i. Solve -5*x**i + x**3 + 2*x**3 + x**3 = 0.
0
Let b(v) be the first derivative of -v**3/12 + 5*v**2/2 - 25*v - 37. Solve b(y) = 0 for y.
10
Find k such that -8/3 - 30*k**2 + 50/3*k**3 + 16*k = 0.
2/5, 1
Let h(d) be the second derivative of -9/20*d**5 + 1/10*d**6 + 0 + 3/4*d**4 + 0*d**2 + 3*d - 1/2*d**3. Factor h(m).
3*m*(m - 1)**3
Let h = -4 - -7. Let f(b) be the first derivative of -1/4*b**6 + 0*b**2 - 1/6*b**h + 3/8*b**4 + 1/10*b**5 + 0*b + 1. Let f(q) = 0. Calculate q.
-1, 0, 1/3, 1
Let m(f) be the second derivative of -f**6/660 - f**5/110 - f**4/44 - f**3/33 + 3*f**2/2 + f. Let y(z) be the first derivative of m(z). Factor y(o).
-2*(o + 1)**3/11
Suppose -5*l + 0*l + 20 = 0. Suppose -4*d = -d - 5*u + 11, -5*u = -2*d - 14. Factor -2*a**3 - d*a**l - a**3 + a**2 + 3*a + 2*a**2.
-3*a*(a - 1)*(a + 1)**2
Solve 3/4*z**2 - 3/2*z + 3/4 = 0 for z.
1
Let z(h) be the third derivative of 0*h**5 - 1/420*h**6 + 0*h**3 + 0 + 1/1176*h**8 + 0*h**4 + 3*h**2 + 0*h**7 + 0*h. Let z(g) = 0. Calculate g.
-1, 0, 1
Let d(k) be the third derivative of 0*k - 1/105*k**7 + 1/30*k**5 + 1/24*k**4 + 8*k**2 + 0*k**3 + 0*k**6 - 1/336*k**8 + 0. Solve d(w) = 0.
-1, 0, 1
Factor 24*j**2 - 14*j**3 - j - 4*j - 4*j + 1 - 2*j**3.
-(j - 1)*(4*j - 1)**2
Let -6*i + 7/4*i**5 + 1 - 19/4*i**3 + 41/4*i**2 - 9/4*i**4 = 0. What is i?
-2, 2/7, 1
Let s(j) be the first derivative of -2*j**3/3 - 3*j**2 - 19. Find v such that s(v) = 0.
-3, 0
Let s be (54/35 + -2)/((-4)/10). Solve 10/7*t**2 - 16/7*t + s - 2/7*t**3 = 0 for t.
1, 2
Let h(b) = 3*b**2 - 2*b - 1. Let n be h(-1). Suppose -3*i - 19 = -2*x, 4*i + 6 = -14. What is s in -s**2 - x*s + s - 3*s**3 + n*s**3 + 1 = 0?
-1, 1
Let h = 88/153 - 6/17. Factor -8/9*o + 8/9 + h*o**2.
2*(o - 2)**2/9
Let s(z) be the first derivative of z**4/2 + 2*z**3/3 - 9*z**2 - 18*z + 2. Factor s(k).
2*(k - 3)*(k + 1)*(k + 3)
Let p(u) be the first derivative of -u**6/36 - u**5/30 + u**4/24 + u**3/18 + 3. Find z, given that p(z) = 0.
-1, 0, 1
Factor -12/5*m**4 + 3/5*m**5 + 0*m + 0 - 6/5*m**2 + 3*m**3.
3*m**2*(m - 2)*(m - 1)**2/5
Suppose 4/9*k + 0 - 2/9*k**2 = 0. What is k?
0, 2
Let f be (-3 + 13/5)/(42/(-15)). Suppose 1/7*j + 0 + 0*j**2 - f*j**3 = 0. What is j?
-1, 0, 1
Let r be (-5)/(-2)*91/70. Let c = -57/20 + r. Factor 0 + 2/5*l**2 - 2/5*l**3 + 2/5*l - c*l**4.
-2*l*(l - 1)*(l + 1)**2/5
Solve 0 - 1/2*a**5 + 3/2*a**3 + 1/2*a**4 - a - 1/2*a**2 = 0 for a.
-1, 0, 1, 2
Factor 23*g**2 - 14*g**2 - g**3 + 5*g - 2 - 4*g**3 - 7*g**4.
-(g - 1)*(g + 1)**2*(7*g - 2)
Let z(b) be the third derivative of 0 - 1/20*b**6 + 1/10*b**5 - 6*b**2 + 1/105*b**7 + 0*b**3 + 0*b - 1/12*b**4. Factor z(d).
2*d*(d - 1)**3
Let z = 214/147 + -6/49. Suppose h + 12 = 4*h + 3*g, -2*h + 16 = 4*g. Find c such that 2/3*c**3 - 2/3*c - 4/3*c**4 + z*c**2 + h = 0.
