Let b(w) be the first derivative of 2/3*w - 1 + 1/9*w**3 + 1/2*w**2. Factor b(g).
(g + 1)*(g + 2)/3
Let y(w) be the third derivative of 0 + 2*w**2 + 0*w - 1/150*w**5 + 1/60*w**4 + 0*w**3. Determine r, given that y(r) = 0.
0, 1
Let r(g) be the first derivative of -1/6*g**4 - 4 + 2/3*g**3 + 2*g - g**2. Let v(i) be the first derivative of r(i). Let v(x) = 0. Calculate x.
1
Let 0*h**2 - h**2 + 4*h + 5 - 8 = 0. Calculate h.
1, 3
Factor 1/2*x - 3/4 + 1/4*x**2.
(x - 1)*(x + 3)/4
Suppose 3*u - u = 4. Let q(x) be the first derivative of 0*x**3 - 3 + 1/10*x**5 + 0*x - x**u + 3/8*x**4. Determine t so that q(t) = 0.
-2, 0, 1
Let a(x) = -x**5 - x**4 - x**3 + 3. Let r(o) = 3*o**5 + 3*o**4 + o**3 - 7. Let s(z) = 7*a(z) + 3*r(z). Solve s(j) = 0.
-2, 0, 1
Suppose 1/8*p**5 + 3/8*p**4 + 3/8*p**3 + 0*p + 1/8*p**2 + 0 = 0. Calculate p.
-1, 0
Let w = -17 + 17. Factor w + 4*s - 4*s - 2*s + s**2 + 1.
(s - 1)**2
Let z be 1052*-2*(-1)/(-612). Let n = 66/17 + z. Determine g, given that 0 + n*g - 2/9*g**2 = 0.
0, 2
Let m(l) be the third derivative of l**7/4200 - l**6/600 + l**5/300 - l**3/2 + 3*l**2. Let w(k) be the first derivative of m(k). Suppose w(v) = 0. What is v?
0, 1, 2
Determine l so that 0 + 2/11*l**2 + 4/11*l = 0.
-2, 0
Suppose -3*z + 12 = -3*w, -2*w = -w + 2. Solve -2*d**3 - 2/3*d + 0 + 2/3*d**4 + z*d**2 = 0 for d.
0, 1
Let k = -7 - -10. Factor -96*o**3 + 95*o**k + 4*o**2 - 3*o**2.
-o**2*(o - 1)
Find n, given that 0*n + 1/4*n**3 + 0 - 1/4*n**4 + 0*n**2 = 0.
0, 1
Let j(v) be the third derivative of 1/60*v**6 + 1/30*v**5 + 0*v + 0 + 0*v**4 - 2*v**2 + 0*v**3 - 1/168*v**8 - 1/105*v**7. Find n such that j(n) = 0.
-1, 0, 1
Let o = -476 - -478. Determine p so that -25/2*p**3 - 12*p + 2 + 45/2*p**o = 0.
2/5, 1
Suppose 2*v + 0*v = v. Let t(b) be the third derivative of 4/3*b**3 + 0*b - 3*b**2 + v + b**4 + 1/6*b**5. Factor t(h).
2*(h + 2)*(5*h + 2)
Let h = 3 + 4. Let -3*g**3 + 0*g**4 - 5*g**4 - h*g**4 - 9*g**5 = 0. Calculate g.
-1, -1/3, 0
Let h(b) = 4*b**3 + 11*b**2 - 6*b - 2. Let n(q) = 27*q**3 + 78*q**2 - 42*q - 15. Let z(o) = 15*h(o) - 2*n(o). Factor z(w).
3*w*(w + 2)*(2*w - 1)
Let o = -17 - -21. Suppose -5*v + 2*p + 14 = o*p, 0 = -v - 4*p + 10. Determine k so that -2/3*k - 2/9*k**v - 4/9 = 0.
-2, -1
Let m(k) = 5*k**4 + 4*k**3 + 10*k**2 + 8*k + 5. Let a(j) = 4*j**4 + 4*j**3 + 9*j**2 + 7*j + 4. Let p(q) = -4*a(q) + 3*m(q). Factor p(w).
-(w + 1)**4
Suppose -3*j - j + 8 = 0. Factor j*w**2 + 2*w**3 + 0*w**2 - w - 2 - w.
2*(w - 1)*(w + 1)**2
Let u(o) = 2*o**2 + 4*o + 4. Let c(x) = -3*x**2 - 7*x - 8. Let w(j) = -3*c(j) - 5*u(j). Let f be w(0). Factor 3*l**5 + 0*l**5 + 0*l**4 + l**f - 2*l**3.
l**3*(l + 1)*(3*l - 2)
Let x be 8/(-40)*10/(-12). Factor 0 + x*q**3 + 0*q**2 + 0*q.
q**3/6
Let g(c) = c**2 - 16*c + 30. Let r be g(14). Let v(z) be the first derivative of 1/7*z**r + 0*z + 1/14*z**4 + 2 + 4/21*z**3. Find o such that v(o) = 0.
