2
Let 556/3*k + 0 - 1/3*k**2 = 0. Calculate k.
0, 556
Let p(o) be the third derivative of o**6/120 - 3*o**5/5 + 65*o**4/6 - 5816*o**2. Determine l, given that p(l) = 0.
0, 10, 26
Let q be (-6)/288*4*(13 + -58). Suppose -9/4*o**5 - 3/4*o**2 + 0 + 0*o - 21/4*o**4 - q*o**3 = 0. What is o?
-1, -1/3, 0
Factor 1340 + 95*x - 13*x**2 + 585*x + 31*x**2 - 13*x**2.
5*(x + 2)*(x + 134)
Factor -118*i + 2/3*i**2 + 352/3.
2*(i - 176)*(i - 1)/3
Let y = -409 - -90. Let s be (-58)/y - (-31)/11. Factor 4*q**2 - s*q**2 + 2 - 3*q**2 - 2*q + 2*q**3.
2*(q - 1)**2*(q + 1)
Let 532/5 - 2/5*n**3 - 622/5*n + 92/5*n**2 = 0. Calculate n.
1, 7, 38
Let t = 18 - -2. Suppose 0 = 43*k - 47*k + t. Factor 2*n**2 + 6*n**2 - 28*n**3 + 8*n - 3*n**5 - 4*n**4 + 22*n**3 + 5*n**k.
2*n*(n - 2)**2*(n + 1)**2
Let g(h) = -4*h**5 - 48*h**4 + 24*h**3 - 80*h**2 - 44*h + 4. Let i(l) = l**4 - 5*l**3 - l**2 - l - 1. Let u(m) = -g(m) - 20*i(m). Factor u(y).
4*(y + 1)**3*(y + 2)**2
Let k be 72/2 - (9 - 5). Suppose -m + 4*s = -4, 0 = -m + 2*s + 34 - k. Factor m*h - 1/4*h**3 + 0 + 7/4*h**2.
-h**2*(h - 7)/4
Let w = 128476/3 + -42825. Factor -8 + 2/3*a + w*a**2.
(a - 4)*(a + 6)/3
Let h(k) be the first derivative of -k**3/9 + 379*k**2/6 + 254*k - 7768. Suppose h(n) = 0. What is n?
-2, 381
Let f be 2 + 1 - (2 - (-4 + 6)). Let -12*y**2 + 56 - 104 + 3*y**3 - f*y + 48 + 12*y**4 = 0. Calculate y.
-1, -1/4, 0, 1
Let -1/5*a**4 - 93/5*a**2 + 17/5*a**3 - 162/5 + 207/5*a = 0. What is a?
2, 3, 9
Suppose -212 = -137*q - 18*q - 212. Factor 1/2*m**4 + 3/2*m**3 + 0 + 0*m**2 + q*m.
m**3*(m + 3)/2
Determine j, given that -90*j**3 - 3260*j - 1220*j - 940*j**2 + 4800 + 2152*j**2 + 2*j**4 = 0.
2, 3, 20
Let x = 18 + -16. Suppose 0 = x*h + 5*h - 112. Factor -h - 6 - 4*z**2 - 16*z + 6.
-4*(z + 2)**2
Let h(x) be the second derivative of -7*x - 1/42*x**7 + 0*x**2 - 3/40*x**5 + 1/12*x**6 + 1/12*x**3 - 1/24*x**4 + 0. Factor h(f).
-f*(f - 1)**3*(2*f + 1)/2
Factor 77/2 - 1/4*s**2 - 3/4*s.
-(s - 11)*(s + 14)/4
Suppose 0 + 603/2*f**2 - 3/8*f**4 + 0*f + 591/8*f**3 = 0. What is f?
-4, 0, 201
Let k(h) = 36*h**4 - 91*h**3 + 49*h**2 + 10*h - 4. Let r(p) = 35*p**4 - 91*p**3 + 49*p**2 + 10*p - 3. Let s(g) = -3*k(g) + 4*r(g). Factor s(a).
a*(a - 2)*(a - 1)*(32*a + 5)
Let l(z) be the second derivative of -2*z**7/147 - 2*z**6/15 - 16*z**5/35 - 8*z**4/21 + 32*z**3/21 + 32*z**2/7 + z - 922. Factor l(c).
-4*(c - 1)*(c + 2)**4/7
Let j = 1366577/427060 + 3/85412. Let y = -4 - -6. Factor j + 14/5*w**y - 28/5*w - 2/5*w**3.
-2*(w - 4)*(w - 2)*(w - 1)/5
Let g(u) = u**2 + 1. Suppose 8 = -18*a + 10*a. Let q(r) = -4*r**2 + 6*r + 6. Let v(f) = a*q(f) - 2*g(f). What is d in v(d) = 0?
-1, 4
Let y(z) be the second derivative of z**4/60 + 77*z**3/30 + 36*z**2 + 1528*z + 3. Factor y(w).
(w + 5)*(w + 72)/5
Let a(k) be the third derivative of -k**5/30 - 104*k**4/3 + 139*k**3 - 3*k**2 - 161*k - 5. Factor a(o).
-2*(o - 1)*(o + 417)
Suppose -708*a + 724*a - 18 - 46 = 0. Let g(q) be the first derivative of 1/2*q**a + 0*q + 19 + 8/3*q**3 + 3*q**2. Determine o, given that g(o) = 0.
