 - 3. Let n be k(2). Determine x so that 1/2*x**2 - n + 1/2*x = 0.
-2, 1
Let i be (26/91)/((-1)/(-14)). Suppose -11 = 3*s - i*p, 5*p = 5*s - 0*s + 10. Factor 2*f**2 + s - 3 + 2*f**2 + 4*f.
4*f*(f + 1)
Let c(h) = -34*h**3 + 60*h**2 - 32*h - 2. Let m(g) = 69*g**3 - 119*g**2 + 66*g + 4. Let d(n) = -5*c(n) - 2*m(n). Solve d(j) = 0.
-1/16, 1
Let c be (-12 + 12)*5*6/(-60). Factor 1/3*v**3 + c + 1/3*v**2 - 2*v.
v*(v - 2)*(v + 3)/3
Let w be ((-3)/24)/(93/(-496)). Factor w*d + 1/3*d**3 - d**2 + 0.
d*(d - 2)*(d - 1)/3
Let z(v) be the second derivative of 1/15*v**6 + 0 + 1/2*v**4 + 0*v**3 - 25*v - 2/5*v**5 + 0*v**2. Factor z(o).
2*o**2*(o - 3)*(o - 1)
Let f = -1918 + 3837/2. Factor -2*p**4 + 2*p**2 + 3/2*p**3 - 2*p + 0 + f*p**5.
p*(p - 2)**2*(p - 1)*(p + 1)/2
Solve -6/7*k**4 - 8/7*k**5 + 72/7 + 138/7*k**3 - 330/7*k + 134/7*k**2 = 0.
-3, 1/4, 1, 4
Let q(i) = -2*i**3 + 6*i**2 - 5*i - 1. Let j be q(5). Let v = -628/5 - j. Factor -v*p - 2/5*p**3 + 0 + 4/5*p**2.
-2*p*(p - 1)**2/5
Let c(z) be the first derivative of z**5/10 - 5*z**4/8 - 4*z**3/3 + 3*z**2 - 97. Find x, given that c(x) = 0.
-2, 0, 1, 6
Let x(w) = w**3 + 2*w**2 - w + 1. Let f(c) = 8*c**3 + 52*c**2 + 194*c + 6. Let z(r) = f(r) - 6*x(r). Find b such that z(b) = 0.
-10, 0
Suppose -3*c - 29 - 91 = 0. Let f be (-3)/4*c/15. Factor 3*u**2 - 2*u - 6*u**2 - u**3 - 2*u**3 + f*u**3.
-u*(u + 1)*(u + 2)
Let d(c) = c**4 - 2*c**3 + c**2 + c. Let k(y) = 3*y**4 + 3*y**3 - 38*y**2 + 68*y - 32. Let u(g) = 12*d(g) - 3*k(g). Solve u(r) = 0 for r.
1, 2, 4
Let f(s) be the second derivative of -s**6/165 - 5*s**5/2 - 4186*s**4/11 - 753296*s**3/33 + 778688*s**2/11 + 2*s + 18. Factor f(l).
-2*(l - 1)*(l + 92)**3/11
Let b(l) = l**3 + 3*l**2 + 4. Let i be b(-3). Determine z so that -28*z**2 + 0*z - 20*z**3 + z - 4*z - 9*z - 4*z**i = 0.
-3, -1, 0
Solve -12*s + 3/5*s**2 + 0 = 0 for s.
0, 20
Let h = 20493/95 - 1068/5. Let m = 44/19 - h. Factor 3/5*f**4 + m*f**3 - 3/5*f**2 + 1/5*f**5 - 2/5*f + 0.
f*(f - 1)*(f + 1)**2*(f + 2)/5
Let o be 38/16 - (786/48 - 16). Suppose -2/3 - 10/3*x**o - 4*x = 0. Calculate x.
-1, -1/5
Let b(k) be the first derivative of 2*k**3/3 + 17*k**2 + 32*k + 92. Solve b(d) = 0.
-16, -1
Let u be (-6)/15 + (-88)/(-20). Let l(d) be the second derivative of 1/2*d**3 - 3*d**2 + 0 + 1/2*d**u - 6*d - 3/20*d**5. Factor l(q).
-3*(q - 2)*(q - 1)*(q + 1)
Let h(r) = 3*r**4 + 20*r - 6*r - r**2 - 8 - 4. Let u(z) = -z**4 - z**3 + z**2 - z + 1. Let i(y) = -h(y) - 4*u(y). Determine d so that i(d) = 0.
-4, -2, 1
Suppose 0 = -p + 3*r + 9, -2*p = 2*p - 4*r - 20. Suppose p + 5 = 4*y. Factor -2/3*c**4 + 0 - 2*c**y - 2*c**3 - 2/3*c.