-1, 0, 1/2, 1
Let m(g) be the second derivative of g**5/30 - g**4/18 - g**3/9 + g**2/3 + 8*g. Factor m(x).
2*(x - 1)**2*(x + 1)/3
Let w(b) be the third derivative of b**8/588 + 2*b**7/245 + b**6/105 - 2*b**5/105 - b**4/14 - 2*b**3/21 + 6*b**2. Factor w(s).
4*(s - 1)*(s + 1)**4/7
Let d(g) = -4*g**2 - 4*g + 5. Let a(q) = -3*q**2 - 3*q + 4. Let t(b) = 5*a(b) - 4*d(b). Factor t(r).
r*(r + 1)
Let j = 6 + -8. Let u = 10 - 5. Let i(b) = -2. Let r(h) = -h**2 - h - 5. Let a(w) = j*r(w) + u*i(w). Factor a(p).
2*p*(p + 1)
Let x = -4 - -4. Let h(o) be the third derivative of -1/210*o**5 - 1/420*o**6 + 0*o**3 + x*o**4 + 0 + o**2 + 0*o. Let h(i) = 0. Calculate i.
-1, 0
Solve 4/13*c**4 + 0 - 2/13*c**3 + 2/13*c - 4/13*c**2 = 0.
-1, 0, 1/2, 1
Let q(g) = 5 + 3 - 1 + 3*g**4 + 15*g**2 + 6*g + 0 + 12*g**3. Let h(d) = -d**4 - 4*d**3 - 5*d**2 - 2*d - 2. Let y(w) = -7*h(w) - 2*q(w). Factor y(m).
m*(m + 1)**2*(m + 2)
Factor -6/5*g**2 + 2/5*g**4 + 0 + 4/5*g + 0*g**3.
2*g*(g - 1)**2*(g + 2)/5
Let h(w) = 2*w - 4 - 3*w + 0*w - 4. Let v be h(-10). Solve 2 - 3*z**v - 1 + 2*z**2 = 0 for z.
-1, 1
Let u(d) be the first derivative of d**3/5 - 9*d**2/10 - 4. Factor u(b).
3*b*(b - 3)/5
Let n = -53 + 56. Let 0*v**4 + 0*v + 0 - 2/7*v**5 + 0*v**n + 0*v**2 = 0. What is v?
0
Determine r, given that 6 - 22 + 2*r**2 + 2*r**2 = 0.
-2, 2
Let p(l) be the third derivative of l**9/2520 + l**8/840 - l**7/252 - l**6/180 + l**4/8 + 4*l**2. Let x(t) be the second derivative of p(t). Factor x(k).
2*k*(k - 1)*(k + 2)*(3*k + 1)
Let l = -21 - -25. Find p such that 0*p**4 + 4*p + 0*p**4 + 6*p**2 + 3*p**4 - 5*p**l = 0.
-1, 0, 2
Determine d so that 15/7*d + 3/7 + 9/7*d**2 - 15/7*d**3 - 12/7*d**4 = 0.
-1, -1/4, 1
Suppose -2*r + 32 = 6*r. Factor 2/3 - 8/3*h**3 - 8/3*h + r*h**2 + 2/3*h**4.
2*(h - 1)**4/3
Let c(s) = 2*s**3 - s**2 + 2*s - 1. Let o be c(1). Find a, given that -2 - 3*a + 8 + 2*a**2 - 5*a**o = 0.
-2, 1
Let c(s) = 11*s + 13. Let l be c(-1). Factor 3/2*y**l + 1/4 + 1/4*y**4 - y - y**3.
(y - 1)**4/4
Suppose -5*b + 19 = 3*f - 0*f, -4*f - 8 = 0. Let u(n) be the third derivative of 0*n + 2*n**2 - 1/120*n**b + 0 - 1/32*n**4 - 1/24*n**3. Factor u(j).
-(j + 1)*(2*j + 1)/4
Solve s - s**3 + 7 - 4 - 3 - s**4 + s**2 = 0 for s.
-1, 0, 1
Suppose 2*f = k + 5, 2 - 19 = -4*f - 5*k. Determine t so that -9*t**f - 3*t**2 + 9*t + 6*t**2 + 3*t**2 - 6 = 0.
-1, 2/3, 1
Let x(d) be the second derivative of d**8/5376 - d**7/840 + d**6/320 - d**5/240 + d**4/4 - 4*d. Let y(r) be the third derivative of x(r). Factor y(w).
(w - 1)**2*(5*w - 2)/4
Let u(r) be the first derivative of 1/9*r**2 - 1/54*r**4 - 3 + 1/27*r**3 - 3*r - 1/90*r**5. Let f(k) be the first derivative of u(k). Factor f(i).
