2
Let k(f) = 9*f**4 - 5*f**2 - 5*f - 5. Let u(z) = -3*z. Let o be u(4). Let x(r) = 22*r**4 - 12*r**2 - 12*r - 12. Let i(n) = o*k(n) + 5*x(n). Factor i(h).
2*h**4
Let d = 7877/10412 + -17/2603. Factor -d*f**2 - 33/4 + 9*f.
-3*(f - 11)*(f - 1)/4
Determine n so that -140/9*n**3 + 226/9*n**2 - 44/9*n - 5 + 1/3*n**4 = 0.
-1/3, 1, 45
Suppose 2*q - q = 14. Suppose -42 = -m + q. Let -32*j + 37 - 45 - 4*j**2 - m = 0. Calculate j.
-4
Let x = -57/5 + 414/35. Find m such that x*m**4 + 6/7*m + 0*m**2 - 3/7 - 6/7*m**3 = 0.
-1, 1
Let a(l) be the third derivative of -45*l**2 + 1/252*l**7 - 1/8*l**5 - 5/9*l**3 + 0 + 0*l - 55/144*l**4 - 1/144*l**6. Factor a(w).
5*(w - 4)*(w + 1)**3/6
Let d(a) be the first derivative of -a**8/112 + 3*a**6/40 - a**5/10 + 2*a**2 + 4*a - 46. Let u(q) be the second derivative of d(q). Factor u(c).
-3*c**2*(c - 1)**2*(c + 2)
Let w(y) = 8*y**2 - 28*y + 40. Let g be 15/((-6)/8*-4). Let l(a) = 9*a**2 - 29*a + 41. Let z(m) = g*w(m) - 4*l(m). Factor z(h).
4*(h - 3)**2
Factor -9604/9 - 4/9*k**2 + 392/9*k.
-4*(k - 49)**2/9
Let v(t) be the second derivative of 3/20*t**5 - 4*t - 3/4*t**4 + 3/2*t**3 - 3/2*t**2 + 0. Factor v(y).
3*(y - 1)**3
Suppose -k = 3*j - 5*j + 10, -3*j + k + 15 = 0. Suppose 3*y - 1 = j. Suppose -11 + 3*v**2 - 3*v**4 + 3*v**y + v + 9 + 5*v**4 - 7*v**3 = 0. Calculate v.
-1/2, 1, 2
Let g(k) be the second derivative of 2/15*k**5 + 0 + 0*k**4 + 0*k**3 + 14*k + 1/63*k**7 + 4/45*k**6 + 0*k**2. Let g(x) = 0. What is x?
-2, 0
Let s(y) = 4*y**4 - 11*y**3 - 7*y**2 + 2*y - 6. Let a be 2/4*72/6. Let n(f) = 11*f**4 - 32*f**3 - 20*f**2 + 6*f - 17. Let o(l) = a*n(l) - 17*s(l). Factor o(p).
-p*(p + 1)*(p + 2)*(2*p - 1)
Let m(k) be the second derivative of k**7/210 - 7*k**6/270 + k**5/18 - k**4/18 - 19*k**3/6 + 28*k. Let l(x) be the second derivative of m(x). Factor l(w).
4*(w - 1)**2*(3*w - 1)/3
Let p(i) = 8*i + 40. Let j be p(-5). Let o(n) be the second derivative of -5/12*n**4 + 3*n + j - 7/6*n**3 - n**2. Factor o(a).
-(a + 1)*(5*a + 2)
Suppose -319*z + 568 = -19*z - 932. Factor -22/5*c**2 - 18/5*c**3 + 2/5*c**z - 8/5*c - 2/5*c**4 + 0.
2*c*(c - 4)*(c + 1)**3/5
Let j be ((-2)/(-12))/(7/(2 + 5)). Let d(o) be the third derivative of 0 + o**2 + 1/60*o**5 + 0*o**4 + 0*o - j*o**3. Suppose d(q) = 0. Calculate q.
-1, 1
Let j(u) be the third derivative of -25*u**8/2688 - u**7/24 - 23*u**6/320 - 7*u**5/120 - u**4/48 - u**2 + 39*u. Suppose j(s) = 0. Calculate s.
-1, -2/5, 0
What is d in -13/5*d + 22/5 + 1/5*d**2 = 0?
2, 11
Let h(n) = n**3 + 7*n**2 - 75*n + 41. Let o be h(-13). Let f(m) be the first derivative of 7 + 1/15*m**5 - 1/4*m**4 + 0*m**o + 0*m + 2/9*m**3. Factor f(z).
z**2*(z - 2)*(z - 1)/3
Let f(y) = y**2 + 3*y + 2. Let t be f(-3). Suppose 3*d + 12 = 12. Suppose 2/11*v - 2/11*v**t + d = 0. Calculate v.
