*3 = 0.
-2/3, 1
Let t be 129/(-602)*(-14 + 0). Factor -11*u**2 + 2 + 3*u**t + 11/3*u + 7/3*u**4.
(u - 1)**2*(u + 3)*(7*u + 2)/3
Determine a, given that 1/2 - 3/4*a**2 + 7/4*a**3 - 3/4*a**4 - 3/4*a = 0.
-2/3, 1
Let x be (-3 - (-248)/60) + (-5)/15. Find o, given that 0*o + 0 + 2/5*o**4 - 6/5*o**3 + x*o**2 = 0.
0, 1, 2
Suppose 5*i - 4 - 6 = 0. Factor -2/3*t**3 + 0 + 0*t + 2/3*t**i.
-2*t**2*(t - 1)/3
Let f(m) = m**2 + 18*m - 31. Let b(a) = 2*a + 3. Let h be b(-4). Let v(t) = -2*t**2 - 18*t + 32. Let p(i) = h*f(i) - 4*v(i). Factor p(w).
3*(w - 3)**2
Factor -5/7*p**5 - 9/7*p**3 - 13/7*p**4 + 1/7*p**2 + 2/7*p + 0.
-p*(p + 1)**3*(5*p - 2)/7
Factor 0*l - 1/2*l**4 - 7/2*l**2 + 4*l**3 + 0.
-l**2*(l - 7)*(l - 1)/2
Let j be (-3)/3 - -2*6/8. Factor j - 1/2*a**2 - 1/2*a**3 + 1/2*a.
-(a - 1)*(a + 1)**2/2
Suppose 0 = -4*s - 9 + 25. Suppose 19 = 3*m + s. Factor 2/11*x**2 + 2/11*x**m + 6/11*x**3 + 0*x + 6/11*x**4 + 0.
2*x**2*(x + 1)**3/11
Let z(r) be the second derivative of 5/3*r**6 + 4/3*r**2 + 4/15*r**5 - 50/63*r**7 + 0*r**3 - 37/18*r**4 + r + 0. Let z(q) = 0. Calculate q.
-1/2, -2/5, 2/5, 1
Let p = 986 + -984. Let j + 1/3*j**p + 0 = 0. What is j?
-3, 0
Let l(c) = c + 9. Let a = -8 - -1. Let x be l(a). Factor -b**2 - 1 + x*b**2 + 0*b**2.
(b - 1)*(b + 1)
Let m(d) be the third derivative of 7*d**5/270 + d**4/12 + 2*d**3/27 + 17*d**2. Factor m(z).
2*(z + 1)*(7*z + 2)/9
Let i = 3371/3 + -1123. Factor 1/6*w**5 + 0*w - i*w**4 + 0 - 1/3*w**2 + 5/6*w**3.
w**2*(w - 2)*(w - 1)**2/6
Let q be (-532)/(-4410) - 1/9. Let h(g) be the second derivative of 0*g**3 - q*g**6 + 1/35*g**5 + 0*g**2 + 2*g + 0 - 1/42*g**4. Determine i so that h(i) = 0.
0, 1
Let z(r) be the third derivative of -r**5/300 - r**4/30 + 2*r**2. Factor z(p).
-p*(p + 4)/5
Let z(c) be the third derivative of -5*c**8/336 + c**7/21 - c**6/24 + 13*c**2. Factor z(w).
-5*w**3*(w - 1)**2
Let o(a) be the second derivative of a**4/12 + 5*a**3/6 - 3*a**2 + 2*a. Let w be o(-6). Factor w*i**3 - 21*i**4 - 17*i**3 - 6*i**2 - 17*i**3 + 7*i**3.
-3*i**2*(i + 1)*(7*i + 2)
Let o be (-2)/(-5) + 16/10. Find z such that 2*z**3 + 2*z**4 - 3*z**2 - z**2 + o*z**2 - 2*z**5 = 0.
-1, 0, 1
Let p(o) = -11*o**4 - 29*o**3 - 16*o**2 + 2*o. Let q(j) = -21*j**4 - 57*j**3 - 31*j**2 + 5*j. Let r(b) = 11*p(b) - 6*q(b). Factor r(t).
t*(t + 1)*(t + 4)*(5*t - 2)
Factor 1/6*j**5 - 2/3*j + 2/3*j**4 + 1/2*j**3 - 2/3*j**2 + 0.
j*(j - 1)*(j + 1)*(j + 2)**2/6
Let h be ((-18)/1)/(-3) + -2. What is z in 12/5*z - 24*z**2 + 0 - 123*z**h + 60*z**5 + 423/5*z**3 = 0?
0, 1/4, 2/5, 1
Let k(b) be the third derivative of 0 - 4*b**2 + 0*b + 1/6*b**3 - 1/120*b**5 + 1/48*b**4. Factor k(w).
