2*r**4 + h*r - 8*r**2.
-4*(r - 1)**4*(r + 1)
Suppose 5*j - 4*i - 54 = 67, 4*j + 2*i - 76 = 0. Let s be ((-12)/18)/((-2)/j). Solve -2*w**3 + 4*w - 3*w**5 + s*w**5 - 6*w - 6*w**4 + 6*w**2 = 0 for w.
-1, 0, 1/2, 1
Suppose 145*g - 116 = 87*g. Factor 0*u + 5*u**3 + 0 + 5/3*u**4 + 10/3*u**g.
5*u**2*(u + 1)*(u + 2)/3
Let s be 2/(-24)*(-7200)/1400. Let s*c**2 + 3/7 + 6/7*c = 0. Calculate c.
-1
Let s = 199 + -2387/12. Let a(j) be the second derivative of -1/40*j**5 + 0 + 0*j**2 + 0*j**4 - 3*j + s*j**3. Suppose a(l) = 0. What is l?
-1, 0, 1
Suppose 5*y = -z + 12, -2*y + 40 = -4*z - 0*y. Let h be (-36)/z + 2 + (-2 - 0). Factor -h*t**2 - 1/2 + 3*t.
-(3*t - 1)**2/2
Let b(l) be the first derivative of -4*l**5 - 55*l**4/4 + 5*l**3 + 40*l**2 - 20*l + 55. Find z such that b(z) = 0.
-2, 1/4, 1
Let x(c) be the second derivative of 4*c**9/567 + 2*c**8/315 - c**7/90 + c**6/270 - 4*c**3/3 + 7*c. Let o(r) be the second derivative of x(r). Factor o(d).
4*d**2*(d + 1)*(4*d - 1)**2/3
Suppose -5 = -7*x + 6*x. Suppose w = -3*y + 7, 4*y + x*w - 12 = 1. Determine o so that 19*o**2 + 3*o**2 - 10*o**y - 3*o = 0.
0, 1/4
Let l be 2 - (-20 + 7 + -4). Let h = 21 - l. Factor 0*k**2 + 1 + 2 - 4*k**2 + k**h.
-3*(k - 1)*(k + 1)
Let s(y) = -2*y**2 + 33*y - 98. Let b be s(4). What is f in 2/7*f**b + 0 - 2/7*f = 0?
0, 1
Let p(x) = x**3 - 9*x**2 - 22. Let q be p(9). Let i = q - -22. Factor -2/3 + 2/3*j**2 + i*j.
2*(j - 1)*(j + 1)/3
Let w(r) = -r. Let l be w(0). Solve -5 - 98*k**2 + 20*k**4 + 25*k**3 + l + 83*k**2 - 25*k = 0.
-1, -1/4, 1
Let g(i) be the second derivative of -i**5/100 + i**4/10 - 11*i**3/30 + 3*i**2/5 + 91*i. Factor g(a).
-(a - 3)*(a - 2)*(a - 1)/5
Let r be (405/(-60) - (1 + -8))*0. Let a(g) be the second derivative of -11*g + 5/6*g**3 - 5/42*g**7 - 5/6*g**4 + 0*g**2 + r*g**5 + 0 + 1/3*g**6. Factor a(k).
-5*k*(k - 1)**3*(k + 1)
Let n(o) be the second derivative of -4*o**6/75 + 29*o**5/100 - 7*o**4/15 + o**3/30 + 3*o**2/5 + 865*o. Solve n(t) = 0.
-3/8, 1, 2
Let o(z) be the first derivative of -5*z**4/12 + 5*z**3/6 + 5*z + 20. Let s(y) be the first derivative of o(y). Solve s(h) = 0.
0, 1
Let 65*m**3 - 62*m**2 + 212*m**2 + 20 + 1 + 140*m + 0*m**3 + 10*m**4 + 19 = 0. Calculate m.
-2, -1/2
Let l(u) be the third derivative of u**6/40 - u**5/10 - 7*u**4/8 - 2*u**3 - 91*u**2. Suppose l(j) = 0. What is j?
-1, 4
Let z(m) be the first derivative of m**6/2 - 27*m**5/5 - 39*m**4 - 284. Factor z(q).
3*q**3*(q - 13)*(q + 4)
Let w be 3 + -1 + -3 + 5. Suppose -5*q + w*q = -2. Let 4*a - 4*a**q + 8 + 0 + 0 = 0. Calculate a.
-1, 2
Let f = 21 - 14. Let n(l) be the first derivative of -f*l - l**3 + 6*l**2 - 5 - 6*l + 4*l + 0*l. Factor n(q).
-3*(q - 3)*(q - 1)
Let d be ((392/70 - 4) + -1)*10/4. Solve -11/4*m**2 - 35/4*m - d = 0 for m.