0, 1
Let c = 20 - 32. Let w(g) = -g**3 - 1. Let a(y) = -2*y**3 + 3*y**2 + 3*y - 2. Let o(h) = c*w(h) + 4*a(h). Factor o(i).
4*(i + 1)**3
Let w(m) = m**3 - 28*m**2 + 31*m + 53. Let f be w(27). Determine h, given that 16 - 160*h + f*h**2 - 365*h**3 + 307*h**2 + 41*h**3 = 0.
2/9, 1
Let k(h) be the first derivative of h**5/10 + 11*h**4/4 + 157*h**3/6 + 99*h**2 + 162*h + 27. Factor k(n).
(n + 2)**2*(n + 9)**2/2
Let c(x) = x**3 + 6*x**2 - 8*x - 5. Let n be c(-7). Factor -6*z**4 + 4*z**4 + z**2 + z**n - 2*z**3 + 2*z**5.
2*z**2*(z - 1)**2*(z + 1)
Let z(t) be the third derivative of -t**5/300 - t**4/10 - 6*t**3/5 + 2*t**2 + 2*t. Factor z(l).
-(l + 6)**2/5
Let g(k) be the first derivative of -k**6/12 - 2*k**5/5 - k**4/2 + k**3/3 + 5*k**2/4 + k + 85. Factor g(m).
-(m - 1)*(m + 1)**3*(m + 2)/2
Let i = -8343 + 8346. Suppose -6348/17*p**2 + 552/17*p + 24334/17*p**i - 16/17 = 0. Calculate p.
2/23
Let c(k) be the third derivative of k**8/252 - k**7/15 + 29*k**6/90 - 34*k**5/45 + k**4 - 7*k**3/9 + 61*k**2 + 2. Find a such that c(a) = 0.
1/2, 1, 7
Suppose 4*w + 29 = 2*w - 5*m, 2*w = 5*m + 1. Let u(s) = -s - 7. Let j be u(w). Find k such that j*k - 1/3 + 0*k**3 - 1/3*k**4 + 2/3*k**2 = 0.
-1, 1
Let j(h) be the second derivative of -h**7/28 - 2*h**6/5 - 39*h**5/40 - 3*h**4/4 + 46*h. Let j(u) = 0. Calculate u.
-6, -1, 0
Factor -20*d - 21*d**2 - 30*d**2 + 47*d**2 + 96.
-4*(d - 3)*(d + 8)
Let h(r) be the third derivative of -r**5/80 - 5*r**4/8 + 12*r**3 - 46*r**2. Suppose h(q) = 0. Calculate q.
-24, 4
Let b = -1/79 - -241/316. Let q = -206 + 833/4. Find j such that 0*j**2 - 3/2 - q*j + b*j**3 = 0.
-1, 2
Suppose 3*d - 6 = -0*x + x, d - 3 = 0. Suppose -v - z - 6 = -3*z, -4*v - x*z + 9 = 0. Factor -1/2*s**2 + v - 1/2*s + 1/2*s**3 + 1/2*s**4.
s*(s - 1)*(s + 1)**2/2
Let x(b) be the second derivative of -3*b**6/10 + 21*b**5/10 - 3*b**4 - 12*b**3 + 48*b**2 - 366*b. Factor x(f).
-3*(f - 2)**3*(3*f + 4)
Let h = -4096 - -20481/5. Suppose 2/5*l**2 - 2/5 + 1/5*l - h*l**3 = 0. Calculate l.
-1, 1, 2
What is a in 35*a**5 + 21 - 181 + 80*a**2 - 1350*a**3 + 1070*a**3 - 10*a**4 + 560*a = 0?
-2, 2/7, 2
Suppose -825 = 13*b - 851. Let p(y) be the second derivative of -1/10*y**5 - 9/4*y**b - y - 7/2*y**3 + 0 - 25/24*y**4. Factor p(n).
-(n + 3)**2*(4*n + 1)/2
Determine u, given that -2/11*u**5 + 0*u - 16/11*u**2 + 0 - 28/11*u**3 - 14/11*u**4 = 0.
-4, -2, -1, 0
Let f be (-3 + 0)*8998/(-198). Let d = f - 131. Find q, given that d*q - 2/3*q**5 + 10/3*q**4 - 4*q**3 + 0 - 8/3*q**2 = 0.
-1, 0, 2
Factor -17*n + 22*n - 29*n**2 - 37*n - 27 + 23 - 7*n**3.
-(n + 2)**2*(7*n + 1)
Suppose 4/9*z - 40/3 + 4/9*z**2 = 0. Calculate z.
-6, 5
Let b be (-189)/(-405)*24/28. Factor -6/5*l**2 + 0 - 4/5*l - b*l**3.