-2*c*(c + 1)**3/3
Let h(o) = 2*o**2 + 21*o - 11. Let p be h(-11). Let m(t) be the first derivative of 1/5*t**2 + p*t - 5 - 1/20*t**4 - 1/15*t**3. Factor m(g).
-g*(g - 1)*(g + 2)/5
Let x be 16/(-28) + 76/35. Determine s so that 2/5*s**2 + 8/5 + x*s = 0.
-2
Let y(s) = -s**3 + 17*s**2 - 29*s - 12. Let c be y(15). Solve 5*p**3 - p**c + 4*p**3 - 3*p**3 = 0 for p.
0
Let 32*z**4 - 11*z**2 + 150*z**3 + 5*z**5 + 151*z**2 - 29*z + 28*z**4 + 74*z = 0. What is z?
-9, -1, 0
Let d(o) = 4*o**3 - 40*o**2 + 36*o. Suppose -54 = -4*k - 2*u + 5*u, -5*k - 4*u = -52. Let i(j) = j**2 - j. Let a(b) = k*i(b) + d(b). Factor a(v).
4*v*(v - 6)*(v - 1)
Let c(i) be the first derivative of -i**3/24 + 67*i**2/16 - 65*i/4 + 91. Factor c(q).
-(q - 65)*(q - 2)/8
Let d(x) be the first derivative of x**4/2 + 2*x**3/3 - x**2 - 2*x - 7. Find c, given that d(c) = 0.
-1, 1
Let j = 58 + 45. Let 20*w**2 - 20*w**4 + 6*w + 98*w**3 - w - j*w**3 = 0. Calculate w.
-1, -1/4, 0, 1
Let 30/7 + 3/7*m**2 + 3*m = 0. What is m?
-5, -2
Let a = 5921/5 + -1184. Solve -1/5*y**3 + a*y**2 - 1/5 + 1/5*y = 0.
-1, 1
What is t in -5/3*t**2 - 69360 + 680*t = 0?
204
Factor k**3 + 0*k - 1/5*k**4 - 6/5*k**2 + 0.
-k**2*(k - 3)*(k - 2)/5
Find a, given that -144 + 9*a**3 + 81*a**2 + 3*a**3 - 30*a - a**3 + a**3 - 108*a = 0.
-8, -3/4, 2
Suppose 5/4*g**5 + 5/4 + 5/4*g - 5/2*g**3 + 5/4*g**4 - 5/2*g**2 = 0. What is g?
-1, 1
Let b(x) = -x - 1. Let k be (-8)/3 + 2/(-6). Let r be b(k). Factor -2*p + p + 0*p - p**r.
-p*(p + 1)
Let 46/17*a**2 + 22/17*a + 26/17*a**3 + 0 + 2/17*a**4 = 0. Calculate a.
-11, -1, 0
Let n(u) be the second derivative of -2/3*u**3 - 26*u + 1/15*u**6 + 3*u**2 + 1/5*u**5 + 0 - 2/3*u**4. What is r in n(r) = 0?
-3, -1, 1
Let f(o) be the first derivative of 2*o**3/3 - 9*o**2 - 72*o + 228. Determine w, given that f(w) = 0.
-3, 12
Let w(a) be the third derivative of -a**6/30 + 2*a**5/15 + 2*a**4/3 - 16*a**3/3 + a**2 + 2. Solve w(m) = 0 for m.
-2, 2
Let l(s) be the third derivative of -s**8/60480 + s**6/540 - s**5/60 - 20*s**2. Let m(r) be the third derivative of l(r). Solve m(p) = 0.
-2, 2
Let a be ((-1)/(-6)*2)/(-11 + 646/51). Suppose 0 + 0*w + a*w**3 + 4/5*w**2 = 0. Calculate w.
-4, 0
Let s(l) be the first derivative of l**7/525 - l**6/300 - l**5/50 + l**4/12 - 2*l**3/15 - 6*l**2 - 7. Let m(j) be the second derivative of s(j). Factor m(x).
2*(x - 1)**3*(x + 2)/5
Let a(f) be the third derivative of -f**5/30 + 9*f**4/4 - 131*f**2. Factor a(w).
-2*w*(w - 27)
Factor 8*v + 38*v - 10*v + 4*v**2 - 4*v.
4*v*(v + 8)
Suppose 0 = -9*f - 18 - 9. Let z(a) = -3*a**3 + 2*a**2 - 2*a - 1. Let o be z(f). Factor o - 12*y**3 - 4*y**4 + 0*y**4 - 104.
-4*y**3*(y + 3)
Let j(u) be the third derivative of u**7/11340 + u**6/540 + u**5/108 + 7*u**4/24 + 16*u**2. Let x(n) be the second derivative of j(n). Solve x(p) = 0 for p.
-5, -1
Let o(i) be the second derivative of i**4/4 - 2*i**3 - 15*i**2/2 + 7*i - 3. Suppose o(s) = 0. What is s?
