i).
4*i*(i - 1)/5
Let y be (-8)/3*(8 - 152/16). Let j(b) be the first derivative of -1/3*b**6 + 0*b - 4/5*b**5 + 4/3*b**3 + 0*b**y + 2 + b**2. Factor j(m).
-2*m*(m - 1)*(m + 1)**3
Let t(q) be the second derivative of -q**4/12 - 7*q**3/6 + 4*q**2 + 27*q. Let t(v) = 0. Calculate v.
-8, 1
Let q = -90/43 - -18943/9030. Let p(j) be the second derivative of 1/42*j**3 + q*j**6 + 6*j + 0 - 1/140*j**5 + 0*j**2 - 1/84*j**4. Factor p(h).
h*(h - 1)**2*(h + 1)/7
Let p(j) be the third derivative of -j**7/42 + 7*j**6/24 - 17*j**5/12 + 85*j**4/24 - 5*j**3 + 30*j**2. Factor p(s).
-5*(s - 3)*(s - 2)*(s - 1)**2
Factor -269*o + 445*o**2 - 5*o**3 + 269*o.
-5*o**2*(o - 89)
Let l(q) = 7*q**5 - 10*q**4 + 11*q**3 + 29*q**2 - 61*q + 24. Let v(z) = -z**5 - z**3 + z**2 + z. Let d(r) = l(r) + 5*v(r). Suppose d(i) = 0. What is i?
-2, 1, 2, 3
Let q(l) = -2*l**5 + l**4 + l**3. Let a(z) = -10*z**5 + 43*z**4 + 107*z**3 + 108*z**2 + 40*z. Let k(y) = -a(y) + 7*q(y). Let k(w) = 0. What is w?
-5, -2, -1, 0
Suppose -18 = -5*r + 2. Factor -7*x**2 + 3*x**4 + 8*x + x**r - 5*x**2.
4*x*(x - 1)**2*(x + 2)
Let 21/2*h**3 + 15 + 39*h + 135/4*h**2 + 3/4*h**4 = 0. What is h?
-10, -2, -1
Suppose -132 = -5*w + 3*c, 140 = 5*w - 0*c - 5*c. Factor -2*d + 3*d**2 + d + 13*d**4 - 5*d + w*d**3 + 2*d**4.
3*d*(d + 1)**2*(5*d - 2)
Let s(p) be the third derivative of -p**7/280 - p**6/80 + p**5/80 + p**4/16 + 350*p**2. Factor s(z).
-3*z*(z - 1)*(z + 1)*(z + 2)/4
Let v(u) be the third derivative of 2*u**7/105 - 2*u**6/15 - 4*u**5/5 + 78*u**2. Factor v(h).
4*h**2*(h - 6)*(h + 2)
Suppose -556*n - 104 = -608*n. Determine l so that -121/7 + 143/7*l + 1/7*l**3 - 23/7*l**n = 0.
1, 11
Factor 127*d + 37*d + 59*d**2 - 2 + 28*d**2 + 80*d**3 + 26 + 205*d**2.
4*(d + 3)*(4*d + 1)*(5*d + 2)
Let l(c) = 15*c**2 - 70*c - 10. Let k(q) = 2*q**2 - 2. Let y(h) = 5*k(h) - l(h). Find d such that y(d) = 0.
0, 14
Suppose -6*h - 13 = -55. Factor h*o**2 - 39*o**2 - 4*o - 2*o**3 + 9 - 1 - 18*o**3.
-4*(o + 1)**2*(5*o - 2)
Suppose 816 = 6*p + 780. Let i(d) be the third derivative of -d**2 + 0 + 0*d**3 + 1/315*d**7 - 2/45*d**5 + 2/9*d**4 - 1/90*d**p + 0*d. Factor i(m).
2*m*(m - 2)**2*(m + 2)/3
Determine l, given that -4/3*l**4 + 0*l - 5/3*l**3 - 1/3*l**5 + 0 - 2/3*l**2 = 0.
-2, -1, 0
Let q be (-3)/(-10) - (-741)/(-5070). Factor 12/13*k**2 - 8/13*k + 2/13 + q*k**4 - 8/13*k**3.
2*(k - 1)**4/13
Let f(d) be the second derivative of d**4/12 - 4*d**3 + 44*d - 1. Suppose f(l) = 0. What is l?
0, 24
Let h = 34 + -36. Let q(k) = k**4 - k**3 + k**2 - 1. Let c(w) = 7*w**4 - 11*w**3 + 11*w**2 + 2*w - 9. Let o(x) = h*c(x) + 18*q(x). Factor o(j).
4*j*(j - 1)*(j + 1)**2
Let b(c) be the second derivative of -c**4/4 + 13*c**3 - 507*c**2/2 + 54*c. Determine x, given that b(x) = 0.
