 1)/6
Let j = -367 - -367. Suppose 2/5*m + 8/5*m**3 - 2*m**2 + j = 0. Calculate m.
0, 1/4, 1
Let h(z) be the second derivative of 6*z**6/5 + 47*z**5/5 + 37*z**4/3 - 50*z**3 - 36*z**2 + 13*z. Factor h(x).
4*(x - 1)*(x + 3)**2*(9*x + 2)
Let q be ((-32)/40)/(2/(-5)). Factor -f + 1/2*f**q + 1/2.
(f - 1)**2/2
Suppose -9 = -4*c - q, c + 2*q - 6*q = -2. Suppose -5*z = o - 2*o + 7, 0 = -c*o - z + 3. Factor 2*x**5 + 6*x**3 + 1 - 1 - 2*x**o - 6*x**4.
2*x**2*(x - 1)**3
Let a be ((-147)/(-392))/(((-3)/(-18))/1). Factor a*q + 0 - 3/4*q**3 - 3/2*q**2.
-3*q*(q - 1)*(q + 3)/4
Let m(v) be the first derivative of 2*v**3/15 + v**2/5 - 4*v/5 + 3. Suppose m(w) = 0. Calculate w.
-2, 1
Let b(p) be the first derivative of p**6/18 - p**5/5 + p**4/4 - p**3/9 + 3. Suppose b(y) = 0. Calculate y.
0, 1
Let k = 133793/26 + -15434/3. Let g = k - -3/26. Factor -16/9 - g*v**2 - 2/9*v**3 - 8/3*v.
-2*(v + 2)**3/9
Find j, given that 0 - 3/2*j**2 + 3*j = 0.
0, 2
Let v(i) be the second derivative of -i**5/20 - i**4/12 - 3*i. Suppose v(r) = 0. Calculate r.
-1, 0
Let r be (5 - 4)/(2/6). Suppose 5 = -t + 2*t - 3*q, -5*t = 2*q - 8. Factor -z**t + 2*z - z**r - 2*z + z**4 + z**5.
z**2*(z - 1)*(z + 1)**2
Let a(h) be the second derivative of 0*h**2 + 0 + 4*h + 1/4*h**4 + 1/6*h**3. Solve a(g) = 0 for g.
-1/3, 0
Let k(h) be the second derivative of h**5/70 + h**4/42 - 2*h. Determine s, given that k(s) = 0.
-1, 0
Let b(o) = -4*o**3 + 10*o**2 - 1 - 10*o**2. Let g be b(-1). Determine h, given that 2*h**2 - 7*h**2 + 2*h - h**2 - g*h**3 - 5*h = 0.
-1, 0
Let x(s) be the second derivative of 8/27*s**3 + 0 + 1/3*s**2 + 3*s - 1/18*s**4. Solve x(a) = 0 for a.
-1/3, 3
Let z(f) be the third derivative of 0*f**7 + 0*f**4 + 0 - 2*f**2 + 0*f**3 + 1/112*f**8 - 3/40*f**6 - 1/10*f**5 + 0*f. Find h such that z(h) = 0.
-1, 0, 2
Let u(p) = 10*p**3 + 6*p**2 + 5*p + 7. Let a(w) = w**3 + w**2 + w + 1. Let b(c) = 21*a(c) - 3*u(c). Factor b(k).
-3*k*(k - 1)*(3*k + 2)
Let h be (-1 + 34/(-20))/(9/(-24)). Factor 0*m + 54/5 + 16/5*m**3 - 2/5*m**4 - h*m**2.
-2*(m - 3)**3*(m + 1)/5
Let q = 1/73 - -141/365. Find j, given that -2/5*j**2 + 2/5*j**4 - q*j**5 + 2/5*j**3 + 0 + 0*j = 0.
-1, 0, 1
Let g be 2*(-3 - (-37)/12). Factor -5/6*a + 1/3 + 2/3*a**2 - g*a**3.
-(a - 2)*(a - 1)**2/6
Let c = -112 - -115. Let f(r) be the second derivative of -4/3*r**c + 0 - 5/18*r**4 - 4/3*r**2 + 3*r. Factor f(q).
-2*(q + 2)*(5*q + 2)/3
Suppose 57 = -2*v + 63. Let j be 2 + (-1)/1 + -1. Suppose j*g + 0*g**v + 0*g**2 - 2/3*g**4 + 0 = 0. What is g?
0
Let v = 13/22 + -1/11. Let l(g) be the first derivative of 1/2*g**2 + v*g + 2 + 1/6*g**3. Factor l(t).
(t + 1)**2/2
Let m be ((-10)/(-12))/((-30)/(-24)). Factor 10/3*r - 23/6*r**2 - m + 7/6*r**3.