-1, 0
Suppose -k = 1, -u + 5*k + 5 = -5. Let m(o) be the first derivative of 2/5*o**4 + 0*o + 2 + 6/25*o**u + 0*o**2 + 2/15*o**3. Factor m(x).
2*x**2*(x + 1)*(3*x + 1)/5
Suppose 2*c = 6, -3*n + 0*n + 4*c - 12 = 0. Let u(w) be the first derivative of n*w + 1 - 1/3*w**3 + 1/4*w**4 + 0*w**2. Factor u(b).
b**2*(b - 1)
Let g(b) = 7*b**3 - 24*b**2 + 96*b - 133. Let f(y) = 6*y**3 - 24*y**2 + 96*y - 132. Let c(k) = 5*f(k) - 4*g(k). Solve c(z) = 0.
4
Let o(t) be the second derivative of 0*t**2 + 1/130*t**5 - 2/39*t**3 - 3*t + 0 - 1/78*t**4. Factor o(p).
2*p*(p - 2)*(p + 1)/13
Suppose -3*u = -4*o + 48, 0 = -3*o - 2*u + 31 + 5. Suppose -o = -5*q + 8. Factor -1/2*x**5 + 0 - 1/4*x**2 + 0*x + 0*x**3 + 3/4*x**q.
-x**2*(x - 1)**2*(2*x + 1)/4
Find h such that 2/9 + 2/9*h**4 - 4/9*h**2 + 0*h**3 + 0*h = 0.
-1, 1
Factor 6*c**2 - 513*c + 447*c + 363 - 3*c**2.
3*(c - 11)**2
Let r(z) be the third derivative of -z**6/2 - 11*z**5/12 - 5*z**4/12 + 19*z**2. Factor r(w).
-5*w*(3*w + 2)*(4*w + 1)
Let g(d) be the third derivative of 0*d**3 + 0 + 0*d + 7*d**2 - 7/300*d**6 + 1/75*d**5 + 0*d**4. Let g(u) = 0. What is u?
0, 2/7
Find o, given that -4*o**3 + 4*o**4 + 31*o**2 + 24*o**2 - 63*o**2 = 0.
-1, 0, 2
Let a be (3 + 55/(-15))*-12. Let s be (a/(-16))/(1 - 2). Factor -7/4*l - 3/4*l**3 + s + 2*l**2.
-(l - 1)**2*(3*l - 2)/4
Let r(h) be the second derivative of h**4/72 - h**3/12 + h**2/6 + 3*h. Let r(w) = 0. What is w?
1, 2
Let j(n) be the second derivative of -n**5/10 - n**4/3 - n**3/3 - 8*n. Factor j(i).
-2*i*(i + 1)**2
Let m(r) be the second derivative of 3*r**5/20 - r**4/4 - r. Determine d so that m(d) = 0.
0, 1
Let g(c) be the third derivative of 0*c**3 + 2/15*c**5 + 1/60*c**6 + 0*c + 0*c**4 + 0 - 9*c**2. Factor g(b).
2*b**2*(b + 4)
Let h(s) be the second derivative of -s**7/63 - s**6/9 - 3*s**5/10 - 7*s**4/18 - 2*s**3/9 - 7*s. Suppose h(n) = 0. What is n?
-2, -1, 0
Suppose 2*q = 6*q - 28. Suppose -1 + q = 2*g. Factor 8*c**4 - 10*c**g - 1 + 2*c + 5 - 9*c**2 - 3*c**2 + 2*c**3 + 6*c**5.
2*(c - 1)*(c + 1)**3*(3*c - 2)
Let g = 10 - 7. Factor 4*u**2 + 2*u - g*u**2 + 0*u**2 - 3*u.
u*(u - 1)
Let d(w) be the third derivative of -1/210*w**5 + w**2 - 1/420*w**6 + 0 + 0*w + 1/84*w**4 + 0*w**3 + 1/735*w**7. Factor d(k).
2*k*(k - 1)**2*(k + 1)/7
Suppose 68 = 3*p + p. Suppose 0 = 2*f + f + 5*w - 28, 3*f - 4*w = -p. Find l such that 10*l**2 - f - 4 + 16*l - 3 = 0.
-2, 2/5
Let w(n) = -n**3 - 2*n**2 + 3*n. Let u be w(-3). Let l be 1 + 1 + u + -2. Let l*d + 1 - 5 - 6*d**3 + 2*d + 8*d**2 = 0. Calculate d.
-2/3, 1
Let n(j) be the third derivative of j**5/330 - j**4/132 - 7*j**2. Suppose n(b) = 0. Calculate b.