-(w - 2)*(w + 1)/2
Let x = 15 - 13. Let -8*g**2 + 3*g**3 + 9*g**4 - 13*g**2 + 0*g**x - 3*g**5 + 12 = 0. What is g?
-1, 1, 2
Let v(b) be the first derivative of -5*b**3/3 + 10*b**2 - 15*b - 14. What is l in v(l) = 0?
1, 3
Suppose -3/7*n**3 + 6/7 - 15/7*n + 12/7*n**2 = 0. What is n?
1, 2
Let j = 41 + -73/2. Let h(p) be the first derivative of 4*p**3 + 5 + j*p**2 - 3*p. Factor h(g).
3*(g + 1)*(4*g - 1)
Let 2/7*r**2 + 0 + 6/7*r = 0. Calculate r.
-3, 0
Suppose -8/9*c + 2/9*c**2 + 0 = 0. What is c?
0, 4
What is a in 4*a**4 + 17*a**2 + a**2 + 4 + 12*a**2 + 16*a**3 + 16*a - 6*a**2 = 0?
-1
Let a be 5/12 + (-11)/(-44). Factor 2/3*m**2 - 2/3 - 2/3*m**3 + a*m.
-2*(m - 1)**2*(m + 1)/3
Let k(q) = q**3 + 22*q**2 + 121*q. Let i be k(-11). Let i*d - 1/3*d**4 + 0 + 0*d**2 - 2/3*d**3 = 0. Calculate d.
-2, 0
Let o(g) = -3*g - 3 + 1 + 2 - 6. Let p be o(-4). Factor 3*k**2 - 9*k - k**4 + p*k + 2*k**4 + 3*k**3 - 4*k**4.
-3*k*(k - 1)**2*(k + 1)
Let b(x) be the second derivative of -x**7/231 - 4*x**6/165 - x**5/22 - x**4/33 + 3*x. Factor b(i).
-2*i**2*(i + 1)**2*(i + 2)/11
Let o be (-2)/4 - (-45)/(-6). Let v be (-14)/o*(-4)/(-14). Determine j, given that v*j**4 + j**3 + 0 + 0*j + 1/2*j**2 = 0.
-1, 0
Suppose 40 = -2*k + 16. Let j = -10 - k. Factor z**2 - 4*z**3 - 2 - z**4 + j + 4*z**5 + 0*z**4.
z**2*(z - 1)*(z + 1)*(4*z - 1)
Let v(a) be the second derivative of -a**10/20160 - a**9/3360 - 3*a**8/4480 - a**7/1680 + a**4/4 - 2*a. Let c(i) be the third derivative of v(i). Factor c(n).
-3*n**2*(n + 1)**3/2
Let w(d) be the third derivative of -2/45*d**5 - 1/9*d**4 - 1/180*d**6 + 0 + 0*d + 0*d**3 - d**2. Factor w(a).
-2*a*(a + 2)**2/3
Let x(h) be the second derivative of -h**4/12 - 3*h**3/5 + 4*h**2/5 - 2*h. Factor x(a).
-(a + 4)*(5*a - 2)/5
Let w(g) be the second derivative of -3/4*g**4 - 1/20*g**5 - g + 0 - 8*g**2 - 4*g**3. Solve w(f) = 0 for f.
-4, -1
Let l be (-22)/(-60) + (-32)/(-240). Let d(n) be the first derivative of 1/6*n**3 + 1/2*n - 3 + l*n**2. Determine r so that d(r) = 0.
-1
Suppose -3*g - 56 = -4*x, -x - 3*g - 4 = -3. Determine j so that -6*j - 9*j**2 + 0*j - 14*j**3 + x*j**3 = 0.
-2, -1, 0
Factor 1/4*n**4 + 1/2*n**3 + 1/4*n**2 + 0*n + 0.
n**2*(n + 1)**2/4
Let h(p) be the second derivative of -3/10*p**6 + 3/2*p**4 + 6*p + 6*p**3 - 21/20*p**5 - 12*p**2 + 0. Find l, given that h(l) = 0.
-2, 2/3, 1
Let l(h) = -2*h - 6. Let o be l(-7). Suppose 0 = -4*s + o, -2*d = -3*d - 5*s + 14. Let 4 - 6 - 8*f**2 + d*f**2 - f + 5*f**2 = 0. What is f?
-1, 2
Let k be 22 + -17 - 18/4. Determine o so that -1/2*o + 3/2*o**3 - k*o**4 - o**5 + 0 + 1/2*o**2 = 0.
-1, 0, 1/2, 1
Let w(f) be the third derivative of f**8/2240 - f**7/420 + f**6/240 + f**4/24 - 6*f**2. Let a(v) be the second derivative of w(v). Find d such that a(d) = 0.
