0
Let z(h) be the second derivative of -1/24*h**4 + 1/80*h**5 + 1/24*h**3 + 0 - 9*h + 0*h**2. Suppose z(q) = 0. What is q?
0, 1
Let q(r) be the second derivative of -r**4/8 + r**3/2 + 660*r. Solve q(s) = 0 for s.
0, 2
Let b be (6*2/3 - 1) + 1. Factor -3*c**3 - 3*c + 4*c**2 + 4*c**5 + 2*c - c**4 - 3*c**b.
c*(c - 1)*(c + 1)*(2*c - 1)**2
Let n(k) be the second derivative of -k**7/147 + k**6/35 - k**5/35 - k**4/21 + k**3/7 - k**2/7 - 2*k - 8. Factor n(p).
-2*(p - 1)**4*(p + 1)/7
Let c = -351 + 1358. Factor 1007 - 4*j**4 - c + 8*j**3 - 4*j**2.
-4*j**2*(j - 1)**2
Let x = 0 + 5. Let r = 576 - 574. Factor 4*i**4 - i**x + 0*i + 18*i**2 - i - 6*i**3 + 0*i**4 - 14*i**r.
-i*(i - 1)**4
Let b(h) = 2*h**2 - 56*h + 2. Suppose -147 - 133 = -10*j. Let a be b(j). Factor -2/5*q**a + 4/5 + 2/5*q.
-2*(q - 2)*(q + 1)/5
Let j(v) = v**3 + v**2 - 4*v - 1. Let t(y) = 7*y**3 + 3*y**2 - 30*y - 11. Let z(n) = 10*j(n) - 2*t(n). Factor z(g).
-4*(g - 3)*(g + 1)**2
Suppose 115 = 39*n - 124 + 239. Factor -2/9*c**3 - 2/9*c + n - 4/9*c**2.
-2*c*(c + 1)**2/9
Factor 4/3 - 3*y**2 + 16/3*y.
-(y - 2)*(9*y + 2)/3
Let x(n) be the second derivative of 0 + 1/2*n**2 + 5/36*n**3 - 1/72*n**4 + 9*n. Factor x(k).
-(k - 6)*(k + 1)/6
Factor 0 - 8*s**2 - 6*s - 3/2*s**3 + 1/2*s**4.
s*(s - 6)*(s + 1)*(s + 2)/2
Let o = -8 + 15. Let 5*h + 12*h - 26*h**3 - 2*h + 16*h**2 + 2 - o*h**3 = 0. Calculate h.
-1/3, -2/11, 1
Factor 0*v**3 + 3*v**3 + 9993*v**2 + 79*v - 10059*v**2 - 16*v.
3*v*(v - 21)*(v - 1)
Let c(h) be the second derivative of h**5/100 + h**4/20 - 2*h**2/5 + 28*h. Factor c(t).
(t - 1)*(t + 2)**2/5
Let u(o) be the second derivative of 11*o**4/16 - 5*o**3/2 - 3*o**2/2 - 2*o + 1. Solve u(w) = 0 for w.
-2/11, 2
Factor 21*h + 4*h - 43*h**2 - 5*h**4 + 20 + 28*h**2 - 25*h**3.
-5*(h - 1)*(h + 1)**2*(h + 4)
Let d(r) be the second derivative of r**5/70 + 4*r**4/21 - 20*r**3/21 + 4*r - 6. Suppose d(k) = 0. Calculate k.
-10, 0, 2
Suppose -1 = -4*y + 3. Let l(z) = -1. Let s(g) = 5*g**2 + g + 2. Let i(p) = p**2 - 1. Let m(j) = -4*i(j) + s(j). Let f(q) = y*m(q) + 6*l(q). Factor f(u).
u*(u + 1)
Let l(z) = 9*z**2. Let j(d) be the second derivative of -d**5/20 + 2*d**4/3 + 4*d - 2. Let t(x) = 3*j(x) - 2*l(x). Factor t(r).
-3*r**2*(r - 2)
Let v = -1675 - -1675. Let s(x) be the first derivative of 5 + 1/2*x**6 + 0*x + v*x**2 + 3/5*x**5 + 0*x**4 + 0*x**3. Factor s(a).
3*a**4*(a + 1)
Let d(s) be the first derivative of -s**7/189 - 2*s**6/45 - 13*s**5/90 - 2*s**4/9 - 4*s**3/27 + 10*s - 1. Let k(p) be the first derivative of d(p). Factor k(q).
-2*q*(q + 1)**2*(q + 2)**2/9
Let a(v) be the first derivative of 3*v**6/2 + 24*v**5/5 + 3*v**4/4 - 8*v**3 - 6*v**2 + 149. Suppose a(d) = 0. Calculate d.