-1, 5
Let q = 3989/8 - 19921/40. Factor 0 + 4/5*x + 1/5*x**4 - q*x**3 + 0*x**2.
x*(x - 2)**2*(x + 1)/5
Let 0*u + 0*u**2 - 3/5*u**4 + 1/5*u**5 + 0*u**3 + 0 = 0. Calculate u.
0, 3
Suppose 32 = 4*h - 7*t + 4*t, 2*t + 13 = h. Let u(w) = 4*w - 18. Let x be u(h). Solve 2/7*r**5 - 54/7*r - 36/7*r**x + 2*r**4 + 20/7*r**3 + 54/7 = 0 for r.
-3, 1
Suppose -5*t - 5*t = -210. Suppose -t = 19*j - 26*j. Find y such that -2/3*y + 0 - 10/9*y**j + 2/9*y**4 + 14/9*y**2 = 0.
0, 1, 3
Let z be (-2)/2*1*5. Let r(x) = 1 + 64*x + 52*x - 115*x. Let b(v) = 3*v**2 + 5*v + 2. Let c(t) = z*r(t) + b(t). Determine w, given that c(w) = 0.
-1, 1
Factor 3/2*f**4 + 45/2*f**3 + 21*f**2 + 0*f + 0.
3*f**2*(f + 1)*(f + 14)/2
Suppose -127 + 7 = -5*r. Let o(s) = -2*s**2 + s + 3. Let v(c) = 9*c**2 - 6*c - 15. Let n(t) = r*o(t) + 5*v(t). Determine i so that n(i) = 0.
-1
Let y = -208 - -210. Let l(p) be the first derivative of 0*p**2 + 0*p + 1/16*p**4 + y + 1/12*p**3. Factor l(z).
z**2*(z + 1)/4
Let a(z) be the third derivative of 0*z - 1/1176*z**8 + 1/735*z**7 + 0*z**4 + 0 + 1/420*z**6 - 1/210*z**5 + 21*z**2 + 0*z**3. Factor a(t).
-2*t**2*(t - 1)**2*(t + 1)/7
What is a in -501*a**3 - 1995*a**3 - 478*a**3 - 492*a**3 - 80*a**4 - 31512*a**2 + 3200 + 278*a**3 + 5120*a = 0?
-20, -1/4, 2/5
Let q(z) be the first derivative of 2*z**5/35 - z**4/7 + 89. Factor q(v).
2*v**3*(v - 2)/7
Factor m**2 + 0 + 6/5*m**3 + 0*m + 1/5*m**4.
m**2*(m + 1)*(m + 5)/5
Let q(h) be the first derivative of -8*h**3/3 + 31*h**2 + 16*h + 140. Factor q(d).
-2*(d - 8)*(4*d + 1)
Let y = -15341/3 + 5114. Suppose -1/3*w**3 + 1/6*w**5 + 1/6*w**4 - y*w**2 + 1/6*w + 1/6 = 0. Calculate w.
-1, 1
Factor 0*m**3 - 2/3*m + 0 + m**2 - 1/3*m**4.
-m*(m - 1)**2*(m + 2)/3
Let u(d) be the first derivative of d**6/7 + 57*d**5/35 + 45*d**4/14 - 4*d**3/7 - 48*d**2/7 - 45*d/7 - 98. Let u(g) = 0. Calculate g.
-15/2, -1, 1
Let r(u) be the third derivative of u**5/90 - 13*u**4/36 + 4*u**3/3 + 50*u**2. Suppose r(x) = 0. What is x?
1, 12
Factor 176/3*g - 172/3*g**2 + 0 - 4/3*g**3.
-4*g*(g - 1)*(g + 44)/3
Let r(g) be the third derivative of g**5/45 + 17*g**4/18 + 140*g**3/9 - 6*g**2 + 51. Factor r(y).
4*(y + 7)*(y + 10)/3
Suppose g + 56 = 15*g. Let w be ((-172)/(-42) - g)*(-6)/(-1). Factor -w*b**4 + 4/7*b + 4/7*b**2 - 4/7*b**3 + 0.
-4*b*(b - 1)*(b + 1)**2/7
Let b(n) be the first derivative of n**6/3 + 22*n**5/5 + 18*n**4 + 32*n**3/3 - 64*n**2 + 217. Suppose b(x) = 0. What is x?
-4, 0, 1
Let d = 569/68 + -138/17. Find g, given that -3/4*g**2 + 1/2 + 1/4*g**4 + 1/4*g**3 - d*g = 0.
-2, -1, 1
Let i(m) be the second derivative of m**7/105 - m**6/30 + m**4/6 - m**3/3 + 10*m**2 - m. Let p(o) be the first derivative of i(o). Factor p(b).
2*(b - 1)**3*(b + 1)
Suppose 290