m + 1)**2/4
Let i be 2/(24/81) + (-2)/(-8). Factor 5*z**4 - 19*z**3 + 6*z**2 - 5*z**3 + i*z**4 + 3*z**3 + 3*z.
3*z*(z - 1)**2*(