13
Let n be -15*8/320 + 19/8. Let q(m) be the second derivative of 1/2*m**3 + 9/10*m**5 - m**4 + 1/14*m**7 - 4*m + 0 + 0*m**n - 2/5*m**6. Factor q(t).
3*t*(t - 1)**4
Let w(a) be the second derivative of 0 - 13*a - 2/45*a**6 - 8/3*a**2 + 1/3*a**4 + 2/15*a**5 - 8/9*a**3. Factor w(g).
-4*(g - 2)**2*(g + 1)**2/3
Let q(u) be the third derivative of 0 + 0*u - 5/3*u**3 + 5/6*u**4 - 1/8*u**5 - u**2. Let q(j) = 0. What is j?
2/3, 2
Suppose -4*r + 12 = -r. Find c such that 13*c**3 + c - c - 3*c**4 - 6*c**2 - r*c**3 = 0.
0, 1, 2
Let b(o) = o + 1. Let l(u) = -442*u**2 + 445*u**2 + 20*u + 5 + 39. Let s = -15 + 11. Let a(v) = s*b(v) - l(v). Factor a(i).
-3*(i + 4)**2
Find f, given that -4159*f + 3*f**3 + 4147*f - 8*f**4 + 17*f**3 + 16*f**2 = 0.
-1, 0, 1/2, 3
Let s = 54 - 48. Suppose -5*d + 3*t + 7 - s = 0, 5*d - 22 = -4*t. Solve -1/5 - 3/5*m - 2/5*m**d = 0 for m.
-1, -1/2
Let m(t) be the third derivative of t**7/1260 - 29*t**6/360 + 841*t**5/360 + 641*t**2. Factor m(s).
s**2*(s - 29)**2/6
Let x(k) = k. Let c be x(-16). Let y(s) = -6*s**2 - 72*s - 216. Let i(u) = 2*u**2 + 24*u + 72. Let f(b) = c*i(b) - 5*y(b). Factor f(g).
-2*(g + 6)**2
Let a = 7 + -5. Suppose a*o = 1 + 1, 4*u - 2*o + 2 = 0. Let 4*n**4 + u*n**3 - 2*n**4 + 2*n**3 = 0. What is n?
-1, 0
Solve 28*p + 12*p + 20*p**4 - 15*p**2 + 6*p + 20 - 55*p**3 + 34*p = 0.
-1, -1/4, 2
Factor 5827 - 5*s**4 - 45*s**3 - 2912 - 2915 + 45*s + 5*s**2.
-5*s*(s - 1)*(s + 1)*(s + 9)
Let k = -23 + 26. Factor -5*r**3 + 3*r**3 - k*r**5 + r**5 + 4*r**4 - 8*r**4.
-2*r**3*(r + 1)**2
Suppose 144*r - 67*r = 154. Determine f, given that -6/7*f**3 + 0 + 8/7*f**r - 8/7*f**4 + 8/7*f - 2/7*f**5 = 0.
-2, -1, 0, 1
Let l(r) be the first derivative of -1/48*r**4 - 1/80*r**5 + 1 + 0*r**3 + 0*r**2 + r. Let k(u) be the first derivative of l(u). Factor k(h).
-h**2*(h + 1)/4
Find l such that 2/17*l**2 + 108/17*l + 1458/17 = 0.
-27
Let t(s) be the first derivative of 0*s**3 + 4/15*s**5 - 1 + 0*s**4 + 1/9*s**6 + 0*s**2 + 0*s. Factor t(h).
2*h**4*(h + 2)/3
Let j be ((-2)/(-27))/(108/729). Determine a, given that 1/2*a + 1 - j*a**2 = 0.
-1, 2
Let w(y) be the second derivative of -y**8/2940 - y**7/735 + y**5/105 + y**4/42 + y**3/6 + 4*y. Let b(x) be the second derivative of w(x). Factor b(r).
-4*(r - 1)*(r + 1)**3/7
Let m be 2835/14*2/(-20). Let v = -20 - m. Solve -v*k - 1/2*k**4 + 1/4*k**5 + 0*k**3 + 0 + 1/2*k**2 = 0.
-1, 0, 1
Suppose 2761 = -2*u - 9*u. Let q = 254 + u. Solve 0 + 4/9*c**q + 0*c - 2/9*c**4 - 2/9*c**2 = 0.
0, 1
Let h(n) = -107*n + 11984. Let s be h(112). Factor b**2 + b**3 + 0*b + s + 1/4*b**4.
b**2*(b + 2)**2/4
Let w = -34 - -38. Factor -2*m**3 + 4 - w*m**2 + 2*m + 0 + 0.
-2*(m - 1)*(m + 1)*(m + 2)
Factor 44/13 + 2/13*u**2 - 46/13*u.