0, 1
Let u(p) = p + 9. Suppose 31 = -5*o + 4*c, o - 3*c + 4 = -0*o. Let j be u(o). Factor -2*h**4 + 2*h**j + 3*h**3 - 4*h**3 + h**5 + 0*h**5.
h**2*(h - 2)*(h - 1)*(h + 1)
Suppose -4*l + 48 = 5*f, -3*f + 4*l - 1 = -17. Let p be (-1 + 4/f)/(-1). Let 0*a**2 + p*a**4 - 1/2*a**3 + 0 + 0*a = 0. Calculate a.
0, 1
Let r(q) be the first derivative of q**4/16 - q**3/12 + 25. Factor r(g).
g**2*(g - 1)/4
Suppose -5 + 5/4*c**2 + 0*c = 0. What is c?
-2, 2
Let i(w) = -w**3 + 7*w**2 - 7*w + 8. Let v be i(6). Suppose 0*k + v*k**3 + k + k - 4*k**2 = 0. What is k?
0, 1
Let a(s) be the third derivative of s**5/40 + 5*s**4/8 - 11*s**3/4 + 56*s**2. Factor a(u).
3*(u - 1)*(u + 11)/2
Solve 0 + 2*n**3 - 4/7*n + 10/7*n**2 = 0.
-1, 0, 2/7
Let c = -53 - -53. Let i(f) be the third derivative of 0*f**5 + 0 - 3*f**2 - 1/24*f**4 + c*f + 1/120*f**6 + 0*f**3. What is h in i(h) = 0?
-1, 0, 1
Let s(y) be the second derivative of -y**6/15 - y**5/10 + y. What is v in s(v) = 0?
-1, 0
Suppose 0 = 2*x - 3*h - 0*h - 9, 2*x - 2*h - 10 = 0. Let n be 2/x*0/(-2). Factor 0*l - 2/9*l**3 - 2*l**5 - 4/3*l**4 + n + 0*l**2.
-2*l**3*(3*l + 1)**2/9
Let p(l) = 7*l**3 - 2*l**3 - 6*l**3 + 5. Let g be p(0). Let 2/5*v**3 + 0*v + 0 + 2/5*v**4 - 2/5*v**2 - 2/5*v**g = 0. What is v?
-1, 0, 1
Suppose -x**3 - 6*x**2 + 3*x - 2*x**3 - 2*x**4 - 5*x - 3*x**3 = 0. Calculate x.
-1, 0
Determine s so that -40*s**2 + 62*s**5 - 68*s**5 + 21*s**3 + 15*s**4 + 24*s - 3*s**3 - 20*s**2 = 0.
-2, 0, 1/2, 2
Let x(q) = -q**2 - 3*q + 1. Let b(t) = 6*t**2 + 17*t - 6. Let y = -46 + 80. Let i(u) = y*x(u) + 6*b(u). Factor i(z).
2*(z - 1)*(z + 1)
Let d(q) = -q**2 + 6*q. Let m be d(5). Factor 0*o**3 + 14*o**4 - 35*o**2 - 4*o**3 + 33*o**2 - 8*o**m.
-2*o**2*(o - 1)**2*(4*o + 1)
Let u(a) be the first derivative of a**3/2 - 3*a**2/4 - 7. Solve u(j) = 0.
0, 1
Let g(h) = -29*h**2 - 81*h - 11. Let x(f) = 10*f**2 + 27*f + 4. Let i(m) = -2*g(m) - 7*x(m). Factor i(s).
-3*(s + 2)*(4*s + 1)
Let h(a) be the first derivative of -a**4/30 + a**3/10 - a**2/10 - a - 3. Let b(o) be the first derivative of h(o). Determine m so that b(m) = 0.
1/2, 1
Let w be 1*(-2 - -3 - 0). Suppose -3*z + 7 + 4*z**2 - 8 - 2*z**4 - w - 3*z**5 + 6*z**3 = 0. What is z?
-1, -2/3, 1
Suppose 0 + 2/7*t + 18/7*t**3 + 12/7*t**2 + 8/7*t**4 = 0. Calculate t.
-1, -1/4, 0
Factor -3/5*v**2 + 9/5*v - 6/5.
-3*(v - 2)*(v - 1)/5
Factor 3 + 5*j + j**2 - 9 + 10.
(j + 1)*(j + 4)
Let g(r) be the third derivative of 6*r**2 + 0*r + 1/2*r**4 - 1/30*r**5 - 3*r**3 + 0. Solve g(s) = 0 for s.
3
Let m = 12 + 3. Factor 4*a + 2*a**3 - 10*a + 15*a**4 + 4*a**3 - m*a**2.
3*a*(a - 1)*(a + 1)*(5*a + 2)
Let p(w) be the third derivative of -w**7/10080 - w**6/1440 - w**5/480 - w**4/12 - 3*w**2. Let x(q) be the second derivative of p(q). Let x(d) = 0. What is d?
-1
Let s be -2*356/(-3150)*3. Let d = s + -2/175. Determine h so that -d*h**3 + 2/3*h**2 + 2/9*h**4 -