-2, -1, -2/3, 0, 1
Let m = -292 + 292. Let r(t) be the first derivative of 1 - 3/14*t**4 + 8/21*t**3 + m*t - 1/7*t**2. Suppose r(j) = 0. What is j?
0, 1/3, 1
Factor 1/4 + 2*h**2 + 5/4*h + h**3.
(h + 1)*(2*h + 1)**2/4
Let d(x) be the second derivative of x**7/1680 + 13*x**6/720 + x**5/5 + 3*x**4/4 + 23*x**3/6 + 2*x - 2. Let u(y) be the second derivative of d(y). Factor u(f).
(f + 1)*(f + 6)**2/2
Let j = 209141 - 3552029/17. Let b = j - 198. Factor -b*x**2 + 8/17*x - 8/17.
-2*(x - 2)**2/17
Suppose 1/2*t**3 + 15/2*t - 9/2*t**2 - 7/2 = 0. Calculate t.
1, 7
Let d be (-6)/5 + (-186)/(-30). Let w(o) be the first derivative of 0*o - 3/20*o**4 - 7 - 1/25*o**d + 0*o**2 - 2/15*o**3. Factor w(v).
-v**2*(v + 1)*(v + 2)/5
Let c(u) = -5*u**2 - 4*u. Let h(k) = 14*k**2 + 11*k. Let d be -1 - 1 - (2 - 0). Let q(a) = d*h(a) - 11*c(a). Factor q(x).
-x**2
Let u(i) be the second derivative of -i**5/20 - i**4/8 + i**3 + 3*i**2/2 + 6*i. Let t(f) be the first derivative of u(f). Factor t(y).
-3*(y - 1)*(y + 2)
Find i, given that 15*i + 0*i + 7*i**4 - 6*i + 278*i**3 - 80*i**2 - 9*i = 0.
-40, 0, 2/7
Let r be (-4)/14 - 3*112/(-147). Let l(w) be the second derivative of -3/100*w**5 - 3/20*w**4 + w + 0 - 1/5*w**3 + 0*w**r. Factor l(n).
-3*n*(n + 1)*(n + 2)/5
Let b(w) = -w**5 - w**4 - w**3 - w**2 + 2*w. Let v(p) = -12*p**5 - 8*p**4 - 4*p**3 - 12*p**2 + 16*p. Let r(u) = -10*b(u) + v(u). Let r(t) = 0. Calculate t.
-1, 0, 1, 2
Let j(r) be the third derivative of -r**5/270 - r**4/9 - 4*r**3/3 - 5*r**2 + 1. What is n in j(n) = 0?
-6
Suppose 11*q + 60 = 16*q. Suppose -q*g = -9*g. Factor -1/5*j**4 + g*j + 0 - 1/5*j**2 - 2/5*j**3.
-j**2*(j + 1)**2/5
Let t be (-240)/72 - 1*-4. Let o(z) be the first derivative of -2/5*z**5 + 0*z**2 - 6 + 0*z**4 + t*z**3 + 0*z. Factor o(y).
-2*y**2*(y - 1)*(y + 1)
Let u(m) = m**3 + 177*m**2 - 350*m + 1434. Let g be u(-179). Let j = -151/3 - -51. Let -b**g + 0 - j*b - 1/3*b**3 = 0. What is b?
-2, -1, 0
Let q be 2 - (16/7 - 2). Suppose 10*c - 5*c = 0. Determine m, given that -q*m**4 + 4/7*m**2 + 0*m + c + 2/7*m**3 = 0.
-1/2, 0, 2/3
Let m be (-2)/((-180)/(-2054)) + (-4)/(-18). Let a = m - -23. Suppose 2/5*o**2 + 0*o - a*o**4 + 0*o**3 + 0 = 0. What is o?
-1, 0, 1
Suppose 0 = -0*d + 2*d - 14. Factor 0*b - d*b - 8*b**2 - 9*b + 4*b**3 + 4*b**4 - 2*b**4.
2*b*(b - 2)*(b + 2)**2
Suppose 3*s + 294 = -162. Let y = 154 + s. Factor 4/3*x**3 + 0*x + 0 - 4/3*x**4 + 0*x**y.
-4*x**3*(x - 1)/3
Let x(o) be the second derivative of o**5/20 - 19*o**4/12 + 68*o. Factor x(k).
k**2*(k - 19)
Suppose -37*y = -19*y - 25*y. Factor 0*w**2 + 0*w + y*w**3 - 2/7*w**5 + 0 - 4/7*w**4.
-2*w**4*(w + 2)/7
Suppose -41 = 3*m - 164. Let k = m + -39. Determine w so that 1/2*w**2 + k*w + 2 = 0.
-2
Let h(j) be the second derivative of j**6/120 - j**5/15 - j**4/24 + 2*j**3/3 - 39*j**2/2 - 45*j. Let b(v) be the first derivative of h(v). Factor b(o).