-3, -2/11
Factor 0 + 33/7*o**2 - 3/7*o**3 + 0*o.
-3*o**2*(o - 11)/7
Let p(r) be the third derivative of r**5/40 - r**4/2 + 4*r**3 - 6*r**2 + 19*r. Factor p(g).
3*(g - 4)**2/2
Let m = 7 + -4. Let r(n) = 2*n + m*n + 3 + 2*n**3 - 10 - n**2 - n**3. Let j(t) = t - 1. Let u(s) = 21*j(s) - 3*r(s). Factor u(a).
-3*a*(a - 2)*(a + 1)
Let s(z) be the first derivative of z**4 + 332*z**3 + 41334*z**2 + 2287148*z + 77. Factor s(o).
4*(o + 83)**3
Suppose 186*c = 206*c. Let p(b) be the second derivative of 1/5*b**5 + 2/45*b**6 - 4/3*b**2 + c + 1/9*b**4 + 7*b - 2/3*b**3. Factor p(k).
4*(k - 1)*(k + 1)**2*(k + 2)/3
Let y = -128 + 132. Determine l, given that 16*l - 29*l**4 + 16*l**3 + 64*l**2 - 13*l**5 - 35*l**4 - 15*l**5 - y*l**3 = 0.
-2, -1, -2/7, 0, 1
Let v(u) be the first derivative of -u**5/180 + u**4/6 - 2*u**3 + 19*u**2/2 - 16. Let p(m) be the second derivative of v(m). Suppose p(q) = 0. What is q?
6
Let a(o) = -2*o**2 + 1. Suppose 3*b + 3*r + 1 = -5, 5*b + 10 = 4*r. Let l(g) = -g**3 + 1. Let f(k) = b*l(k) + 2*a(k). Factor f(u).
2*u**2*(u - 2)
Let h = -1722 - -1722. Factor -1/4*l**3 + h + 0*l**2 + 1/4*l.
-l*(l - 1)*(l + 1)/4
Let b(n) = n**2 - 13*n - 14. Let h be b(14). Let f be -2*2/30 - (-56)/120. Suppose f*z**2 + h - 1/6*z**3 - 1/6*z = 0. Calculate z.
0, 1
Let j(n) be the first derivative of -5*n**4/8 - 185*n**3/6 - 1615*n**2/4 + 1805*n/2 - 47. Factor j(r).
-5*(r - 1)*(r + 19)**2/2
Let l(u) be the first derivative of -5*u**4/32 - 67*u**3/24 + 11*u**2/4 + 7*u/2 + 326. Factor l(k).
-(k - 1)*(k + 14)*(5*k + 2)/8
Let r(t) be the third derivative of -t**6/720 - t**5/60 - 29*t**3/6 - 18*t**2. Let q(a) be the first derivative of r(a). Solve q(x) = 0 for x.
-4, 0
Let a = -6 + 12. Let t be -2 + (-2 - -2) - a/(-3). Factor -1/2*s**2 + 1/2*s**4 + 0*s + t*s**3 + 0.
s**2*(s - 1)*(s + 1)/2
Factor 13*q**2 + 3*q - 11*q**2 - 50 + 12*q.
(q + 10)*(2*q - 5)
Factor 10/7*n**2 - 72/7 - 1/7*n**3 - 12/7*n.
-(n - 6)**2*(n + 2)/7
Let a(x) be the first derivative of -x**6/30 + 4*x**5/15 + x**4/2 - 12*x**3 + 29*x**2/2 - 17. Let v(p) be the second derivative of a(p). Factor v(n).
-4*(n - 3)**2*(n + 2)
Let w(y) be the first derivative of -7*y**6/6 + 6*y**5 - 2*y**4 - 112*y**3/3 + 72*y**2 - 32*y - 82. Find n such that w(n) = 0.
-2, 2/7, 2
Let j(n) be the first derivative of 2*n**6/75 + n**5/25 - n**4/15 - 2*n**3/15 - 9*n - 8. Let q(f) be the first derivative of j(f). Find g such that q(g) = 0.
-1, 0, 1
Suppose 2*v - 18 = -8. Let k(r) = -7*r**3 - 3*r**2 - 8*r. Let l(b) = 6*b**3 + 2*b**2 + 7*b. Let q(x) = v*k(x) + 6*l(x). Factor q(t).
t*(t - 2)*(t - 1)
Suppose 28*d = 27*d. Let k(n) be the third derivative of 0*n + 0 + 7*n**2 + 0*n**3 - 1/300*n**5 + 1/1050*n**7 - 1/1680*n**8 + 1/600*n**6 + d*n**4. Factor k(c).
