0
Let m(u) be the first derivative of -u**6/120 - u**5/15 - 5*u**4/24 - u**3/3 - u**2 - 2. Let o(p) be the second derivative of m(p). Factor o(h).
-(h + 1)**2*(h + 2)
Let o(u) be the third derivative of u**5/270 - u**4/27 + 4*u**3/27 - u**2 - 2*u. Factor o(k).
2*(k - 2)**2/9
Let p(d) be the first derivative of -15*d**4/4 + 25*d**3/3 + 5*d**2 + 3. Factor p(l).
-5*l*(l - 2)*(3*l + 1)
Find f, given that -8/5 - 2/5*f**3 + 2/5*f**2 + 8/5*f = 0.
-2, 1, 2
Factor 4*r**3 + 9*r**3 + 0*r**4 + 8*r + 3*r + 3*r**4 + 19*r**2 + 2.
(r + 1)**2*(r + 2)*(3*r + 1)
Let h(j) be the first derivative of j**4/2 + 2*j**3/3 - 5. Factor h(t).
2*t**2*(t + 1)
Let f(c) be the third derivative of c**5/60 - c**4/12 + 4*c**2. Find v such that f(v) = 0.
0, 2
Factor 140*t**2 + 6*t - 2*t - 2*t - 4 - 2*t**3 - 136*t**2.
-2*(t - 2)*(t - 1)*(t + 1)
Let h = 2015/2 - 1002. Find x, given that -h*x**3 - 9/2*x**4 - 2*x**2 + 1/2 - 5/4*x**5 + 3/4*x = 0.
-1, 2/5
Suppose 94*w - 96*w = -6. Let q(i) be the second derivative of -1/8*i**3 + 0*i**2 + 1/16*i**4 + w*i + 0. Factor q(l).
3*l*(l - 1)/4
Suppose -21*a**3 - 64*a - 15*a**4 + 32*a + 32*a - 6*a**2 = 0. What is a?
-1, -2/5, 0
Let v be (-4)/(-3)*16*(-3)/(-5). Factor -48/5*s**2 - 2/5*s**4 - v*s - 16/5*s**3 - 32/5.
-2*(s + 2)**4/5
Let j be (0 + -3)/((-15)/10). Factor -3*o**j + 5*o**3 - o - 6*o**3 + o**2.
-o*(o + 1)**2
Let l be 20/(-75)*(-3)/2. Determine y so that 0*y**3 - 4/5*y**2 + 0 + 4/5*y**4 + l*y**5 - 2/5*y = 0.
-1, 0, 1
Let h be (-2581)/(-3815) + 6/(-21). Let q = h + 1/109. Solve -3/5*z - 1/5*z**2 - q = 0.
-2, -1
Let c(o) be the third derivative of o**6/120 - o**5/15 + 5*o**4/24 - o**3/3 + 2*o**2. Factor c(i).
(i - 2)*(i - 1)**2
Let o(g) = g**2 - g + 2. Let k be o(0). Determine a, given that k - 4*a + 1 + a + 3 - 3*a**2 = 0.
-2, 1
Suppose 2*k = 10 - 6. Factor 0 - 2*w**3 - 4/5*w**k + 0*w.
-2*w**2*(5*w + 2)/5
Let l(s) = -s**2 + 5*s. Let g(c) = c + 15. Let i be g(-10). Let u be l(i). Solve -2/3*o + u + 2/3*o**2 = 0.
0, 1
Let f(u) = u**3 - 3*u**2 - 4*u + 6. Let r be f(4). Let b be r/15 - (-12)/(-80). Let -b + 3/4*j**2 + 1/2*j = 0. Calculate j.
-1, 1/3
Suppose 5 + 4 = 3*c. Factor 4*m**2 + m**2 - c*m**2 + 2*m.
2*m*(m + 1)
Let c(v) be the second derivative of v**4/78 - 2*v. Factor c(a).
2*a**2/13
Let u(k) be the third derivative of 3/20*k**6 + 1/8*k**4 + 1/5*k**5 + 0 + 1/112*k**8 - 2*k**2 + 0*k**3 + 2/35*k**7 + 0*k. Factor u(i).
3*i*(i + 1)**4
Find g, given that 0*g + 0 - 1/5*g**2 + 1/5*g**4 + 0*g**3 = 0.
-1, 0, 1
Let o(s) be the third derivative of s**6/120 + s**5/60 - 5*s**4/24 + s**3/2 + 7*s**2. Factor o(y).
(y - 1)**2*(y + 3)
Let q(v) be the first derivative of v**3/3 - 14*v**2 + 196*v + 41. Factor q(c).
(c - 14)**2
Let y = 7 + -4. Let -i**5 + 25*i**3 - 25*i**y = 0. Calculate i.
