- 1)*(n + 1)**2/5
Let n(p) be the first derivative of -11/9*p**3 + 2 - 4/3*p - 2*p**2 + 1/5*p**5 - 1/12*p**4 + 1/18*p**6. Factor n(d).
(d - 2)*(d + 1)**3*(d + 2)/3
Let x(m) = m**3 + 6*m**2 - 4. Let i be x(-5). Suppose -i = -5*z - 6. Suppose 3 + 2*u**2 - z*u - 6 + 4 = 0. What is u?
1/2, 1
Let p = 135/572 - -2/143. Factor 0*t + 0*t**2 + 0 + 1/2*t**4 - p*t**3.
t**3*(2*t - 1)/4
Let k(a) be the third derivative of -a**7/1400 + a**6/225 - a**5/200 - a**4/60 + a**3/2 - a**2. Let u(o) be the first derivative of k(o). Factor u(h).
-(h - 2)*(h - 1)*(3*h + 1)/5
Let b(d) be the first derivative of d**4/36 + d**3/9 + d**2/6 + d + 1. Let x(g) be the first derivative of b(g). Factor x(j).
(j + 1)**2/3
Let h(x) be the second derivative of -x**8/33600 - x**7/6300 + x**4/12 + 3*x. Let b(v) be the third derivative of h(v). Factor b(w).
-w**2*(w + 2)/5
Let i be (-3)/(-9) + (-5)/(-3). Let s(k) = 2*k**5 - 6*k**4 + 2*k. Let f(p) = p**4 + p**3 - p. Let x(v) = i*f(v) + s(v). Factor x(d).
2*d**3*(d - 1)**2
Let y = 3148/237 + 4/79. Factor y*j**2 + 2*j - 4/3.
2*(4*j - 1)*(5*j + 2)/3
Find c such that -2/5*c**3 + 0*c**2 + 1/5*c**5 + 0*c**4 + 1/5*c + 0 = 0.
-1, 0, 1
Let k(h) be the third derivative of -h**5/360 + h**4/36 - h**3/12 + 6*h**2. Find r, given that k(r) = 0.
1, 3
Let v(t) be the first derivative of t**4/4 + 7*t**3/3 + 4*t**2 - 16*t - 1. Suppose v(k) = 0. What is k?
-4, 1
Factor 8 + 0*o - 8*o + 4*o**2 + 0*o**2 - 2*o**2.
2*(o - 2)**2
Find i such that 0*i + 4*i**2 + 0 + i**3 - 113/2*i**4 + 14*i**5 = 0.
-1/4, 0, 2/7, 4
Factor 4*r + 8 - 2 - 7 - 3*r**2.
-(r - 1)*(3*r - 1)
Let r(d) = d**2 - d - 3. Let i be r(3). Factor 2*g**2 + 3*g + 2*g + 8 + i*g.
2*(g + 2)**2
Let u(k) be the third derivative of -k**6/300 - k**5/60 - k**4/30 - k**3/30 + 57*k**2. Factor u(y).
-(y + 1)**2*(2*y + 1)/5
Let y(h) be the first derivative of -2*h**3/3 + 2*h + 5. Solve y(z) = 0.
-1, 1
Let b(v) be the third derivative of -1/60*v**4 + 0*v + 0 + 2/15*v**3 + 3*v**2 + 1/300*v**6 - 1/75*v**5. Find n such that b(n) = 0.
-1, 1, 2
Factor -4/9*f**2 + 0 + 2/3*f**4 - 2/9*f**3 + 0*f.
2*f**2*(f - 1)*(3*f + 2)/9
Suppose -n + 3*n - 5 = o, 35 = 3*n + 4*o. Factor -n*v + v**2 + v + 2 - 2*v + 3*v.
(v - 2)*(v - 1)
Let x be 2/(-8) + (0 - 63/(-28)). Factor 2/9*z**3 + 4/9*z + 0 + 2/3*z**x.
2*z*(z + 1)*(z + 2)/9
Let c(z) = z**3 + 2*z**2 - 2*z + 8. Let v be c(-3). Determine x, given that 1/2*x + 0 + 1/2*x**v - x**3 + 0*x**2 + 0*x**4 = 0.
-1, 0, 1
Let j(d) be the third derivative of -d**5/12 - 5*d**4/8 + 11*d**2. Determine w, given that j(w) = 0.
-3, 0
Let c(l) be the second derivative of -5/3*l**3 + l**2 + l + 0 + 2/3*l**4. Solve c(u) = 0 for u.
1/4, 1
Let p = 37 - 17. Suppose 4*c - c = 2*j - 8, 0 = 3*c + 5*j - p. Factor 2*w**3 + c*w + w - 3*w**3.