2*(u - 22)*(u - 1)/13
Let w = -6/325 - -361/1950. Find h such that 4/3 - 2/3*h + w*h**3 - 1/3*h**2 = 0.
-2, 2
Factor 26*w**2 - 256*w - 230*w - 2*w**3 + 1458 + 28*w**2.
-2*(w - 9)**3
Factor -3/2*z**2 - 10 - 16*z + 5*z**3 + 1/2*z**4.
(z - 2)*(z + 1)**2*(z + 10)/2
Suppose 2*y = 2*u + 40, -3*y - 5*u = -46 - 14. Let -17*s**4 - y*s**3 - 2*s**2 + 37*s**2 - 17*s**4 + 14*s**4 - 10*s = 0. Calculate s.
-2, 0, 1/2
Let a(q) = 9*q**4 - 6*q**3 - 48*q**2 - 72*q - 6. Let w(c) = -c**4 - 2*c**2 + 1. Let y(x) = -a(x) - 6*w(x). Factor y(u).
-3*u*(u - 6)*(u + 2)**2
Let u = 398 - 398. Let o(p) be the first derivative of -3 + 0*p**2 + 5/3*p**3 + u*p - p**5 + 0*p**4. Find i such that o(i) = 0.
-1, 0, 1
Factor 2/13*s**3 - 22/13*s**2 + 48/13*s + 0.
2*s*(s - 8)*(s - 3)/13
Suppose 4*q + 5*g - 22 = 3*g, 3*q + g - 15 = 0. Suppose 0 = 2*s - s. Solve 2*z**q + z**3 + 6*z**2 - 7*z**3 + s*z - 2*z = 0 for z.
0, 1
Let d = -610 + 610. Let t be (-4 - (4 - 8))/1. Factor 2/3*k + d*k**3 + 1/3*k**4 + t - k**2.
k*(k - 1)**2*(k + 2)/3
Let g(o) be the second derivative of -1/18*o**4 + 0 + 7*o + 0*o**2 + 1/3*o**3. Suppose g(w) = 0. What is w?
0, 3
Determine m so that 20*m**4 - 2*m**3 - 21*m**2 + m**2 + 4*m**5 + 0*m**5 + m**3 - 3*m**3 = 0.
-5, -1, 0, 1
Let o(u) be the second derivative of -u**4/10 - 13*u**3/3 - 42*u**2/5 + 44*u. Factor o(t).
-2*(t + 21)*(3*t + 2)/5
Let z be 4/(-18)*-27 - (-42)/(-8). Let l(a) be the first derivative of 1/4*a**3 - 3/4*a**2 + 10 + z*a. Factor l(u).
3*(u - 1)**2/4
Let m(y) = y - 4. Let u be m(8). Let k(c) = c**5 - c**4 + 2*c**3 + 2*c**2 + 5*c - 5. Let l(j) = -j**3 - j + 1. Let x(o) = u*l(o) + k(o). What is n in x(n) = 0?
-1, 1
Let f(z) be the third derivative of 11*z**7/840 - 107*z**6/480 + 49*z**5/48 + 25*z**4/32 - 535*z**2. Find s, given that f(s) = 0.
-3/11, 0, 5
Let f be (14 + -10)*6*(-4)/(-264). Let -f*r - 2/11*r**2 + 20/11*r**3 + 0 = 0. Calculate r.
-2/5, 0, 1/2
Let d be (3/18)/(((-27)/(-15))/9). Find a such that -d*a + 0 + 5/6*a**2 = 0.
0, 1
Let v(k) be the second derivative of k**7/6300 - 2*k**6/225 + 16*k**5/75 + 8*k**4/3 - 4*k. Let l(j) be the third derivative of v(j). Factor l(c).
2*(c - 8)**2/5
Let t = 36 + -34. Let -66*u**4 - 3*u**5 + 5*u**3 - u**3 + t*u**3 + 63*u**4 = 0. Calculate u.
-2, 0, 1
Let p(a) be the second derivative of -a**6/10 + a**4 - 55*a. Suppose p(o) = 0. What is o?
-2, 0, 2
Let y(k) = -3*k**3 + 65*k**2 - 134*k - 893. Let d(q) = q**3 - 21*q**2 + 44*q + 298. Let z(g) = 14*d(g) + 4*y(g). Factor z(t).
2*(t - 10)**2*(t + 3)
Let x(g) be the first derivative of -g**6/40 - 13*g**2/2 + 3. Let a(l) be the second derivative of x(l). Find s such that a(s) = 0.
0
Suppose 0*w - 3*w = 0. Suppose w*d**2 - 236 - 4*d**2 + 252 = 0. Calculate d.
-2, 2
Let c = 6412/35871 + 10/3261. Factor c*t**2 - 48/11*t + 288/11.
2*(t - 12)**2/11
Let h(d) 