0
Let u(s) be the second derivative of s**7/21 - 7*s**6/45 + s**5/6 - s**4/18 - 45*s. Factor u(r).
2*r**2*(r - 1)**2*(3*r - 1)/3
Let n(j) be the first derivative of 0*j + 1/2*j**4 - 4/3*j**3 + j**2 - 1. Factor n(m).
2*m*(m - 1)**2
Let j be (-20)/(-40) + ((-10)/(-4) - 1). Factor -7/3*h**j + 2/3 + 5/3*h.
-(h - 1)*(7*h + 2)/3
Let j(f) be the first derivative of f**6/105 - 3*f**5/70 + f**4/14 - f**3/21 - 4*f + 1. Let p(c) be the first derivative of j(c). Factor p(m).
2*m*(m - 1)**3/7
Let l(r) be the third derivative of -r**8/840 - r**7/140 - r**6/60 - r**5/60 - r**4/24 + 2*r**2. Let d(m) be the second derivative of l(m). Factor d(t).
-2*(t + 1)**2*(4*t + 1)
Let b be 21/2 + (-3)/6. Suppose -3*q + b = 2*q. Factor a + a**q - 2 + 2.
a*(a + 1)
Suppose 3*a - 10 = -2*a. Find v such that -4*v**2 - 18 - 24*v + 2*v**2 - 6*v**a = 0.
-3/2
Let c(i) be the first derivative of 1/6*i**3 + 1 + 0*i**2 + 0*i. Solve c(q) = 0.
0
Find n such that -6*n**2 - 9*n - 39*n + 50 - 9*n**2 - 17*n = 0.
-5, 2/3
Determine m, given that 8/3 + 28/3*m**2 - 12*m = 0.
2/7, 1
Let b be 1 - (-1)/((-60)/59). Let d(l) be the second derivative of 1/12*l**3 + 0 - 1/8*l**4 - b*l**6 + 3/40*l**5 + 0*l**2 + l. Factor d(i).
-i*(i - 1)**3/2
Let x(a) = a**2 - 5*a + 6. Let b = 15 + -11. Let o be x(b). Determine q, given that -q - 2 + 2 - q**o = 0.
-1, 0
Let a(y) = -y**3 + 13*y**2 + 33*y - 20. Let c be a(15). Suppose -c = -5*g + n, 0*n = n + 5. Solve 0 + 1/4*o**3 - 1/4*o + 1/4*o**g - 1/4*o**2 = 0.
-1, 0, 1
Let j(v) be the first derivative of 4/9*v**2 - 2/27*v**3 + 8 - 2/3*v. Let j(p) = 0. Calculate p.
1, 3
Let r = 13 - 10. Let -3*c**3 + 19 - 24*c + c**3 + 12*c**2 - r = 0. What is c?
2
Suppose -36/5*c - 3/5*c**2 + 0 = 0. Calculate c.
-12, 0
Factor -1/6*d**5 + 0 - 1/6*d + 0*d**4 + 0*d**2 + 1/3*d**3.
-d*(d - 1)**2*(d + 1)**2/6
Let z(x) be the third derivative of -x**5/150 - x**4/30 - 7*x**2. Suppose z(g) = 0. Calculate g.
-2, 0
Let q(i) be the second derivative of 3*i**3 + 3/40*i**5 - 3/4*i**4 + 0 - 6*i**2 + i. Factor q(g).
3*(g - 2)**3/2
Suppose 0 = -4*o + 5*v + 30, v - 23 = -5*o - 0*o. Factor -3*n**5 - 3*n - o*n**4 + 3*n**4 + 6*n**3 + 2*n**4.
-3*n*(n - 1)**2*(n + 1)**2
Let y(g) be the third derivative of -g**5/60 + g**4/8 + 2*g**3/3 + 13*g**2. Factor y(i).
-(i - 4)*(i + 1)
Let x(n) be the second derivative of -7*n**6/30 - 26*n**5/15 - 10*n**4/3 + 16*n**3/3 - n**2 - 2*n. Let q(a) be the first derivative of x(a). Factor q(c).
-4*(c + 2)**2*(7*c - 2)
Suppose 3 = -f - 4*b + 28, 50 = 5*f + 5*b. Factor -f*c - 3*c**3 + 0*c - 2*c**4 + 4*c - 4*c**2 - 2*c**3.
-c*(c + 1)**2*(2*c + 1)
Let z(l) be the second derivative of l**5/60 - 3*l**2/2 + 7*l. Let u(o) be the first derivative of z(o). Determine t so that u(t) = 0.
0
Let y(s) be the third derivative of s**7/210 + s**6/360 + 5*s**3/6 + 5*s**2. Let w(g) be the first derivative of y(g). Solve w(f) = 0.