-w*(w - 1)*(w + 1)
Let k(f) be the first derivative of 2*f**6/15 - 12*f**5/25 + 2*f**4/5 + 8*f**3/15 - 6*f**2/5 + 4*f/5 + 4. Factor k(s).
4*(s - 1)**4*(s + 1)/5
Let 3/4*f + 0 + 3/4*f**5 - 3*f**2 + 9/2*f**3 - 3*f**4 = 0. Calculate f.
0, 1
Let y = -18 - -34. Factor 3*p + 4*p**3 - y*p**4 + 4*p - 7*p.
-4*p**3*(4*p - 1)
Suppose r - 73 + 70 = 0. Let -2/5*c**4 + 8/5*c**r + 0 - 2*c**2 + 4/5*c = 0. Calculate c.
0, 1, 2
Let d = -14123/14 + 1008. Let g = -2/7 - d. Determine u so that -1/2*u - g*u**3 + u**2 + 0 = 0.
0, 1
Let o be (8 + -9)/((-2)/4). Let m(k) be the third derivative of k**o + 1/2*k**3 + 1/180*k**5 + 0 + 0*k + 1/12*k**4. Factor m(p).
(p + 3)**2/3
Let a(x) = x**2 - 8*x + 9. Let g be a(7). Suppose -5*j + 11 = 5*y - 4, y = -g. Let -3*i**5 + i**j + 7*i**4 - 3*i**4 = 0. Calculate i.
0, 2
Suppose -15 = -3*i - 2*i. Let v be (3 - i) + 12/9. Solve -v*s + 0 - 2/3*s**2 = 0 for s.
-2, 0
Let b(k) be the second derivative of -k**6/90 + k**5/10 - k**4/3 + 5*k**3/9 - k**2/2 - 17*k. Factor b(m).
-(m - 3)*(m - 1)**3/3
Let q(f) = 2*f**2 - 14*f + 24. Let h be q(5). Factor -1/4*i**h + 0*i**2 + 1/4*i**3 + 0*i + 0.
-i**3*(i - 1)/4
Factor 3/7*h - h**2 + 5/7*h**3 + 0 - 1/7*h**4.
-h*(h - 3)*(h - 1)**2/7
Suppose 4 = t - 2*q, -q + 1 = t - 0*q. Factor 0*c**3 + c**3 - t*c**5 + 0*c**4 + 6*c - 4*c**2 - 2 + 6*c**4 - 5*c**3.
-2*(c - 1)**4*(c + 1)
Let v(u) be the third derivative of -u**8/112 - 3*u**7/70 - 3*u**6/40 - u**5/20 - u**3 - u**2. Let r(t) be the first derivative of v(t). Factor r(y).
-3*y*(y + 1)**2*(5*y + 2)
Let h be 3 - ((-8)/(-39) + 3). Let j = h - -446/273. Find g, given that 8/7 + 32/7*g - 2*g**3 + j*g**2 = 0.
-1, -2/7, 2
Let 4/17 + 56/17*h**2 - 30/17*h = 0. Calculate h.
1/4, 2/7
Let u(z) be the third derivative of z**7/189 - 23*z**6/540 + 5*z**5/54 - z**4/108 - 2*z**3/9 + 47*z**2. Solve u(a) = 0.
-2/5, 1, 3
Let k(w) be the first derivative of -5*w**4/4 + 5*w**3/3 - 11. Factor k(d).
-5*d**2*(d - 1)
Let n = 7 - 5. Solve 3*a**2 - 4*a - 1 - 3*a**2 - 1 - n*a**2 = 0 for a.
-1
Let n(v) be the third derivative of -v**5/10 + 13*v**4/24 - 7*v**3/6 - v**2. Let y(m) = -3*m**2 + 6*m - 3. Let i(z) = 3*n(z) - 5*y(z). Factor i(d).
-3*(d - 2)*(d - 1)
Let f(h) = -17*h**4 - 7*h**3 + 24*h**2 + 32*h - 23. Let x(y) = -4*y**4 - 2*y**3 + 6*y**2 + 8*y - 6. Let a(z) = 4*f(z) - 18*x(z). Determine t so that a(t) = 0.
-2, 1
Suppose -3 = g, 2*s + 3*g = 3*s - 9. Factor 0 + 0*v + 2/11*v**5 + s*v**2 - 4/11*v**4 + 2/11*v**3.
2*v**3*(v - 1)**2/11
Suppose 5 - 8 = -3*t. Let c be (-1 - 1/(-2))*-4. Let c + 2*s - t - s**2 - 2 = 0. Calculate s.
1
Let y(g) be the first derivative of g**6/420 + g**5/210 - g**2 - 6. Let l(u) be the second derivative of y(u). Find i such that l(i) = 0.
