, 1
Let q be (-1)/(-4) - 26/8. Let u be (0 - q)*12/9. Let -20/3*r**2 - 22*r**3 + 4/3 + 14/3*r + 12*r**u = 0. What is r?
-1/3, 1/2, 2
Let y be ((-8)/(-18))/((-100)/(-30)). Factor y*w**2 + 0 + 2/15*w.
2*w*(w + 1)/15
Let o(p) be the second derivative of -p**6/20 + p**5/4 - p**4/6 - 2*p**3/3 - 10*p. Suppose o(w) = 0. What is w?
-2/3, 0, 2
Let m(s) = -2*s - 10. Let j be m(-7). Factor -2/9*h**2 + 0 + 0*h - 2/9*h**3 + 2/9*h**5 + 2/9*h**j.
2*h**2*(h - 1)*(h + 1)**2/9
Let k(u) = 2*u**3 + 16*u**2 - 28*u + 15. Let n(r) = r**3 + 17*r**2 - 29*r + 15. Let w(f) = -4*k(f) + 5*n(f). Factor w(o).
-3*(o - 5)*(o - 1)**2
Suppose -5*i - 3*n + 59 = -4, -3*i - 3*n = -39. Let j = -10 + i. Suppose 2 + 2*y - 16*y**j + 32*y**3 - 7 + 5 = 0. What is y?
0, 1/4
Let k(t) = t**3 - t**2 - t + 1. Let x(f) = -28*f**3 - 4*f**2 - 36*f - 60. Let o(n) = -24*k(n) - x(n). Factor o(q).
4*(q + 1)*(q + 3)**2
Let x(y) be the third derivative of y**5/180 - 5*y**4/18 + 50*y**3/9 - 37*y**2. What is q in x(q) = 0?
10
Let x(b) = -8*b - 44. Let t be x(-6). Factor 2/7*l**t + 10/7*l**2 - 4/7*l + 0 - 8/7*l**3.
2*l*(l - 2)*(l - 1)**2/7
Suppose 0 = l - 3 - 2. Suppose 18 = l*a - 2*a. Factor 4 + 4*d**2 - 4*d**3 + a*d - 2*d**5 - 6*d**4 - 2 + 0*d**4.
-2*(d - 1)*(d + 1)**4
Let s(o) be the second derivative of o**7/7560 - o**4/12 - 5*o. Let m(t) be the third derivative of s(t). Factor m(w).
w**2/3
Let t = -1368 + 1370. Factor 18/5 - 12/5*s + 2/5*s**t.
2*(s - 3)**2/5
Let x be (9/2)/((-7)/(-14)). Let j = x + -6. Factor -i**2 - 4*i**j - i**2 + 2*i**3.
-2*i**2*(i + 1)
Factor 49*c - 37*c - 4*c**2 + 15 + 1.
-4*(c - 4)*(c + 1)
Suppose 339*i + 22 = 4*r + 341*i, -i = -5. Factor -8/13 + 6/13*g**2 - 40/13*g - 98/13*g**4 + 140/13*g**r.
-2*(g - 1)**2*(7*g + 2)**2/13
Let m be 8/(-14) - (-4 - (-12)/28). Let o(c) be the first derivative of -1/10*c**4 - 2/15*c**m + 4 + 0*c**2 + 0*c. Suppose o(p) = 0. Calculate p.
-1, 0
Let h(l) = -3*l**4 - 12*l**3 + 13*l**2 + 2*l - 2. Let k(j) = -20*j**4 - 85*j**3 + 90*j**2 + 15*j - 15. Let b(n) = 15*h(n) - 2*k(n). Find u such that b(u) = 0.
-3, 0, 1
Let v(h) = -h. Let x be v(-5). Suppose -3*i**2 - i**2 - 10*i + i**2 - x*i**2 - 2 = 0. Calculate i.
-1, -1/4
Let x(s) = 13*s**2 - 38*s - 4. Let l(c) = 38*c**2 - 113*c - 13. Let u(b) = -4*l(b) + 11*x(b). Suppose u(o) = 0. Calculate o.
-2/9, 4
Factor 6*c - 24*c**2 + 12*c**3 + 3*c**2 + 6*c**3 - 3*c**3.
3*c*(c - 1)*(5*c - 2)
Let d be (-55)/(-50)*(5 - -1). Factor -d*t - 27/5*t**2 - 6/5.
-3*(t + 1)*(9*t + 2)/5
Let s(i) = -i + 1. Let p be s(-2). Suppose -16 = -2*k + 3*o, -5*k + 10*k + p*o - 40 = 0. Find z such that 22*z**2 - 4*z**3 + k - 40*z + 34*z**3 + 40*z**3 = 0.
-1, 2/7, 2/5
Factor -14*g**3 + g**2 + 5*g**2 - 4*g**2 + 2*g**2.
