3*n. Let j = 1 + n. Factor -1/2*o**2 + 1/2 + j*o.
-(o - 1)*(o + 1)/2
Let o(z) = -5*z**3 + z + 1. Let q be o(-1). Suppose q*l - 3 = -4*i + 8, 4*l = -4. Solve -4*j**2 - j**3 + j + 2*j**3 - 2 + i*j = 0 for j.
1, 2
Let z(y) be the first derivative of -5*y**3/3 - 5*y**2 - 5*y - 39. Find m such that z(m) = 0.
-1
Suppose 0 = 4*s + i - 2*i - 21, 10 = -2*i. Find n such that -6*n**4 + 2*n**3 - 4*n + 2*n**3 + 0*n**4 + 2*n**5 - 2*n + 2 + s*n**2 = 0.
-1, 1
Let x(v) be the first derivative of v**4/4 + v**3 + v**2 + 4. Factor x(y).
y*(y + 1)*(y + 2)
Let r be 6/33 - 10/(-55)*-1. Factor 2/9*d**3 + 0*d**2 + r*d + 0 + 4/9*d**4 + 2/9*d**5.
2*d**3*(d + 1)**2/9
Suppose 3*m + m - 5*m = 0. Factor 3/7*z**3 + 1/7*z**4 + m + 2/7*z**2 + 0*z.
z**2*(z + 1)*(z + 2)/7
Let x(y) be the second derivative of y**4/12 + y**3 + 15*y. Factor x(a).
a*(a + 6)
Let t(v) = -v**3 - v**2 - 2*v + 2. Let l(q) = q**3 - q**2 + q + 1. Let f(m) = 2*l(m) + t(m). Let x be f(3). Factor -4*y**2 - 4*y**3 - y**x + y**2 - y + y**3.
-y*(y + 1)**3
Let l(v) be the first derivative of -v**4/30 + 2*v**3/15 - v**2/5 + 3*v + 2. Let p(w) be the first derivative of l(w). Factor p(h).
-2*(h - 1)**2/5
Let k(o) be the third derivative of o**8/6720 - o**6/480 + o**5/240 + 2*o**3/3 - o**2. Let u(t) be the first derivative of k(t). Factor u(c).
c*(c - 1)**2*(c + 2)/4
Let j(y) be the second derivative of -2*y**4/21 - 4*y**3/21 - y**2/7 - 4*y. Find b, given that j(b) = 0.
-1/2
Suppose 15 = 3*d, -5*u = d - 8 - 7. Suppose 5*y - u*y = 0. Factor t**2 + t**4 - t**3 + y*t**4 + 0*t**2 - t**3.
t**2*(t - 1)**2
Let c be 8/(-20) - (-6)/15. Let g(f) be the third derivative of 0*f + c - f**2 + 0*f**3 - 1/18*f**4 + 1/90*f**5. Factor g(l).
2*l*(l - 2)/3
Suppose -5*a + 33 = -2*a. Suppose 3*q - a = -3*u + 5*u, -10 = 5*u - 4*q. What is t in 2*t + 2*t - 4*t + t - t**u = 0?
0, 1
Let g = -5/3 - -37/6. Factor -g*b**2 - 7/2*b**3 - b**4 - 5/2*b - 1/2.
-(b + 1)**3*(2*b + 1)/2
Let t(w) be the second derivative of -w**6/30 - 3*w**5/5 - 9*w**4/2 - 18*w**3 - 81*w**2/2 + 6*w. Solve t(x) = 0 for x.
-3
Let u = -7035934/5763 + 20766/17. Let i = u - -2/113. Factor 4/3*b - i*b**2 + 0.
-2*b*(b - 2)/3
Suppose -3*q + 9 + 6 = 2*t, -3*t + 5*q = -13. Let c be t/9*(-6)/(-16). Factor c*n**5 - 1/4*n**4 + 0*n + 0 + 0*n**2 + 0*n**3.
n**4*(n - 1)/4
Factor m - 1 - 1/4*m**2.
-(m - 2)**2/4
Let c = 13 + -7. Suppose m - c*m - 4*a = -26, 2*m - a = 0. Suppose 0*s**m - 1/2*s**3 + 1 + 3/2*s = 0. What is s?
-1, 2
Let y be 168/260 + -5*(-10)/325. Factor 0 - 2/5*h**3 + 0*h + y*h**2.
-2*h**2*(h - 2)/5
Let k(j) = j. Let l(n) = -10*n + 4. Let p(h) = 3*k(h) - l(h). Let g be p(6). Find o such that -98*o**3 - o - g*o**2 + 18*o**2 - 7*o + 0*o = 0.
-2/7, 0
Let j = -4387/11 - -399. Factor -6/11 - j*d**2 + 8/11*d.
