et k be 9/(-3)*(-1)/3. Let c(z) = 12*z**2 + 2*z + 8. Let b(r) = r**2 + r. Let j(t) = k*c(t) - 10*b(t). Suppose j(g) = 0. Calculate g.
2
Find j such that 0 + 24/5*j**3 - 2/5*j**4 + 0*j**2 + 0*j = 0.
0, 12
Let x(v) be the second derivative of 0 + 1/170*v**5 - 5/51*v**4 + 41*v + 0*v**2 + 25/51*v**3. Factor x(m).
2*m*(m - 5)**2/17
Let o(f) be the third derivative of 5*f**2 - 1/36*f**4 + 0*f + 1/180*f**6 - 1/30*f**5 + 1/3*f**3 + 0. Determine r so that o(r) = 0.
-1, 1, 3
Let x(p) be the first derivative of 1/40*p**5 - 13 + 0*p**2 + 1/24*p**3 + 0*p - 1/16*p**4. Solve x(q) = 0.
0, 1
Factor 14/3*t**3 + 2/3*t**4 + 20/3*t**2 + 0 + 0*t.
2*t**2*(t + 2)*(t + 5)/3
Let v = 2 + 5. Suppose 946*i**5 + 3*i**4 - 951*i**5 + v*i**4 = 0. Calculate i.
0, 2
What is t in 6/7*t**2 + 0 - 2/7*t**3 + 8/7*t = 0?
-1, 0, 4
Find o, given that 20/19*o + 50/19 + 2/19*o**2 = 0.
-5
Let f(j) = 12*j**3 + 12*j**2 + 2*j - 26. Let u(b) = -4*b**3 - 4*b**2 - b + 9. Let o = -34 - -39. Let s(a) = o*f(a) + 14*u(a). Factor s(r).
4*(r - 1)*(r + 1)**2
Let g(w) be the first derivative of w**3/12 + 25*w**2/8 + 68. Factor g(v).
v*(v + 25)/4
Let y = -77 + 77. Let l(r) be the second derivative of 0*r**3 + 1/18*r**4 - 6*r - 1/15*r**5 + y*r**2 + 0. Suppose l(z) = 0. What is z?
0, 1/2
Let m(w) = 10*w**2 + 4*w. Suppose 28 = -4*y + 4. Let t(v) = v**2. Let s(z) = y*t(z) + m(z). What is a in s(a) = 0?
-1, 0
Let f(q) = 0*q**2 - 2 + 0*q + 6*q**2 + 11 - 8*q. Let d(w) = w**2 - w + 1. Let s(c) = -14*d(c) + 2*f(c). Solve s(r) = 0 for r.
-2, 1
Let v(x) be the first derivative of -x**6/33 + 14*x**5/55 - 5*x**4/11 - 4*x**3/33 + x**2 - 10*x/11 + 80. Let v(y) = 0. What is y?
-1, 1, 5
Factor 7 - 1 + 8*t**2 - 26*t**2 + 9*t**2 + 3*t + 6*t**2.
-3*(t - 2)*(t + 1)
Let -3*o**4 + 5*o - 3*o**2 - 10*o**4 + 3*o**4 - 5*o**5 + 13*o**2 = 0. Calculate o.
-1, 0, 1
Let w(o) = -21*o - 38. Let i(x) = -11*x - 20. Let k(r) = -5*i(r) + 3*w(r). Let h be k(-2). Factor 0 + 0*n + 1/6*n**h.
n**2/6
Factor -40/3 + 10/3*f**2 + 8/3*f - 2/3*f**3.
-2*(f - 5)*(f - 2)*(f + 2)/3
Let i = -20/77 + 6/11. Find b such that i*b**2 - 8/7*b + 6/7 = 0.
1, 3
Let f(v) be the first derivative of 28*v**5/5 - 68*v**4 - 36*v**3 + 136*v**2 + 80*v - 568. Suppose f(a) = 0. Calculate a.
-1, -2/7, 1, 10
Solve 4*b**3 - 30*b**2 - 182 + 182 + b**3 = 0 for b.
0, 6
Let r be (-4 - (-1 + (-90)/21))*407. Let f = r - 522. Factor 3/7*w**4 + 3/7*w + 9/7*w**2 + f*w**3 + 0.
3*w*(w + 1)**3/7
Let t(r) = -9*r**2 - 4. Let s(c) = -8*c**2 - 5. Let p(u) = -4*s(u) + 3*t(u). Let g(k) = 4*k**2 + 6. Let x(q) = 4*g(q) - 3*p(q). Factor x(d).
d**2
Let h(r) be the third derivative of r**6/1080 - r**5/360 + 2*r**3 + 7*r**2. Let q(n) be the first derivative of h(n). Let q(p) = 0. Calculate p.