-2*g**2*(7*g - 2)
What is r in -3*r**5 - 10*r**5 + 10*r**5 + 12*r**4 - 9*r**3 = 0?
0, 1, 3
Factor 0*a + 0 + 3/4*a**3 + 3*a**2.
3*a**2*(a + 4)/4
Suppose 0 = 2*l + l - 6. Suppose 0*a - l = -a. Factor 4/5*r + 0 + 2/5*r**a.
2*r*(r + 2)/5
Let z be 1*(-7)/14*0. What is g in z - 1/4*g**3 - 1/4*g**2 + 0*g = 0?
-1, 0
Let i(z) be the second derivative of z**7/3360 - z**5/160 + z**4/48 - z**3/2 + 3*z. Let k(q) be the second derivative of i(q). Factor k(u).
(u - 1)**2*(u + 2)/4
Let g be (-7)/(21/15) - -7. Suppose 0 - 1/6*d**3 + 1/3*d**g - 1/6*d = 0. What is d?
0, 1
Determine n so that -2*n + 2 + 1/2*n**3 - 1/2*n**2 = 0.
-2, 1, 2
Suppose 111 = 16*t + 31. Suppose 0*y**2 + 0*y + 1/6*y**3 + 0 - 1/3*y**4 + 1/6*y**t = 0. Calculate y.
0, 1
Let h be (-56)/(-10) + 28 + -32. Suppose -6*w**2 + 12/5*w + 3*w**4 + h - 19/5*w**3 = 0. Calculate w.
-1, -2/5, 2/3, 2
Let j(d) = -d**3 - 1. Let n = -6 + 5. Let p(c) = 3 + c**2 - 3 + 1. Let l(y) = n*p(y) - j(y). Factor l(x).
x**2*(x - 1)
Let n be 6/(12/(-27)*45/(-10)). Let -4/5 - 5*h**n - h**2 + 16/5*h = 0. Calculate h.
-1, 2/5
Let s(l) be the third derivative of l**8/30240 - l**7/1890 + l**6/360 + l**4/3 + 2*l**2. Let h(u) be the second derivative of s(u). Factor h(w).
2*w*(w - 3)**2/9
Factor 13*t**2 - 8 + 19*t**2 - 18*t**5 + 31*t - 19*t - 2*t**5 - 88*t**3 + 72*t**4.
-4*(t - 1)**4*(5*t + 2)
Let o(b) = 4*b**3 + 5*b**2 + 4*b - 3. Let i(j) = 4*j**3 + 4*j**2 + 4*j - 4. Let s(a) = 3*i(a) - 4*o(a). Let s(u) = 0. What is u?
-1, 0
Let o(j) be the first derivative of -1/4*j**2 - 1/3*j**3 + 1/10*j**5 + 3 - 1/12*j**6 + 1/4*j**4 + 1/2*j. Determine y, given that o(y) = 0.
-1, 1
Let r(w) be the first derivative of 2*w**3/9 - 2*w**2 + 6*w + 15. Determine h, given that r(h) = 0.
3
Let s(f) be the second derivative of 0 - 1/8*f**4 + 1/60*f**5 + 1/3*f**3 + f**2 - 2*f. Let w(z) be the first derivative of s(z). Factor w(q).
(q - 2)*(q - 1)
Let v be 64/15 - (-2)/(-3). Let m = 204 + -201. Suppose 26/5*f**m - v*f**2 - 2*f**4 + 4/5 - 2/5*f = 0. Calculate f.
-2/5, 1
Suppose 60 - 195 = 3*g. Let i be (g/(-100))/(12/20). Factor 3/2*n**2 - i*n**3 + 3/4*n - 3/2.
-3*(n - 2)*(n - 1)*(n + 1)/4
Let w be (-12)/9*(18/(-4))/3. Factor -4/3*m - 1/3*m**4 - 4/3*m**3 - 1/3 - 2*m**w.
-(m + 1)**4/3
Let z(v) = v - 12. Let h be z(12). Suppose h = 3*n - 5*l + 8, 2*n + 4*l - 20 = l. Factor -10*g - 8*g**2 - 3 - 6*g**3 + 2*g**2 + 19*g + 9*g**n - 3*g**5.
-3*(g - 1)**4*(g + 1)
Let f = 0 + 2. Let o = 162 - 160. Suppose f*i**4 + 2/3*i**o + 2*i**3 + 0 + 0*i + 2/3*i**5 = 0. What is i?
-1, 0
Factor -108*f - 24*f**3 - 57*f**3 + 24 - 62*f**2 + 224*f**2.
-3*(3*f - 2)**3
Suppose 17 = 4*j - 23. Suppose 3*v - j = -x, v - 2*v - 2*x = 0. Suppose 10*z**4 - v*z**3 - 7*z**2 - z + 5*z - 3*z**2 = 0. Calculate z.
-1, 0, 2/5, 1
Let v(w) be the first derivative of -w**5/10 + w**4/12 + w**3/6 + w - 1. Let k(n) be the first derivative of v(n). Factor k(p).