-2*(i - 1)*(i + 1)**2/9
Let d(h) be the first derivative of h**7/280 + h**6/80 - h**5/80 - h**4/16 - h**2/2 + 2. Let v(q) be the second derivative of d(q). Factor v(z).
3*z*(z - 1)*(z + 1)*(z + 2)/4
Let j be 10/(-16)*2/3. Let q = -1/6 - j. Factor q - 1/2*r + 1/4*r**2.
(r - 1)**2/4
Let f(o) = -o - 8. Let v be f(-8). Let c(k) be the third derivative of v - 1/18*k**4 - 7/90*k**5 + 0*k**3 + 3*k**2 + 0*k. Solve c(l) = 0.
-2/7, 0
Let f(n) = n + 1. Let p be f(-1). Let b be (-3)/6*0 + 2. Suppose 2*l**5 + 6*l**4 + b*l**2 + 0 + p + 6*l**3 = 0. Calculate l.
-1, 0
Let i(j) be the third derivative of -3*j**8/280 - 38*j**7/525 - 31*j**6/150 - 8*j**5/25 - 17*j**4/60 - 2*j**3/15 + 8*j**2. Factor i(b).
-2*(b + 1)**4*(9*b + 2)/5
Let n(m) = 3*m - m**3 + m - 3*m. Let r = 0 + -1. Let w(v) = 4*v**3 + 3*v**2 + 1. Let g(o) = r*w(o) - 3*n(o). Factor g(f).
-(f + 1)**3
Let t(y) be the second derivative of -3/20*y**5 + 1/56*y**7 + 0 + 3/8*y**3 + 0*y**6 - 3/4*y**2 + 4*y + 1/8*y**4. Suppose t(d) = 0. Calculate d.
-2, -1, 1
Let m(j) be the second derivative of j**6/60 - 3*j**5/20 + j**4/24 + 2*j**3 + 4*j**2 + 33*j. What is l in m(l) = 0?
-1, 4
Find v such that -3/4*v**3 + 0*v + 0*v**2 + 0 + 9/4*v**4 - 3/2*v**5 = 0.
0, 1/2, 1
Let c(u) = 2*u**2 + 2*u + 2. Let v(h) = -8*h**2 - 8*h - 9. Let t(z) = -9*c(z) - 2*v(z). Factor t(x).
-2*x*(x + 1)
Let u(j) = -j**2 + j. Let k be 765/63 - (-2)/(-14). Let x(p) = 2*p**3 + 8*p**2 - 12*p. Let b(z) = k*u(z) + x(z). Suppose b(r) = 0. What is r?
0, 2
Let a(s) be the first derivative of -16*s**5 + 10*s**4 - 5*s**3/3 - 7. Determine v so that a(v) = 0.
0, 1/4
Let h(d) be the second derivative of 3*d**5/140 - 3*d**3/14 - 3*d**2/7 - 8*d. Solve h(n) = 0 for n.
-1, 2
Let l(w) be the third derivative of w**7/4620 + 2*w**3/3 - 5*w**2. Let n(o) be the first derivative of l(o). Factor n(d).
2*d**3/11
Let r(a) = -a**2 - a - 1. Let d(m) = 29*m**2 - 19*m - 1. Let u(n) = -d(n) + r(n). Let y(p) = -p**2 - p - 1. Let h(s) = -u(s) - 2*y(s). Factor h(q).
2*(4*q - 1)**2
Let h(t) be the first derivative of t**6/2 + 3*t**5/5 - 3*t**4/2 - 2*t**3 + 3*t**2/2 + 3*t - 11. Factor h(o).
3*(o - 1)**2*(o + 1)**3
Suppose o = -2*a - 6, -3*o + 6 = o - 2*a. Factor -2/5*v**4 + o*v**3 + 2/5*v**2 + 0 + 0*v.
-2*v**2*(v - 1)*(v + 1)/5
Let c(d) = 10*d**2 - 2*d - 1. Let n be c(4). Let q = n - 1053/7. Factor q*a + 6/7*a**2 + 2/7*a**3 + 0.
2*a*(a + 1)*(a + 2)/7
Let h(k) = 5*k**4 - 7*k**3 - 5*k**2 + k + 6. Let u(r) = -6*r**3 - 2*r**2 + 4*r**4 + 0*r**4 + 5 - 2*r**2 + r. Let i(c) = -5*h(c) + 6*u(c). Solve i(a) = 0.
-1, 0, 1
Let s(b) = 26*b**4 + 11*b**3 - 4*b**2. Let k(v) = 5*v**4 + 2*v**3 - v**2. Let a(d) = 11*k(d) - 2*s(d). Determine g so that a(g) = 0.
-1, 0, 1
Suppose 3*r**3 - 9*r**4 - 15*r**5 - 11*r**5 + 20*r**5 + 9*r**2 + 3*r = 0. What is r?
-1, -1/2, 0, 1
Suppose -2*t + t + 12 = -3*k,