(r - 2)*(r - 1)*(7*r - 2)/6
Let l(h) be the second derivative of h**7/560 + h**6/48 + 7*h**5/80 + 3*h**4/16 - 7*h**3/6 - h. Let n(c) be the second derivative of l(c). Factor n(y).
3*(y + 1)**2*(y + 3)/2
Suppose o + 0 - 3 = 0. Let a = o - 1. What is n in -a*n**2 + n**4 + 0*n**3 + n**2 - n**3 + n = 0?
-1, 0, 1
Let n = -2846/3 - -958. Let t = -9 + n. Factor 1/3*s**3 + 0 - t*s - 1/3*s**4 + 1/3*s**2.
-s*(s - 1)**2*(s + 1)/3
Let r(s) = 3*s**4 - 4*s**4 + 0*s**4 - s**2 + 0*s**2. Let u(o) = 2*o**4 - 4*o**3 + 4*o**2 + 4*o + 2. Let n(k) = 4*r(k) + u(k). Factor n(y).
-2*(y - 1)*(y + 1)**3
Let r(p) = 15*p**3 + p**2 - 2*p + 1. Let i be r(1). Let y be ((-10)/(-3))/(10/i). Factor 2/7*l**2 + 0*l - 2*l**4 + 8/7*l**y + 0 + 4/7*l**3.
2*l**2*(l - 1)**2*(4*l + 1)/7
Let 51*g**3 - g**2 - 48*g**3 + 4*g**2 = 0. Calculate g.
-1, 0
Let g(i) be the third derivative of 2*i**7/15 + i**6/6 - 2*i**5/15 + 17*i**2. Solve g(l) = 0 for l.
-1, 0, 2/7
Let r(z) be the third derivative of -z**10/50400 + z**9/10080 + z**8/6720 - z**7/840 + z**5/60 + 7*z**2. Let d(h) be the third derivative of r(h). Factor d(x).
-3*x*(x - 2)*(x - 1)*(x + 1)
Let j(m) = m**2 + 4. Let r(a) = 1. Let z(l) = -3*j(l) + 24*r(l). Find k, given that z(k) = 0.
-2, 2
Factor 0 - 1/4*t**2 - 1/4*t**3 + 1/4*t + 1/4*t**4.
t*(t - 1)**2*(t + 1)/4
Let r be (32/(-100))/((-32)/(-20) - 2). Factor 1/5*c + 0 + 3/5*c**3 + r*c**2.
c*(c + 1)*(3*c + 1)/5
Suppose -x = -1 - 2. Solve -s**4 + 2*s**3 - 2*s**3 + x*s**2 - 2*s**2 = 0 for s.
-1, 0, 1
Let q(o) = o - 1. Let j be q(-3). Let f = 4 + j. Factor 4*a**3 + f*a**2 - 2*a**4 + a**2 - 3*a**2.
-2*a**2*(a - 1)**2
Factor 6*w - 6*w**3 + 3/2*w**4 + 9/2*w**2 - 6.
3*(w - 2)**2*(w - 1)*(w + 1)/2
Let z(n) be the first derivative of 2*n**3/3 + 9*n**2 + 16*n + 27. Solve z(t) = 0 for t.
-8, -1
Let q(m) be the third derivative of m**6/1140 - m**4/76 + 2*m**3/57 - 12*m**2. Factor q(s).
2*(s - 1)**2*(s + 2)/19
Let t(i) be the third derivative of -i**6/120 + i**4/8 - i**3/3 - 10*i**2. Find j such that t(j) = 0.
-2, 1
Let n(u) be the first derivative of 2*u**6/3 + 4*u**5/5 - 2*u**4 - 8*u**3/3 + 2*u**2 + 4*u + 17. Factor n(q).
4*(q - 1)**2*(q + 1)**3
Suppose 11*f - 9*f = 6. Suppose -c - 3*c = -4, 5*p + c = 16. Suppose 2*t**3 + 2*t**4 - 2*t**5 - f*t**p + 5*t**3 = 0. Calculate t.
-1, 0, 2
Factor -3*m**4 + 56*m + 11*m**4 - 26*m**3 - 60*m + 22*m**2.
2*m*(m - 2)*(m - 1)*(4*m - 1)
Let h = -437/2 - -219. Determine a, given that -a**2 - h*a + 0 - 1/2*a**3 = 0.
-1, 0
Let y = -36 + -1. Let v = 39 + y. Determine q, given that 3/2*q**v + 0 + 9/2*q**4 - 15/2*q**3 + 3/2*q = 0.
-1/3, 0, 1
Suppose 4/9 + 2/9*d + 4/9*d**3 - 10/9*d**2 = 0. What is d?
-1/2, 1, 2
Suppose 2*k - 25 = 5*z, -z - 3*z = 2*k + 20. Let i(v) be the second derivative of v + 1/24*v**3 - 1/80*v**5 + k - 1/48*v**4 + 1/8*v**2. Factor i(d).