-1, 0
Let x(p) be the first derivative of -2 - 1/20*p**5 + 1/4*p**2 - 5/12*p**3 + 0*p + 1/4*p**4. Factor x(f).
-f*(f - 2)*(f - 1)**2/4
Suppose -d - 4 = -3*d. Factor r**d - r**2 - r**3 - r**2.
-r**2*(r + 1)
Let r(k) be the first derivative of -k**6/5 + 14*k**5/25 - 3*k**4/10 - 2*k**3/5 + 2*k**2/5 + 11. What is b in r(b) = 0?
-2/3, 0, 1
Let n = 92/387 + -2/129. Find p such that 2/9*p**3 - n*p**4 - 2/9*p + 2/9*p**2 + 0 = 0.
-1, 0, 1
Let j(t) be the third derivative of -t**6/120 - t**5/20 - t**4/8 - t**3/6 - 14*t**2. Factor j(s).
-(s + 1)**3
Let y(h) be the first derivative of h**4/14 + 4*h**3/21 + h**2/7 - 7. Find a, given that y(a) = 0.
-1, 0
Let 12*b - 6 + 14 + 3*b**2 + b**2 = 0. What is b?
-2, -1
Let w(d) = 7*d**4 - d**3 + 12*d**2 - 26*d + 8. Let j(h) = -6*h**4 + 2*h**3 - 13*h**2 + 25*h - 8. Let x(i) = 6*j(i) + 5*w(i). Let x(z) = 0. Calculate z.
1, 2
Let j(x) = 2*x**2 + 3*x. Let q be (2/(-3))/((-5)/(-15)). Let m be j(q). Suppose 0*l + 1/4 - 1/4*l**m = 0. Calculate l.
-1, 1
Let z(q) be the third derivative of 5*q**5/4 - 2*q**3 + 3*q**2. Factor z(g).
3*(5*g - 2)*(5*g + 2)
Let z(o) be the third derivative of o**6/40 + o**5/4 + o**4/2 + 20*o**2 + o. Find s, given that z(s) = 0.
-4, -1, 0
Let d(m) be the first derivative of -m**5/5 + m**4/4 + 2*m**3/3 - 14. Factor d(g).
-g**2*(g - 2)*(g + 1)
Let n(w) be the first derivative of -3 + 0*w + 15/4*w**4 - 2*w**3 + 21/5*w**5 + 0*w**2. Factor n(x).
3*x**2*(x + 1)*(7*x - 2)
Let n(s) be the second derivative of 5*s**7/27 - 4*s**6/135 - 2*s**5/45 - 19*s. Factor n(r).
2*r**3*(5*r - 2)*(7*r + 2)/9
Let u = 361 + -359. Factor 2/7*x + 0 + 2/7*x**u.
2*x*(x + 1)/7
Factor 0*l**3 - 2/7*l**4 - 4/7*l + 6/7*l**2 + 0.
-2*l*(l - 1)**2*(l + 2)/7
Let t(s) be the second derivative of s**5/20 - s**3/2 + s**2 - 10*s. Factor t(i).
(i - 1)**2*(i + 2)
Let l = -14 + 14. Let j(a) be the first derivative of 0*a + 2 - 1/12*a**3 + l*a**4 + 1/20*a**5 + 0*a**2. Factor j(s).
s**2*(s - 1)*(s + 1)/4
Let w be (-3)/2*(-8)/6. Suppose -w*j + 3*r = -3, 3*r - r + 4 = 2*j. Factor -2*v**3 + 2*v**3 - v**2 + v**j.
v**2*(v - 1)
Factor -5*u**3 + 484 + 21*u**2 - 396*u - 48*u**2 + u**3 - 57*u**2.
-4*(u - 1)*(u + 11)**2
Factor 1/2*o**3 + o**2 - 1/2*o - 1.
(o - 1)*(o + 1)*(o + 2)/2
Suppose -f = 3*z - 33, -2*z + 2*f = -4*z + 26. Determine n so that -4 - 9/2*n**3 - 3*n**2 + z*n = 0.
-2, 2/3
Find o, given that -5/4*o - 1/4*o**3 + o**2 + 1/2 = 0.
1, 2
Let c(l) be the first derivative of 0*l**2 - 1 - 1/5*l**5 - 1/12*l**4 + 0*l + 0*l**3. Find s such that c(s) = 0.
-1/3, 0
Let c(w) be the first derivative of -w**7/210 - w**6/15 - 2*w**5/5 - 4*w**4/3 + 2*w**3 - 5. Let u(h) be the third derivative of c(h). Factor u(l).
-4*(l + 2)**3
Let g = -22 - -14. Let n = 16 + g. What is z in n*z**2 - 3 - 6*z**3 - 1 + 2*z + 0*z = 0?
-2/3, 1
Let z(a) be the third derivative of -a**5/30