-p*(p - 1)*(2*p + 1)
Suppose 4*k - 36 = -5*k. Suppose k = 4*z - 4. Solve 2/3*r**z + 4/3*r + 0 = 0.
-2, 0
Let w = -32 - -20. Let t be w*(16/6)/(-4). Factor -9 + 2*f**2 + 4*f + t + 3.
2*(f + 1)**2
Suppose -2*q - x + 0 = 12, 22 = -4*q - x. Let k = q - -8. Factor 9*t + 10*t**2 + 2 - 5*t**5 - 3*t**k - t**3 + 0 - 12*t**4.
-(t - 1)*(t + 1)**3*(5*t + 2)
Let w(s) = -s**3 - 12*s**2 + 12*s - 11. Suppose -2*k + 3*i = 23, 0 = -0*k - 3*k - i - 40. Let l be w(k). Find f such that 3*f + 0*f**2 + f**2 + l*f**2 = 0.
-1, 0
Let n be (7/(-14))/((-1)/(-12)). Let g(x) = -x - 2. Let t be g(n). Factor 2*f**3 - f**t + 0*f**4 + f - 3*f + 1.
-(f - 1)**3*(f + 1)
Suppose 0 = -0*b - 3*b - 15, 0 = -2*w + 3*b + 35. Suppose 2*l = 2*v + w, 3*v = -4*l + 2*l - 15. Factor l - 8/11*h**2 + 2/11*h.
-2*h*(4*h - 1)/11
Let s(u) be the third derivative of 0*u + 0 - 1/40*u**6 - 1/8*u**4 + 0*u**3 - 1/10*u**5 + 4*u**2. Factor s(h).
-3*h*(h + 1)**2
Let o(h) be the third derivative of h**5/80 - h**3/2 - h**2 - 7. Factor o(g).
3*(g - 2)*(g + 2)/4
Let f(b) be the second derivative of 0 + 1/6*b**3 - b - 1/12*b**4 + 0*b**2. Suppose f(r) = 0. Calculate r.
0, 1
Let z(n) = 15*n**4 - 23*n**3 + 8*n**2 - 7*n + 7. Let o(l) = -8*l**4 + 12*l**3 - 4*l**2 + 4*l - 4. Let v(u) = 7*o(u) + 4*z(u). Let v(y) = 0. What is y?
0, 1
Let i(u) be the second derivative of 0*u**2 + 0*u**3 + 0 + 0*u**5 - 1/90*u**6 + 0*u**4 - 3*u. Factor i(y).
-y**4/3
Suppose 0 = 2*i - 0*i. Suppose -4*f + u = 6 - 22, 4*f + 3*u - 16 = i. Suppose -10*v**5 + 12*v**f - 8/5*v - 24/5*v**2 + 22/5*v**3 + 0 = 0. What is v?
-2/5, 0, 1
Suppose 5*q = i + 2 + 5, -1 = 4*q - 3*i. Suppose -13 = q*j - 5, f = -j - 1. Factor 0*p**2 + 0 + 1/3*p**f + 0*p.
p**3/3
Let f(n) be the third derivative of -n**7/630 + 7*n**6/1080 - n**5/180 - n**4/72 + n**3/2 + 4*n**2. Let v(s) be the first derivative of f(s). Factor v(b).
-(b - 1)**2*(4*b + 1)/3
Let b(q) = 2*q**3 - 2*q**2 - q + 2. Let j be b(0). Factor -2/5*g + 2/5*g**j - 2/5 + 2/5*g**3.
2*(g - 1)*(g + 1)**2/5
Let d(b) be the first derivative of -b**4/2 + 4*b**3/3 - b**2 + 14. Factor d(s).
-2*s*(s - 1)**2
Suppose 8/3 - 8/3*u + 2/3*u**2 = 0. What is u?
2
Factor 69*z**2 + 0 - 3*z**5 + 0 - 57*z**2 + 21*z**3 + 6*z**4.
-3*z**2*(z - 4)*(z + 1)**2
Factor 2/5*v + 0 - 1/5*v**2.
-v*(v - 2)/5
Let q(g) = 2*g - 4. Let p be q(3). Let -5*f**p + 3*f**2 + 6*f - 2*f = 0. Calculate f.
0, 2
Let q(z) be the first derivative of 0*z + 1/21*z**6 + 0*z**3 + 0*z**5 + 0*z**2 - 1 - 1/14*z**4. Factor q(u).
2*u**3*(u - 1)*(u + 1)/7
Let v = 3 - -3. Factor -5*s**2 + 2*s**2 + 0*s**2 - 3*s + v.
-3*(s - 1)*(s + 2)
Let x be 3 + (2/191 - 3). Let h = x + 376/573. What is s in 2/9*s**2 - h*s + 4/9 = 0?
1, 2
Let z = 7 - 4. Factor -18 + q**