-(d - 1)*(d + 1)**2/4
Let y(m) = m + 4. Let c be y(-2). Let b(n) be the first derivative of 2 - 9*n**3 + 1 - 2 - c*n**2 - n**2. Factor b(z).
-3*z*(9*z + 2)
Factor 8/9*m**3 - 26/9*m**2 + 8/9 - 26/9*m.
2*(m - 4)*(m + 1)*(4*m - 1)/9
What is m in 0 - 2/5*m**3 - 4/5*m - 6/5*m**2 = 0?
-2, -1, 0
Let q(n) = -n**3 - 6*n**2 - 5*n + 2. Let z be q(-5). Factor m**z + 28*m - 28*m.
m**2
Suppose -9*h + 8*h = 0. Let s = 9 - 6. Factor 2*a**3 + 3 - a**2 - 5 + h*a**2 - 2*a + s*a**2.
2*(a - 1)*(a + 1)**2
Let i(x) be the first derivative of x**4/12 - x**3/9 - x**2/6 + x/3 + 3. Factor i(t).
(t - 1)**2*(t + 1)/3
Find o, given that 1/8*o**3 + 0 - 1/8*o - 1/8*o**2 + 1/8*o**4 = 0.
-1, 0, 1
Let u(x) be the third derivative of x**5/120 - 45*x**2. Factor u(t).
t**2/2
Let n(o) be the third derivative of o**6/240 + o**5/60 - o**4/16 + 2*o**2. Suppose n(w) = 0. Calculate w.
-3, 0, 1
Factor -2/7*a**2 - 2/7 + 4/7*a.
-2*(a - 1)**2/7
Suppose 0 = 5*h - 75. Let a be (-8)/(-20) - (-4)/h. Factor 0 + 4/3*l**2 - a*l**3 + 0*l.
-2*l**2*(l - 2)/3
Factor -40*x - 10*x**2 + 200 - 8*x**2 + 20*x**2.
2*(x - 10)**2
Let q(z) be the second derivative of 3*z - 1/2*z**2 + 1/30*z**4 - 1/300*z**5 - 2/15*z**3 + 0. Let k(t) be the first derivative of q(t). Factor k(v).
-(v - 2)**2/5
Let t = 17 - 15. Let s(x) be the second derivative of x + 7/2*x**4 + 0 + 1/10*x**5 - 23/15*x**6 + 2*x**t + 4/7*x**7 - 13/3*x**3. Find d, given that s(d) = 0.
-1, 1/4, 2/3, 1
Suppose 15 = n - 5*f, 5*n + 2*f + 12 = -2*f. Let o(i) be the second derivative of 1/30*i**6 + 0*i**2 + 1/18*i**4 + 1/12*i**5 + n + 0*i**3 - 2*i. Factor o(g).
g**2*(g + 1)*(3*g + 2)/3
Solve 23*h**2 - 50*h**2 + 28*h**2 - 4 = 0 for h.
-2, 2
Let y = 121020/7 + -17224. Let j = y + -64. Factor -8/7*v**2 + 10/7*v + 2/7*v**3 - j.
2*(v - 2)*(v - 1)**2/7
Suppose -2*j = 3*j - 15. Let q(g) be the second derivative of 0*g**2 + 1/3*g**4 + 1/5*g**6 + 0*g**3 + 0 - j*g - 1/2*g**5. Factor q(l).
2*l**2*(l - 1)*(3*l - 2)
Suppose 14 = 3*b + 5*w, 5*w = -8*b + 3*b + 10. Let f = 2 + b. Find y, given that f + 2/3*y - 5/3*y**2 = 0.
0, 2/5
Suppose -3*b = 2*b. Suppose b*v - 3*f = v - 19, 3*v + 2*f = 22. Factor -2*a - 6 - a**2 + v - a.
-(a + 1)*(a + 2)
Let z(v) = -v**2 - 2*v - 7. Let a be (-1 + 0)/(-2)*12. Suppose x - a = -0*x. Let g(d) = 3. Let h(c) = x*g(c) + 3*z(c). Factor h(t).
-3*(t + 1)**2
Let i = 125 + -2499/20. Let k(j) be the first derivative of 1/8*j**4 - 1/8*j**2 + 1/4*j + 1 - 1/6*j**3 + i*j**5 - 1/24*j**6. Factor k(r).
-(r - 1)**3*(r + 1)**2/4
Let g(p) be the first derivative of p**6/6 + 3*p**5/5 - p**4/4 - 7*p**3/3 + 4*p + 8. Suppose g(o) = 0. What is o?
-2, -1, 1
Let f(m) = -m**2 - 7*m - 5. Let k be f(-5). Factor 6*p**2 + 4*p**2 - 2*p - k*p + p - 4.
2*(p - 1)*(5*p + 2)
Let q be (15/40)/(6/4). Solve -3*m - q