-c**2*(c - 1)**2*(c + 1)/5
Let m = 285 - 283. Let j(o) be the third derivative of 7*o**m - 17/180*o**4 + 0*o - 2/15*o**3 + 0 - 1/90*o**5. Suppose j(d) = 0. What is d?
-3, -2/5
Let t(u) be the second derivative of -u**5/5 - 4*u**4/3 + 14*u**3/3 + 20*u**2 + 58*u. Factor t(p).
-4*(p - 2)*(p + 1)*(p + 5)
Let l(f) = f**2 - 2*f + 11. Let b be l(3). Suppose 34*k - 60 = b*k. Factor 2*p**k + 0*p + 0 + 2*p**4 + 2/3*p**5 + 2/3*p**2.
2*p**2*(p + 1)**3/3
Let s be 2/(4/(-398)) + (-24)/(-12). Let x = s - -199. Find q such that -2/5*q**x + 0*q - 2/5*q**3 + 0 = 0.
-1, 0
Let u(h) = -6*h**3 + 25*h**2 + 7*h + 13. Let j(v) = 3*v**3 - 12*v**2 - 3*v - 6. Let m = 31 - 18. Let i(o) = m*j(o) + 6*u(o). Factor i(k).
3*k*(k - 1)**2
Factor -3/4*x**3 - 816*x - 195/4*x**2 - 768.
-3*(x + 1)*(x + 32)**2/4
Determine i so that -3*i + 5*i**5 - 532*i**2 - 20*i**4 - 30 - 2*i + 582*i**2 = 0.
-1, 1, 2, 3
Suppose -5*t = 5*k + 10, -5*k - 2*t - 2 = 2. Suppose 2*o = -k*o + 4. Suppose -4*c**2 + 2*c**2 + 2*c**2 - 3*c**o = 0. What is c?
0
Let a(j) be the second derivative of -j**6/40 + j**5/20 - 7*j**2 - 10*j. Let r(m) be the first derivative of a(m). Factor r(i).
-3*i**2*(i - 1)
Factor 0 + 3*j**4 + 9/7*j**5 + 0*j**2 + 0*j - 60/7*j**3.
3*j**3*(j + 4)*(3*j - 5)/7
Determine b so that 189*b - 46 + 414*b**2 + 576 - 134*b**2 + 352*b + 264*b + 5*b**3 = 0.
-53, -2, -1
Let p(v) = 11 + 15 + 2*v - 34. Let t be p(5). Factor -1/3*n**t + 1/3*n**4 + 0*n - 1/3*n**3 + 1/3*n**5 + 0.
n**2*(n - 1)*(n + 1)**2/3
Let z(y) be the third derivative of 1/150*y**6 + 0*y + 0*y**3 - 1/60*y**4 - 1/150*y**5 + 9*y**2 + 0. What is j in z(j) = 0?
-1/2, 0, 1
Let o(d) be the third derivative of d**5/12 + 5*d**4/12 - 5*d**3/2 + d**2 - 15. Factor o(z).
5*(z - 1)*(z + 3)
Let d be 5*((-192)/(-20))/12. Factor 1/3*c**d + 1/3*c**5 + 0 - 1/3*c**3 - 1/3*c**2 + 0*c.
c**2*(c - 1)*(c + 1)**2/3
Factor 88/9 + 32/3*y + 2/9*y**3 + 10/3*y**2.
2*(y + 2)**2*(y + 11)/9
Let r = 423/5720 - 7/143. Let j(f) be the third derivative of 0 - r*f**5 + 11*f**2 + 0*f - 1/240*f**6 + 0*f**3 - 1/24*f**4. Factor j(q).
-q*(q + 1)*(q + 2)/2
Let t = 6551 + -6547. Determine w so that 0 - 3/5*w + 3/5*w**3 - 3/5*w**t + 3/5*w**2 = 0.
-1, 0, 1
Let b(n) = -81*n**2 + 111*n - 30. Let j(k) = 2*k**3 + 81*k**2 - 112*k + 29. Let u(r) = 5*b(r) + 6*j(r). Factor u(h).
3*(h - 1)*(h + 8)*(4*h - 1)
Let t(r) be the third derivative of 5*r**2 - 1/30*r**5 + 0*r + 0 - 1/2*r**3 + 1/360*r**6 + 1/8*r**4. Let k(g) be the first derivative of t(g). Solve k(l) = 0.
1, 3
Suppose 0 = -3*u + t + 8, -4*t - 3 = 3*u - 1. Let l(p) be the second derivative of 1/3*p**3 + 1/12*p**4 + 1/2*p**u + 0 + 4*p. What is c in l(c) = 0?
-1
Let g be (183/(-21) - -10)/(24/28). Factor g*f**2 + 9/2 + 6*f.
3*(f + 1)*(f + 3)/2
Let w(l) = 3*l**2 - 26*l + 20. Let r be w(8)