-2*(d - 3)*(d - 1)/11
Suppose 0 = 124*y - 128*y + 8. Factor 4/7*c**4 + 0*c**3 + 4/7*c**5 + 0*c + 0 + 0*c**y.
4*c**4*(c + 1)/7
Let h(y) be the third derivative of -y**8/168 - y**7/35 + y**6/60 + y**5/10 - 10*y**2. Suppose h(d) = 0. Calculate d.
-3, -1, 0, 1
Let z = 109/345 + 2/115. Factor 0 + z*l**2 - l.
l*(l - 3)/3
Suppose -2*x + x - 3 = 0, 17 = 4*d + x. Determine n so that -4*n**3 - 4*n**3 - 4*n + d*n**3 + n - 6*n**2 = 0.
-1, 0
Suppose 0 = -2*d - 2 + 6. Suppose -3 = d*n - 9. Find f such that n*f**2 - 3*f + 0 - f**3 + 2 - 1 = 0.
1
Let g(k) be the first derivative of -k**6/60 - k**5/40 + k - 2. Let b(n) be the first derivative of g(n). Find w, given that b(w) = 0.
-1, 0
Let c(o) = 5*o**4 + 3*o**3 + 4*o**2 - 3*o - 3. Let p(r) = 14*r**4 + 10*r**3 + 12*r**2 - 8*r - 8. Let a(k) = 8*c(k) - 3*p(k). Factor a(q).
-2*q**2*(q + 1)*(q + 2)
Let b(k) = k**2 + 6*k - 4. Let r be b(-7). Let d(z) be the first derivative of -5/6*z**2 - 2/9*z**r + 5/12*z**4 + 2/3*z - 1. Factor d(h).
(h - 1)*(h + 1)*(5*h - 2)/3
Find f, given that -8/3*f - 1/3*f**3 + 0 - 3*f**2 = 0.
-8, -1, 0
Factor 8/9*n + 4/9*n**2 + 4/9.
4*(n + 1)**2/9
Factor -4*p + 2*p - 2 - p**2 + 3*p - 4*p.
-(p + 1)*(p + 2)
Let i be (2 - (-1 + 2)) + -1. Factor -8*m**2 + 9*m**3 - 5*m**2 + 6*m + i*m**2 - 2*m**2.
3*m*(m - 1)*(3*m - 2)
Let g = 1209 + -10877/9. Factor 2/9*v**3 + g*v**2 + 0 + 2/9*v.
2*v*(v + 1)**2/9
Suppose 0 = -2*u + 2*u - 3*u. Let n(d) be the second derivative of 1/40*d**5 + 0*d**2 + 1/60*d**6 + 0*d**4 + u*d**3 - 2*d + 0. Determine v so that n(v) = 0.
-1, 0
Let t(u) be the second derivative of -u**5/20 + u**4/12 + 5*u**3/6 + 3*u**2/2 - 5*u - 7. Factor t(f).
-(f - 3)*(f + 1)**2
Let p(o) be the third derivative of o**6/1080 - 7*o**5/180 + 49*o**4/72 - 343*o**3/54 - 25*o**2. What is r in p(r) = 0?
7
Let i(x) be the third derivative of -x**8/2352 + x**7/735 - x**6/840 - 5*x**2. Factor i(p).
-p**3*(p - 1)**2/7
Let r(w) be the first derivative of w**7/280 + w**6/288 - w**5/80 + w**4/96 - w**3/3 + 4. Let a(t) be the third derivative of r(t). Factor a(h).
(h + 1)*(3*h - 1)*(4*h - 1)/4
Let p(h) be the second derivative of -h**5/6 - h**4/18 + 16*h**3/45 - 4*h**2/15 + 12*h. Factor p(f).
-2*(f + 1)*(5*f - 2)**2/15
Factor 24 + 5*s**5 - 5*s**3 - 3*s**4 - 12 + 3*s**2 - 12.
s**2*(s - 1)*(s + 1)*(5*s - 3)
Let i = 114 - 340/3. Factor 1/3*l**2 - i - 1/3*l.
(l - 2)*(l + 1)/3
Suppose 0 = 2*l + l + 18. Let j be l/27*(2 + -6). Factor -98/9*b**2 - j - 56/9*b.
-2*(7*b + 2)**2/9
Let z = 11 - 9. Determine r, given that 4*r**z - 4*r**4 - 29*r**3 - r**5 + 41*r**3 - 3*r**5 - 8*r = 0.
-2, -1, 0, 1
Factor 9*j**4 + 6*j - 2*j**3 + 0 - 1 + 2*j**2 + 0*j**2 - 4*j**5 - 10*j**2.
-(j - 1)**3*(j + 1)*(4*j - 1)
Let l(p) be the first derivative of p**3/2 - 3*p**2 + 6*p - 28. Let l(h) = 0. What is h?