(o - 4)*(o - 1)*(o + 1)
Let n(d) be the third derivative of d**5/75 - d**4/40 - d**3/30 - d**2 - 41. Factor n(b).
(b - 1)*(4*b + 1)/5
Let x be 27 + -30 - (-4 + (-1)/1). What is m in 42*m + 5 - 12*m**2 + 5 - 17*m - 25*m**3 + x*m**2 = 0?
-1, -2/5, 1
Let z = -46 - -191. Let m = -722/5 + z. Factor 0 + 3/5*q**3 + 1/5*q**5 + 0*q - m*q**4 - 1/5*q**2.
q**2*(q - 1)**3/5
Solve -6*a**4 + 91*a - 91*a + 32 - 36*a**2 + 22 + 4*a**4 - 16*a**3 = 0 for a.
-3, 1
Let j(r) = -r + 6 + 8*r**2 + r**3 - 4 - 4. Let t be j(-8). Factor -4/3*v - 8/3*v**3 + t*v**2 + 0.
-2*v*(v - 2)*(4*v - 1)/3
Let l(a) = a**3 + a**2 - a + 5. Let h = 99 + -125. Let d(z) = -4*z**3 - 5*z**2 + 4*z - 21. Let m(q) = h*l(q) - 6*d(q). Solve m(r) = 0 for r.
-1, 1, 2
Suppose -3*l = 5*n - 34, -3*l = -4*n - 0*l + 38. Suppose -23 = -5*v - n. Factor 6*p**2 - 3/2*p + 15/2*p**v + 0.
3*p*(p + 1)*(5*p - 1)/2
Let h(r) = -31*r**2 + 133*r + 34. Let f(p) = -123*p**2 + 531*p + 135. Let x(k) = 4*f(k) - 15*h(k). Factor x(i).
-3*(i - 5)*(9*i + 2)
Factor 2*a + 203*a**2 + 7*a - 224*a**2 + 15*a**3 - 3*a**4.
-3*a*(a - 3)*(a - 1)**2
Let k(q) = -3*q**2 - 6*q + 9. Let l be 13/3 + (-2)/(-3). Let g(f) = 6*f**2 + 13*f - 19. Let d(n) = l*k(n) + 3*g(n). Find w such that d(w) = 0.
-4, 1
Let u(v) be the third derivative of v**7/490 - 9*v**6/280 + 3*v**5/28 - v**4/8 + 18*v**2. Determine j, given that u(j) = 0.
0, 1, 7
Let h(d) be the first derivative of d**6/45 - 4*d**5/75 + 4*d**3/45 - d**2/15 + 75. Suppose h(m) = 0. Calculate m.
-1, 0, 1
Let l = 457/70 + -45/7. Let h(w) be the first derivative of -l*w**4 - 12/5*w**2 + 16/5*w + 4/5*w**3 - 3. Solve h(u) = 0.
2
Let f(t) = -t**3 - 12*t**2 + t + 15. Let k = -264 + 252. Let a be f(k). Solve 4/3*x**4 - 4/3*x**2 + 0*x**a + 2/3*x**5 + 0 - 2/3*x = 0.
-1, 0, 1
Let j = -9 + 12. Suppose 3*a - 5*i = -17 + j, 0 = -3*a + 3*i - 6. Let -2*t**2 - 4*t**a + 0*t**2 + 4*t**2 - t**3 = 0. Calculate t.
-2, 0
Suppose -5*d - 3*r + 4*r = 50, -r = -2*d - 20. Let p = 12 + d. Factor n**2 + 1 - n - n**p + n**2 - 3.
(n - 2)*(n + 1)
Let x(m) = -44 - 3*m**2 + 2*m - 4*m + 47. Let n(o) = 16*o**2 + 9*o - 14. Let s(k) = -6*n(k) - 33*x(k). Find j, given that s(j) = 0.
-5, 1
Let o(d) = d**2 - d - 1. Let j be o(-4). Find m, given that -24*m**3 + j*m**2 - 4*m**4 + 97*m**2 - 156*m**4 + 60*m + 8 = 0.
-1/2, -2/5, -1/4, 1
Let t(s) be the second derivative of 49/96*s**4 + 1/6*s**3 + 4*s - 1/4*s**2 + 2 - 49/80*s**5. Determine o, given that t(o) = 0.
-2/7, 2/7, 1/2
Let k(w) = 3*w + 7. Let t be k(-3). Let h(f) = 3*f**3 + 4*f**2 - 2*f + 4. Let u be h(t). Factor -9/4*g**2 + u - 1/4*g**4 + 3/2*g**3 + g.
-g*(g - 4)*(g - 1)**2/4
Let t(l) be the first derivative of 2*l**3/21 + 23*l**2/7 - 156*l/7 - 306. Factor t(w).
2*(w - 