0, 1
Suppose t + 4*h = 2, -5*h - 3 - 1 = -2*t. Suppose -4*p + t*r = -16, -18 + 0 = p + 5*r. Factor -12/11*z - 18/11 - 2/11*z**p.
-2*(z + 3)**2/11
Suppose 0 = 3*u + 2*y - 13, -38*y + 43*y = 5*u - 5. Factor 1/3*a**u + 0 - 1/3*a**5 - 1/3*a**2 + 0*a + 1/3*a**4.
-a**2*(a - 1)**2*(a + 1)/3
Let a = 499/138960 - -1/1737. Let y(b) be the third derivative of -1/48*b**4 + 1/1680*b**7 + 0 + 1/80*b**5 + 0*b - 6*b**2 - a*b**6 + 1/48*b**3. Factor y(c).
(c - 1)**4/8
Let s = 23 + -3. Let m be ((-1)/2)/((-30)/s). Solve 1/6*r**3 - m*r**2 + 0 + 1/6*r = 0 for r.
0, 1
Let s(f) be the second derivative of 1/3*f**4 + 50*f**2 + 0 - 8*f - 20/3*f**3. Suppose s(v) = 0. Calculate v.
5
Let r = -262/3 + 1840/21. Find d, given that -6/7*d**2 + r*d**4 + 8/7*d + 8/7 - 4/7*d**3 = 0.
-1, 2
Let i(w) be the first derivative of 4/35*w**5 - 10/7*w**2 - 2/3*w**3 + 1/28*w**4 + 1/42*w**6 - 8/7*w + 4. What is n in i(n) = 0?
-2, -1, 2
Let b(j) be the second derivative of j**4/42 + 4*j**3/21 - 96*j**2/7 - 488*j. Factor b(a).
2*(a - 8)*(a + 12)/7
Let z(u) = -u**2 - 29*u - 30. Let d(j) = 6*j**2 + 89*j + 90. Let n(a) = 2*d(a) + 7*z(a). Factor n(w).
5*(w - 6)*(w + 1)
Find g, given that 48 - 195*g - 192*g - 4*g**2 + 383*g = 0.
-4, 3
Let a(t) be the third derivative of t**5/30 + 29*t**4/6 + 841*t**3/3 + 31*t**2 + 2*t. Find r, given that a(r) = 0.
-29
Let d(q) be the third derivative of 0*q - 18*q**2 + 1/6*q**3 + 7/60*q**5 + 1/3*q**4 + 0. Determine j, given that d(j) = 0.
-1, -1/7
Let q(u) be the second derivative of -3*u**5/40 - 11*u**4/48 + 5*u**3/6 - 3*u**2/8 - 80*u. Let q(p) = 0. What is p?
-3, 1/6, 1
Let u(x) = -260*x - 3120. Let d be u(-12). Find w, given that 0 + d*w - 10/7*w**2 + 2/7*w**3 = 0.
0, 5
Let m be (1 - -3) + (0 - (-16 + 0)). Factor -5*s**3 + 10 - 20*s + 22*s - 27*s + m*s**2.
-5*(s - 2)*(s - 1)**2
Let r(t) be the second derivative of -2/11*t**3 - t + 0 + 9/11*t**2 + 1/66*t**4. Factor r(m).
2*(m - 3)**2/11
Let b(v) be the first derivative of 1 + 0*v**2 + 0*v + 1/120*v**5 + 1/12*v**4 - 1/360*v**6 + 5/3*v**3. Let y(g) be the third derivative of b(g). Factor y(s).
-(s - 2)*(s + 1)
Let h(j) be the third derivative of -53*j**5/12 + 45*j**4/2 - 10*j**3/3 - 253*j**2. Factor h(z).
-5*(z - 2)*(53*z - 2)
Let m(d) = -d**2 - 8*d - 3. Let s be m(-7). Let x be (15 + 321/(-21))/(-3 + 1). Factor -1/7*i - 2/7*i**2 + 2/7*i**s + x*i**5 + 0*i**3 + 0.
i*(i - 1)*(i + 1)**3/7
Let i(y) be the first derivative of 0*y + 22 - 1/6*y**2 - 1/9*y**3. Factor i(c).
-c*(c + 1)/3
Factor -6*j**3 + 121/3*j**2 - 120*j + 1/3*j**4 + 400/3.
(j - 5)**2*(j - 4)**2/3
Let h = -34 - -43. Solve 2*g**2 - 11 - 111*g - 23*g**2 - 10 - h = 0 for g.
-5, -2/7
Factor -156/5*g + 0 + 2/5*g**3 + 154/5*g**2.
2*g*(g - 1)*(g + 78)/5
Let p(g) be the third derivative of 1/315*g**7 - 1/36*g**6 + 0*g - 12*g**2 + 4/45*g**5 + 0 - 1/9*g**4 + 0*g**3. Factor p(a).