2
Let f be -1 + 7 + (1 - 2). Suppose -f*z = -3*n - 22, -2*z = -5*z + 4*n + 22. Factor 5*p**4 + 2*p - 4*p**3 - 2 - 2*p**4 - p**4 + z*p.
2*(p - 1)**3*(p + 1)
Suppose 0 = 3*f - 6*f. Suppose -4*h - 5*l = -9*h - 15, 5*h - 4*l = -10. Factor 0 - 1/2*t**4 + 1/2*t**3 + 0*t + f*t**h.
-t**3*(t - 1)/2
Suppose 5*p + 144 = 4*t, -3*t + 85 = -4*p - 30. Let s be ((-7)/(p/24))/8. Determine i, given that s*i + 1/2 + 1/4*i**2 = 0.
-2, -1
Let v(m) be the first derivative of -2 + 1/3*m**3 + 1/2*m**2 + 0*m - 1/2*m**4. Let v(k) = 0. What is k?
-1/2, 0, 1
Factor 7 - 59*m + 15*m**2 + 11 + 8*m.
3*(m - 3)*(5*m - 2)
Let d be ((-8)/36*3)/(-2). Let i(r) be the second derivative of 0 + 2*r - 1/6*r**4 - 1/40*r**5 + 0*r**2 - d*r**3. Let i(k) = 0. What is k?
-2, 0
Factor -45 + 55*a - 9*a - 4*a - 5*a**2 - 12*a.
-5*(a - 3)**2
Let v(c) = -5*c**2 + 5*c - 3. Let d(g) = 9*g**2 - 10*g + 6. Let p(h) = -3*d(h) - 5*v(h). Let n(f) = f - 1. Let r(j) = -n(j) - p(j). Factor r(o).
2*(o - 2)*(o - 1)
Let z(c) be the second derivative of -c**5/12 - c**4/4 - c**3/6 + c**2/6 - 11*c. Factor z(d).
-(d + 1)**2*(5*d - 1)/3
Suppose -1/3*g**2 - 169/3 + 26/3*g = 0. What is g?
13
Let a = 4 + -3. Let l be a - ((-21)/6 + 3). Find r, given that -5/2*r + 1 - 1/2*r**4 + 1/2*r**3 + l*r**2 = 0.
-2, 1
Let l(c) = 2*c**2 + 3*c - 4. Let v be l(-3). Let a(z) be the third derivative of 1/12*z**4 + 0 - 1/30*z**v - 2*z**2 + 0*z**3 + 0*z. Factor a(w).
-2*w*(w - 1)
Let t(m) be the first derivative of m**4 - 4*m**3/3 - 4*m**2 - 9. Determine s so that t(s) = 0.
-1, 0, 2
Suppose 44*m - 27*m - 51 = 0. What is r in 10*r**m - 13*r**4 + 0 + 0*r + 7/2*r**5 + 4*r**2 = 0?
-2/7, 0, 2
Let k = -3577/3 + 1200. Let c - 19/3*c**4 - 5/3*c**2 + 0 - 4/3*c**5 - k*c**3 = 0. Calculate c.
-3, -1, 0, 1/4
Find h such that -4/7*h - 1/7*h**4 - 1/7 - 6/7*h**2 - 4/7*h**3 = 0.
-1
Let f(z) be the third derivative of -5*z**8/336 + 13*z**7/42 - 67*z**6/24 + 57*z**5/4 - 45*z**4 + 90*z**3 - 30*z**2. Determine u, given that f(u) = 0.
2, 3
Let h be -1 + -1 + (0 - -9). Let 8*y**2 + 2*y**3 + y**3 + 4 + h*y - 2 = 0. Calculate y.
-1, -2/3
Let o be (-7 - -3) + 6 + 1. Find p such that 0 + 0*p - 1/4*p**o - 1/4*p**2 = 0.
-1, 0
Factor -44/3*v**2 - 12*v**3 - 8/3*v + 0.
-4*v*(v + 1)*(9*v + 2)/3
Let x be (0 - 0)/(4/2). Factor 0*c**3 - 2*c**3 + 2*c + x*c**3.
-2*c*(c - 1)*(c + 1)
Let p(t) be the second derivative of t**6/120 - t**5/40 - t. What is h in p(h) = 0?
0, 2
Let h = -13 + 23. Let t = h + -8. Factor 0 + 0*m + 4/7*m**3 - 2/7*m**t.
2*m**2*(2*m - 1)/7
Suppose -2*g + 6 = 2. Factor 0*r + 1 + 2*r + 2*r**2 + 3 - g*r**3 - 6*r**2.
-2*(r - 1)*(r + 1)*(r + 2)
Let o(n) = -n**2 - 6*n - 1. Let a be o(-5). Let b be 3/a - 42/(-8). Factor p + b*p**3 - 4*p**3 - 3*p.
2*p*(p - 1)*(p + 1)
Let i = 398 - 396. Factor