-2*l*(l + 1)*(l + 2)/5
Let u = 14/93 - 27/248. Let z(l) be the second derivative of -2*l + 1/60*l**6 + 1/40*l**5 + 0*l**3 - 1/84*l**7 + 0*l**2 + 0 - u*l**4. Factor z(v).
-v**2*(v - 1)**2*(v + 1)/2
Suppose 12/7 - 3/7*j**2 + 0*j = 0. What is j?
-2, 2
Determine c so that -1/7*c**2 - 47/7 + 48/7*c = 0.
1, 47
Determine u so that 1/4*u**4 + 325/4*u**2 + 375*u + 15/2*u**3 + 625 = 0.
-10, -5
Let q = 20726/3 + -6986. Let p = q + 545/6. Factor -9*n + 3/2*n**2 + p.
3*(n - 3)**2/2
Let z(f) be the second derivative of f**7/70 + 2*f**6/25 - 7*f**4/10 - 17*f**3/10 - 9*f**2/5 + f + 2. Factor z(w).
3*(w - 2)*(w + 1)**3*(w + 3)/5
Let r be 4 + (4 - (-2 - -2)). Suppose -3*a**5 - 4*a**3 - r*a**3 + 15*a**3 = 0. What is a?
-1, 0, 1
Factor 1012/5*y - 24 + 68/5*y**2.
4*(y + 15)*(17*y - 2)/5
Suppose 8*z = 13*z + 4*d - 30, 4*z - 2*d = -2. Let w(l) be the second derivative of -1/60*l**4 + 0 + 1/30*l**3 + 9*l + 1/5*l**z. Factor w(s).
-(s - 2)*(s + 1)/5
Let j be 33273/(-18)*(1 + (-13)/11). Let s = 337 - j. What is n in 2/11*n**4 + s*n**2 + 4/11*n + 8/11*n**3 + 0 = 0?
-2, -1, 0
Let j = 7/173 + 1529/692. Find c such that 0 + 0*c + j*c**3 - 3/4*c**5 - 3/2*c**2 + 0*c**4 = 0.
-2, 0, 1
Let l(t) = t**3 + t**2 + 116*t - 242. Let b be l(2). Find s, given that -3/4 - s - 1/4*s**b = 0.
-3, -1
Let a = 23 - 18. Let z be ((-8)/a)/((-104)/(-20) + -8). Determine g, given that 2/7*g + z*g**2 - 4/7 - 2/7*g**3 = 0.
-1, 1, 2
Suppose 19*m - m = 54. Let z(l) be the second derivative of -1/9*l**m + 0*l**4 - 4*l + 0*l**2 + 1/30*l**5 + 0. Let z(b) = 0. Calculate b.
-1, 0, 1
Factor 0 + 14/3*v - 2/3*v**2.
-2*v*(v - 7)/3
Let k(v) be the first derivative of 2*v**3/3 + 5*v**2 + 13. Factor k(g).
2*g*(g + 5)
Let 10/11*l**4 - 64/11*l + 206/11*l**2 - 24 + 114/11*l**3 - 2/11*l**5 = 0. What is l?
-3, -2, 1, 11
Let s = 47/36 + -5/4. Let p(l) be the second derivative of -2/3*l**3 + 0 - s*l**4 - 3*l**2 - 2*l. Factor p(d).
-2*(d + 3)**2/3
Let l be (9/78)/((-840)/(-1820)). Factor -m + l*m**4 + 11/4*m**2 + 1/4*m**5 - 9/4*m**3 + 0.
m*(m - 1)**3*(m + 4)/4
Let j = -18298/15 + 1220. Suppose 4/15*z**2 + 2/15 - 2/5*z + j*z**5 - 2/5*z**4 + 4/15*z**3 = 0. What is z?
-1, 1
Let g(t) be the first derivative of -2*t**3/3 - 2*t**2 + 16*t - 59. Find m such that g(m) = 0.
-4, 2
Let l(y) be the first derivative of 2*y**6/9 - 8*y**5/5 + 14*y**4/3 - 64*y**3/9 + 6*y**2 - 8*y/3 - 153. Factor l(d).
4*(d - 2)*(d - 1)**4/3
Let v = -1859/15 - -124. Let a = v - -2/15. Factor 1/5*c**2 - a*c - 2/5.
(c - 2)*(c + 1)/5
Let q = 15 - 5. Suppose 4 = -2*u + q. Factor u - 12*i**2 + 7 - 9*i**3 - 3*i - 10.
-3*i*(i + 1)*(3*i + 1)
Let u(g) = g**5 + g**4 + 17*g**3 - 40*g**2 + 27*g - 3. Let z(b) = 5*b**5 + 3*b**4 + 69*b**3 - 160*b**2 + 109*b - 13. Let l(x) = -26*u(x) + 6*z(x). Factor l(c).
4*c*(c - 2)**2*(c