2*a*(a - 2)**2*(a - 1)/3
Suppose 3*f + 2*k - 21 - 7 = 0, 2*f - 23 = 3*k. Suppose 4*o + o - f = 0. Solve 0*s**o + 2/7*s**4 + 2/7*s**3 + 0 + 0*s = 0 for s.
-1, 0
Let n(x) be the second derivative of -5*x**4/6 - 35*x**3/2 - 135*x**2/2 + 341*x. Factor n(i).
-5*(i + 9)*(2*i + 3)
Let j(q) = -q**3 - 86*q**2 - 171*q - 249. Let p be j(-84). Factor -50/19*v**p + 4/19 + 2*v + 80/19*v**2.
-2*(v - 2)*(5*v + 1)**2/19
Let g(q) be the third derivative of 0*q**3 + 1/70*q**7 + 0*q + 7/120*q**6 + 0 + 5*q**2 + 1/24*q**4 + 1/12*q**5. Factor g(f).
f*(f + 1)**2*(3*f + 1)
Let w(z) be the second derivative of 0 - 5/12*z**3 - 7/48*z**4 - 3/8*z**2 - 26*z. Factor w(x).
-(x + 1)*(7*x + 3)/4
Let q be (16/(-42))/((-13)/91). Let g(i) be the third derivative of -41/15*i**5 - 14/3*i**4 - q*i**3 + 14/15*i**6 + 0*i + 0 - 14*i**2. Factor g(z).
4*(z - 2)*(4*z + 1)*(7*z + 2)
Determine d so that -2/9*d**2 + 0 - 26/9*d = 0.
-13, 0
Let v(f) = -9*f**2 - 3*f**2 + 232 + 2*f**3 - 228. Let c(z) = z**3 - z**2 + z + 1. Let j(q) = -5*c(q) + v(q). Let j(d) = 0. Calculate d.
-1, -1/3
Let n(h) be the second derivative of h**6/960 - h**4/64 + 14*h**3/3 + 16*h. Let z(t) be the second derivative of n(t). Factor z(x).
3*(x - 1)*(x + 1)/8
Let f(o) = -3*o**3 + 1. Let x be f(-1). Factor 3*a + 6*a + 3*a - x*a + 2*a**4 - 6*a**3.
2*a*(a - 2)**2*(a + 1)
Let j be (-1040)/(-336) - 6/63. Let 6/7*v + 0 + 3/7*v**j - 9/7*v**2 = 0. Calculate v.
0, 1, 2
Let a be ((-36)/(-60))/(22/10 + -2). Determine b so that b**a - 8*b**2 + 4*b**2 + 2*b + 2*b = 0.
0, 2
Let w(d) = 2 + 55*d**2 - 40*d - 25*d - 2. Let o(u) = 5*u**2 - 6*u. Let n(g) = -65*o(g) + 6*w(g). Factor n(c).
5*c**2
Let b(s) be the third derivative of 0 - s**3 + 1/540*s**6 + 1/4*s**4 + 0*s - 1/30*s**5 - 9*s**2. Factor b(c).
2*(c - 3)**3/9
Let w(h) be the third derivative of 17*h**2 + 0*h + 25/54*h**3 + 5/108*h**4 + 1/540*h**5 + 0. Suppose w(r) = 0. Calculate r.
-5
Suppose -1 = 2*n - 9. Let c(x) = x**3 - 13*x**2 - 8*x + 3. Let w(f) = -12*f**2 - 8*f + 2. Let r(d) = n*c(d) - 6*w(d). Factor r(b).
4*b*(b + 1)*(b + 4)
Solve 1/5*r**3 - 7/5*r + 2/5*r**2 + 4/5 = 0.
-4, 1
Let v be 1 - (-8 + 8 + (-2 - -3)). Let c(t) be the second derivative of 3/50*t**5 + 0*t**3 + 1/105*t**7 - 1/25*t**6 - 1/30*t**4 + 2*t + v*t**2 + 0. Factor c(h).
2*h**2*(h - 1)**3/5
Let z = -193/24 - -359/40. Find p such that -z*p**2 + 16/3*p + 8/5 = 0.
-2/7, 6
Factor -1/9*w**2 + 0 + 2/9*w.
-w*(w - 2)/9
Suppose 30*a - 1615 = 25*a. Let o = -3547/11 + a. Factor 8/11*k**5 + 8/11*k**4 + 0 + 2/11*k - 4/11*k**2 - o*k**3.
2*k*(k + 1)**2*(2*k - 1)**2/11
Factor 56*z**2 + 132*z + 85*z**3 + 64 - 75*z**3 - 7*z**3.
(z + 2)*(z + 16)*(3*z + 2)
Let d(m) be the first derivative of -m**7/1400 + m**6/600 - 17*m**3/3 - 14. Let j(c) be