, 6
Let i(r) = -4*r + 14*r - 1 + 13*r + 227*r**2 + 7*r. Let n(u) = -228*u**2 - 30*u + 2. Let q(d) = 3*i(d) + 2*n(d). Factor q(w).
(15*w + 1)**2
Let r(h) = h + 3. Let w be r(0). Factor -109*o + 2 + 106*o - 3*o**2 + 3*o**4 - 2 + 3*o**w.
3*o*(o - 1)*(o + 1)**2
Suppose -1/3*i**2 + 91/3*i + 0 = 0. What is i?
0, 91
Let t(k) be the third derivative of 1/12*k**3 - 1/360*k**5 - 1/72*k**4 - 18*k**2 + 0*k + 0. Factor t(n).
-(n - 1)*(n + 3)/6
Determine s so that -6/11 + 26/11*s - 20/11*s**2 = 0.
3/10, 1
Factor 0*d - 2/15*d**2 + 8/15.
-2*(d - 2)*(d + 2)/15
Find t such that 375*t**3 + 345*t**3 + 65*t + 25 - 677*t**3 - 129*t**2 - 4*t**4 = 0.
-1/4, 1, 5
Let s = 535/1452 - 17/484. Factor 0 + 1/3*j**2 - 2/3*j + s*j**3.
j*(j - 1)*(j + 2)/3
Let v(k) = k**3 - 8*k**2 + 139*k - 126. Let b(w) = 10*w**3 - 90*w**2 + 1530*w - 1385. Let o(y) = 6*b(y) - 65*v(y). Factor o(i).
-5*(i - 3)*(i - 1)*(i + 8)
Let l(d) = -d**3 + 3*d**2 + 4*d - 2. Let h be l(4). Let o be (0 - 1 - h) + 1. Suppose 1 - 2 - 6*j + 9*j**o - 5 + 3 = 0. What is j?
-1/3, 1
Let h(r) = 8*r**4 + 32*r**3 + 40*r**2 + 21*r - 5. Let b(t) = -4*t**4 - 16*t**3 - 20*t**2 - 11*t + 3. Let s(v) = -5*b(v) - 3*h(v). Suppose s(w) = 0. Calculate w.
-2, -1, 0
Let p(k) be the second derivative of -4*k**5 - 10*k**4 + 95*k**3/6 + 15*k**2 + 166*k. Factor p(m).
-5*(m + 2)*(4*m - 3)*(4*m + 1)
Let h = -1076 + 4311/4. Factor -h*u**2 - 1/4*u**3 - 3 - 4*u.
-(u + 2)**2*(u + 3)/4
Suppose -10 = 5*y + 5*m, -166 + 148 = -y + 4*m. Suppose 4*s**y - 12/7 + 16/7*s = 0. What is s?
-1, 3/7
Let n(t) be the first derivative of t**5/30 - t**4/24 - t**3/9 - 11. Solve n(a) = 0 for a.
-1, 0, 2
Factor 35/4*b + 15/4*b**2 - 15/2.
5*(b + 3)*(3*b - 2)/4
Suppose 24*b + 15 + 36 + 3*b**2 - 15 + b**2 = 0. Calculate b.
-3
Solve -24/13 - 14/13*d - 2/13*d**2 = 0.
-4, -3
Factor -47 - 31*l - 25 - 9 - 3 + 3*l**2 - 50*l.
3*(l - 28)*(l + 1)
Let 0*m + 0 - m**3 - 5/4*m**4 + 9/4*m**2 = 0. Calculate m.
-9/5, 0, 1
Let 74/13*p + 72/13*p**2 - 72/13*p**4 + 0 + 2/13*p**5 - 76/13*p**3 = 0. Calculate p.
-1, 0, 1, 37
Let b be (-1)/(-2)*(-4 + 2). Let c be 4/4 - b*1. Factor -28*t**2 + c*t**4 - 28*t**3 - t**5 + 2*t**4 + 8 + 4*t + 9*t**5.
4*(t - 2)*(t + 1)**3*(2*t - 1)
Let c = 1052/9387 + -1/1043. Factor -c*o**2 + 1/9*o + 1/9 - 1/9*o**3.
-(o - 1)*(o + 1)**2/9
Let t(u) be the second derivative of u**6/135 + 7*u**5/90 + 5*u**4/18 + 13*u**3/27 + 4*u**2/9 + 2*u - 84. Factor t(q).
2*(q + 1)**3*(q + 4)/9
Let j(x) be the first derivative of x**7/420 - x**6/252 - x**5/210 - x**3/3 - 3. Let g(f) be the third derivative of j(f). Let g(k) = 0. What is k?
-2/7, 0, 1
Factor 39*p**5 + 26*p**5 - 33*p**3 - 52*p**4 - 68*p**5 + 16*p**4.