0, 1
Let -15 - 408*u**2 - 1 - 16*u + 404*u**2 = 0. What is u?
-2
Factor -4/5*h**2 + 0 - 3/5*h - 1/5*h**3.
-h*(h + 1)*(h + 3)/5
Determine z, given that 0 + 0*z**2 + 0*z**3 - 1/9*z**5 + 0*z - 2/9*z**4 = 0.
-2, 0
Let z = 9983/11 - 907. Let 2/11*j - z*j**2 + 0 - 2/11*j**4 + 6/11*j**3 = 0. Calculate j.
0, 1
Let q(o) be the third derivative of o**6/300 + 3*o**5/50 + 9*o**4/20 + 9*o**3/5 - 9*o**2. Factor q(w).
2*(w + 3)**3/5
Let n(f) = -f**3 + f**2. Let c(y) = 2*y**3 - 3*y**2. Suppose l + l = -6. Let q(o) = l*n(o) - c(o). Factor q(r).
r**3
Suppose -1 - 15 = -8*q. Let z(p) be the second derivative of p + 1/27*p**3 + 1/27*p**4 + 0*p**q + 0 + 1/90*p**5. Factor z(h).
2*h*(h + 1)**2/9
Suppose 5*h + 4*f = -3 + 1, -22 = -5*h + 4*f. Factor 1 + 6*i - 3 + 4*i**4 + 0 - 2*i**h - 6*i**3 + 0*i**3.
2*(i - 1)**2*(i + 1)*(2*i - 1)
Let y = -2/59 - -65/177. Let a(l) be the first derivative of 0*l**2 + 1/4*l**4 + 1 + 0*l - y*l**3. Factor a(m).
m**2*(m - 1)
Let o(d) = 6*d**2 - 14*d + 8. Let n(i) = 63 + i - i**2 - 63. Let j(a) = 2*n(a) + o(a). Factor j(g).
4*(g - 2)*(g - 1)
Let x(f) be the first derivative of 0*f**2 - 2/15*f**3 - 3 + 0*f - 1/10*f**4. Factor x(p).
-2*p**2*(p + 1)/5
Let o(t) = t**3 + 12*t**2 + 11*t - 2. Let k be o(-11). Let v be k/2*6/(-3). Factor -2/9*h**3 + 2/9*h + 0 + 0*h**v.
-2*h*(h - 1)*(h + 1)/9
Find z, given that 8*z - 4/3*z**2 - 12 = 0.
3
Let t(d) be the second derivative of 1/3*d**4 + 5*d + 0 + 4/3*d**3 - 8*d**2 - 1/10*d**5. Factor t(i).
-2*(i - 2)**2*(i + 2)
Let v be (-3)/((-4)/(16/6)). Let 29*w**3 - 9*w - 4 + 9*w**v + 4*w**3 + 18*w**4 + 1 = 0. What is w?
-1, -1/3, 1/2
Let w(s) be the third derivative of -s**6/60 + s**4/4 - 2*s**3/3 + 4*s**2. Determine i, given that w(i) = 0.
-2, 1
Let x(f) be the second derivative of -f**4/60 + f**3/5 - 9*f**2/10 + 9*f. Solve x(n) = 0 for n.
3
Let v be (-27)/2*(-1 + -1). Let x be (-70)/(-63) - (-6)/v. Factor x + 2/3*f**2 - 2*f.
2*(f - 2)*(f - 1)/3
Let m(n) = -4*n**4 - 12*n**3 + 8*n**2 + 16*n - 20. Let h(q) = q**2 + q - 1. Let v(c) = 20*h(c) - m(c). Determine b, given that v(b) = 0.
-1, 0
Let c be 551/174 - 1/6. Find o, given that -2/7*o**4 + 0*o - 2/7*o**c + 0*o**2 + 0 = 0.
-1, 0
Let c be (-2)/1*(0 + 6/(-4)). Determine x so that 2/9*x**c + 0*x**2 + 4/9*x**5 + 0*x - 2/3*x**4 + 0 = 0.
0, 1/2, 1
Let l = -5861/1485 - -110/27. Let x = l + 3/11. Suppose 2/5 + x*j**2 - 4/5*j = 0. What is j?
1
Let f(u) be the second derivative of -u**6/150 + u**4/10 - 4*u**3/15 + 3*u**2/10 - 15*u. Suppose f(w) = 0. Calculate w.
-3, 1
Determine b so that 10*b**3 + 4*b**2 + 13 + 8*b**4 - 13 + 2*b**5 = 0.
-2, -1, 0
Let q(t) be the second derivative of t**5/10 + t**4/6 - t**3/3 - t**2 - 13*t. Let q(n) = 0. What is n?
-1, 1
Let m(i) = -3*i**2 - 8*i - 11. Let f(l) = 7*l**2 + 16*l + 23