-1/4, 0
Let t = -8 + 10. Let f be -9*((-1)/(-3) + -1). Solve 4*x + f*x**3 + x**2 - 8*x**t + x**2 - 4*x**2 = 0 for x.
0, 2/3, 1
Let a(j) be the third derivative of j**6/480 - j**5/120 - 7*j**4/96 - j**3/6 - 43*j**2. Factor a(z).
(z - 4)*(z + 1)**2/4
Let g be (10 + -1)*((-350)/56)/(-25). Factor -3/2 - 3/4*d**3 + 15/4*d + 3/4*d**4 - g*d**2.
3*(d - 1)**3*(d + 2)/4
Let k(s) be the second derivative of s**7/5040 + s**6/2160 + s**3/6 + 3*s. Let n(w) be the second derivative of k(w). Solve n(v) = 0.
-1, 0
Let w = 82 + -80. Let v be (-1 - 0)/((-2)/3). Find j such that v*j + 1/2*j**w + 1 = 0.
-2, -1
Let f(i) = -i - 1. Let v(o) = -2*o**2 - 24*o - 18. Let p(y) = 44*f(y) - 2*v(y). Solve p(u) = 0.
-2, 1
Let c = -1759/4 + 883/2. Suppose -2*p = -r - 7, 2*p - 17 = -r - 8. Factor c*j**2 + 1/4*j - p*j**4 + 0 + 2*j**3.
-j*(j - 1)*(4*j + 1)**2/4
Let y(g) = -g + 20. Let v be y(-11). Let q = v - 3. Factor -q*w**4 - 104/5*w**3 - 16/5*w**2 + 98/5*w**5 + 0*w + 0.
2*w**2*(w - 2)*(7*w + 2)**2/5
Let l be 1*(-1)/1 + 120/72. Factor -2/3*t**5 + l*t**4 + 2/3*t**3 - 2/3*t**2 + 0*t + 0.
-2*t**2*(t - 1)**2*(t + 1)/3
Factor -4/5*h**2 - 8/5 + 12/5*h.
-4*(h - 2)*(h - 1)/5
Let j = 10 - 4. Let o(u) = u**2 - 4*u. Let p(m) = m**2 - m + 1. Let b(g) = j*p(g) + 2*o(g). Suppose b(x) = 0. What is x?
3/4, 1
Let y = -300 - -902/3. Determine r so that -8/3*r**3 + 17/6*r**4 + 0 - 5/6*r**5 + y*r**2 + 0*r = 0.
0, 2/5, 1, 2
Let r(y) = y**2 + y + 1. Let g(o) = o**2 + 6*o - 2. Let v(i) = -2*g(i) + 4*r(i). Suppose v(b) = 0. What is b?
2
Let s(w) be the second derivative of -1/6*w**4 - 1/10*w**5 + 0*w**2 + 5*w + 0*w**3 + 0 - 1/60*w**6. Determine a, given that s(a) = 0.
-2, 0
Let m(q) be the second derivative of 9/8*q**2 + 0 + 1/48*q**4 + 1/4*q**3 - q. What is j in m(j) = 0?
-3
Let s = 37 - 41. Let p = s + 22/5. Solve 12/5*h + 18/5*h**2 + p = 0 for h.
-1/3
Let i(w) be the second derivative of -1/20*w**5 + 0 + 2*w + 0*w**4 + 0*w**2 + 0*w**3 - 1/30*w**6. What is a in i(a) = 0?
-1, 0
Suppose 10*h - 14*h + 8 = 0, 4*z - 2*h - 12 = 0. Factor -6/5*q**2 + 9/5*q**z + 9/5*q - 3/5 - 3/5*q**5 - 6/5*q**3.
-3*(q - 1)**4*(q + 1)/5
Factor 96*p + 22*p**2 + 7*p**2 + 8*p**4 - 3*p**2 + 32 - 33*p**3 - 3*p**4.
(p - 4)**2*(p + 1)*(5*p + 2)
Let h(t) be the third derivative of t**5/240 - 5*t**4/96 + t**3/4 + 32*t**2. Factor h(l).
(l - 3)*(l - 2)/4
Let g be 5 + ((-258)/54 - 3 - -3). Solve -2/9 - 2/9*q**3 + g*q + 2/9*q**2 = 0 for q.
-1, 1
Let d(y) = -y**3 - 6*y**2 - 7*y. Let p be d(-5). Factor 5*g + 2*g - p*g + 3*g**2.
3*g*(g - 1)
Suppose 5*t = -2*j - 8, -3*t + 4*j = -t - 16. Factor t + 1/2*m**4 - 1/2*m - 3/2*m**3 + 3/2*m**2.
m*(m - 1)**3/2
Let r = -9 + 12. Let i = 6 - 4. 