-3*p**3*(p + 1)*(p + 11)
Let j(u) be the second derivative of -u**7/210 + u**6/60 - u**5/60 - 9*u**2/2 + 12*u. Let i(o) be the first derivative of j(o). Suppose i(n) = 0. Calculate n.
0, 1
Let r = 85 + -68. Factor 179*c**3 - 28*c**2 - 109*c**3 - 92*c**3 - c**5 - r*c - 4 - 8*c**4.
-(c + 1)**4*(c + 4)
Factor -3/7*k**2 - 12/7*k - 9/7.
-3*(k + 1)*(k + 3)/7
Let p(u) be the third derivative of u**8/840 + 2*u**7/105 + u**6/9 + 4*u**5/15 - 3*u**3 + 13*u**2. Let t(z) be the first derivative of p(z). Factor t(v).
2*v*(v + 2)**2*(v + 4)
Let b(x) = -5*x**3 - 11*x**2 + 165*x - 405. Let i(s) = -s**3 + 2*s**2 - s. Let j(r) = 5*b(r) - 30*i(r). Factor j(g).
5*(g - 9)**2*(g - 5)
Let p = 1 - 4. Let b be (-6)/(-9)*(p - -9). Let f(g) = 4*g**2 - 7*g - 6. Let o(a) = -3*a**2 + 6*a + 5. Let j(v) = b*f(v) + 5*o(v). Factor j(m).
(m + 1)**2
Determine u so that 24*u**2 + 8/19*u + 0 + 342*u**3 = 0.
-2/57, 0
Let a(r) be the first derivative of -r**4/3 - 8*r**3/3 + 10*r**2 - 36*r - 28. Let v(w) be the first derivative of a(w). Suppose v(k) = 0. What is k?
-5, 1
Let m(q) be the second derivative of -q**7/56 - 7*q**6/40 + 3*q**5/40 + 23*q**4/8 - 65*q**3/8 + 75*q**2/8 + 10*q. Factor m(g).
-3*(g - 1)**3*(g + 5)**2/4
Let d be (8/(-30))/(30/(-100)). Let h = -9/41 - -163/369. Suppose d*n - 8/9 - h*n**2 = 0. What is n?
2
Let u(b) be the third derivative of b**7/210 - b**6/45 + 10*b**3/3 - 11*b**2. Let a(r) be the first derivative of u(r). Factor a(l).
4*l**2*(l - 2)
Let q = 11/69 + 61/483. Find v such that 0*v + 2/7 - q*v**2 = 0.
-1, 1
Let z(j) be the third derivative of j**5/240 + j**4/32 - j**3/6 - 91*j**2. Factor z(f).
(f - 1)*(f + 4)/4
Let z be (4/3)/((-2)/(-6)). Let c = 140 - 136. Factor -2*u**5 + 2*u**c - z*u**2 + 8 + 6 - 12 + 4*u**3 - 2*u.
-2*(u - 1)**3*(u + 1)**2
Factor 4/17*w**2 + 0*w + 8/17*w**4 + 2/17*w**5 + 10/17*w**3 + 0.
2*w**2*(w + 1)**2*(w + 2)/17
Let z = 97 - 76. Let l = z + -18. Solve -12*a + 8*a**2 - 4/3*a**l + 16/3 = 0.
1, 4
Let h(b) = -10*b**2 - 12*b. Let m(f) be the first derivative of f**3/3 + f**2/2 - f - 10. Let r(y) = -h(y) - 2*m(y). Let r(w) = 0. Calculate w.
-1, -1/4
Let u be 144/240 - (-6)/(-10). Let h(r) be the third derivative of u*r + 0 - 1/160*r**6 + 5*r**2 - 1/840*r**7 + 0*r**3 - 1/96*r**4 - 1/80*r**5. Factor h(v).
-v*(v + 1)**3/4
Let s be 390/(-39)*(-1)/45. Factor 0*x + 0 - s*x**4 + 0*x**3 + 2/9*x**2.
-2*x**2*(x - 1)*(x + 1)/9
Suppose 6*u**3 - 10*u**3 + 57*u**2 + 6*u - 62*u**2 + 3*u**3 = 0. Calculate u.
-6, 0, 1
Suppose 25 = 3*u + 4*p, u + 3*u + 4 = 4*p. What is o in -4 + 187*o**3 + 24*o - 38*o**2 - 161*o**u - 6*o**4 - 2*o = 0?
1/3, 1, 2
Let i(b) = -102*b - 3872. Let l be i(-38). Let -4 - y + l*y**3 + 17/2*y**2 - 3/2*y**4 = 0. What is y?
-1, 2/3, 4
Let h(u) be the first derivative of u**4/22 - 8*u**3/11 + 35*u**2/11 - 48*u/11 + 88. Factor h(v).
2*(v - 8)*(v - 3)*(v - 1)/11
Let z(x) = -2*x**4 + 473*x**3 - 36499*x**2 + 949124*x - 5. Let v(q) = -q**3 - q**2 - 4*q + 1. Let n(f) = 5*v(f) + z(f). Factor n(l).
-2*l*(l - 78)**3
Let m = -217 + 176. Let t = m - -87/2. Factor t*f**3 + 1/2*f + 1 - 4*f**2.
(f - 1)**2*(5*f + 2)/2
Let h(f) be the second derivative of 1/8*f**2 + 1/96*f**4 + 0 - 1/16*f**3 + 10*f. Factor h(v).
(v - 2)*(v - 1)/8
Let b = -129/235 - -54/47. Factor 3/5 - 3/5*t**3 - 3/5*t**2 + b*t.
-3*(t - 1)*(t + 1)**2/5
Let m(w) be the third derivative of -w**6/180 + 11*w**5/90 - w**4/2 + 349*w**2. Factor m(z).
-2*z*(z - 9)*(z - 2)/3
Let y(d) be the third derivative of d**6/720 - d**4/48 + d**3/18 - 375*d**2. Factor y(q).
(q - 1)**2*(q + 2)/6
Suppose 4*x - 3*t - 21 = 0, -5*x - 3 = -4*x + 2*t. Let -12*b**2 - 2 + 2 - 4*b + 4*b**3 - 16*b**x - 4*b**4 = 0. Calculate b.
-1, 0
Let n(f) = -f**3 + 9*f**2 + 21*f - 187. Let g be n(9). Find y, given that 6/7 + 9/7*y + 0*y**g - 3/7*y**3 = 0.
-1, 2
Suppose 9*j - 4*j = 5*t + 35, 5*j - 2*t = 35. Factor -j*i**2 + 11*i**3 + 15*i**4 + 27*i**2 - 51*i**3 + 15*i**2 - 10*i.
5*i*(i - 1)**2*(3*i - 2)
Let o be (-6)/10 - 986/(-85). Let y(g) = g - 9. Let p be y(o). Factor -1/3*t**p + 0*t - 1/3*t**3 + 0.
-t**2*(t + 1)/3
Solve 242*m**2 + 246*m**2 - 547*m**2 - 2*m + 126*m**3 = 0 for m.
-2/63, 0, 1/2
Let z be (5 + -4)/((-4)/(-20)). Let f = z - 3. Factor -28*r**2 - 2*r - 23*r**2 + 49*r**f.
-2*r*(r + 1)
Let u(v) be the first derivative of 3/20*v**4 + 3/5*v**3 + 0*v - 24 - 6/5*v**2. Find m such that u(m) = 0.
-4, 0, 1
Let i(y) = y**3 - 5*y**2 + 6*y - 6. Let l be (1 - -1)/((-2)/(-4)). Let g be i(l). Factor s**3 - 4*s**2 - 1 + 3*s**g + 1.
s**2*(s - 1)
Let s(u) be the second derivative of 5*u**8/336 - u**7/21 + u**5/6 - 5*u**4/24 + 6*u**2 - 17*u. Let f(p) be the first derivative of s(p). Factor f(t).
5*t*(t - 1)**3*(t + 1)
Let z(u) = 15*u**2 + 588*u + 6012. Let l(b) = 6*b**2 + 235*b + 2405. Let i(n) = -12*l(n) + 5*z(n). Factor i(a).
3*(a + 20)**2
Let s = 73 - 70. Suppose 4*l - 3*p + 7*p = 4, s*p - 3 = 0. Let -2/5*c**3 + 2/5*c**2 - 2/5*c**4 + 2/5*c + l = 0. What is c?
-1, 0, 1
Let f(o) be the first derivative of -o**3/4 + o**2 + 3*o/4 - 100. Determine c so that f(c) = 0.
-1/3, 3
Let j = 1937/20 + -483/5. Let 0 + 0*f**2 + j*f**3 - 1/4*f = 0. Calculate f.
-1, 0, 1
Let c(i) be the first derivative of -i**6/300 - 2*i**5/75 - i**4/12 - 2*i**3/15 + 11*i**2/2 + 23. Let b(o) be the second derivative of c(o). Factor b(f).
-2*(f + 1)**2*(f + 2)/5
Suppose 0 = 4*g + a - 16, -2*g - 2*a = -0*a - 14. Suppose g*t + m = -t - 4, 4*t = -3*m - 12. Determine o so that 14*o**2 + 4*o + t*o - 10*o**2 = 0.
-1, 0
Suppose 6477*m + 96 = 6480*m. Factor 8*s + 1/2*s**2 + m.
(s + 8)**2/2
Let y = -169 + 169. Let u(l) be the third derivative of 0 + y*l**5 + 1/525*l**7 - 1/30*l**4 + 6*l**2 + 0*l 