-3, -1, 0
Let z(j) be the first derivative of -j**3 + 3177*j**2/2 - 3174*j + 15899. Factor z(s).
-3*(s - 1058)*(s - 1)
Let p(r) = -42*r**2 - 98*r - 978. Let c(s) = -4*s**2 - s - 1. Let l(j) = 10*c(j) - p(j). Suppose l(y) = 0. Calculate y.
-22
Let h(m) be the third derivative of m**6/40 + 37*m**5/10 + 71*m**4/2 + 140*m**3 - m**2 - 43*m + 4. Factor h(n).
3*(n + 2)**2*(n + 70)
Let i(s) = 15*s**2 + 555*s + 10277. Let k(m) = 7*m**2 + 279*m + 5145. Let f(r) = 3*i(r) - 7*k(r). Factor f(c).
-4*(c + 36)**2
Let v(i) be the second derivative of 0 - 9/2*i**2 + 1/20*i**5 - 11/12*i**4 + 19/6*i**3 + 131*i. Let v(a) = 0. What is a?
1, 9
Let t(g) = 4*g**2 - 116*g + 2. Let s be t(29). Let i(a) be the third derivative of 0*a - 1/4*a**4 + a**3 + 0 - s*a**2 + 1/40*a**5. Factor i(m).
3*(m - 2)**2/2
Let t be ((-8)/7)/((-16)/28). Factor -4/9*p - 7/9*p**4 + 4/3*p**t + 0 + p**3.
-p*(p - 2)*(p + 1)*(7*p - 2)/9
Let f(b) be the first derivative of -9*b**5/2 + 447*b**4/4 + 55*b**3/2 - 447*b**2/2 - 60*b - 709. Suppose f(u) = 0. Calculate u.
-1, -2/15, 1, 20
Let l(v) = -11*v**2 + 3*v + 2. Let d be l(6). Let o = -3382/9 - d. Factor -o*b**2 + 0*b - 2/9*b**3 + 0.
-2*b**2*(b + 1)/9
Let q(r) be the first derivative of 139 + 8/7*r + 3/14*r**4 - 10/21*r**3 - 4/7*r**2. Factor q(s).
2*(s - 2)*(s + 1)*(3*s - 2)/7
Let g(i) be the first derivative of -4*i**5/5 + 13*i**4 - 188*i**3/3 + 46*i**2 + 336*i + 2462. Find v such that g(v) = 0.
-1, 3, 4, 7
Solve -4*n**4 - 242*n**3 + 20201*n**2 - 40402*n**2 + 6*n**4 + 20201*n**2 = 0 for n.
0, 121
Let w(v) = -18 - 4*v**2 - 22 - 8 + 32*v. Let p(z) = -28*z**2 + 224*z - 336. Let q(h) = -3*p(h) + 20*w(h). Factor q(x).
4*(x - 6)*(x - 2)
Let n = 952978 + -952978. Find u, given that -2*u**2 + 3/2*u**3 + 1/2*u**4 + n*u + 0 = 0.
-4, 0, 1
Let 33764*j**2 + 33771*j**2 - 2*j + 180 - 67540*j**2 + 2*j = 0. Calculate j.
-6, 6
Let j be 10*((-1383)/(-27) + (-8)/36). Let o = j + -6628/13. Factor o*s**2 - 8/13 + 6/13*s.
2*(s - 1)*(s + 4)/13
Let l = 16848 + -16844. Let c(q) be the first derivative of -17/2*q**l + 28/5*q**5 - 4*q**2 - 21 - 40/3*q**3 + 0*q. Suppose c(x) = 0. Calculate x.
-1/2, -2/7, 0, 2
Factor -21762647 + 650*l - 5*l**4 + 635*l**2 - 20*l**3 + 21762647.
-5*l*(l - 10)*(l + 1)*(l + 13)
Suppose 27 = 15*w - 33. Factor -1 - 30*g**2 + 0 - 20*g**3 - 10 - 5*g**w + 6 - 20*g.
-5*(g + 1)**4
Let i(q) be the first derivative of -q**3/21 + 81*q**2/14 + 82*q/7 + 895. Solve i(h) = 0 for h.
-1, 82
Let l be -7*13/91*(-3 - 2). Factor o**4 + o**2 + 0 + 3/2*o**3 + 1/4*o**l + 1/4*o.
o*(o + 1)**4/4
Let k = 4 - -8. Suppose -3*n + 6 = w, 3*w - 4 + 1 = -4*n. Solve -20*u**2 - 24*u**n - k*u**4 + 0*u**5 - 30*u - 2*u**5 + 24*u = 0.
-3, -1, 0
Let i(o) be the second derivative of 2*o**6/15 - 39*o**5/5 + 105*o**4 + 882*o**3 + 20*o - 5. Find f, given that i(f) = 0.
-3, 0, 21
Let x be (-64)/(-16)*(2 - (-2)/(-4)). Let u be 12/x - 0/5. Factor -2/3*w**u + 2/3*w + 2/9*w**3 - 2/9.
2*(w - 1)**3/9
Let k(l) be the third derivative of 0 + 1/270*l**5 - 1/27*l**4 + 0*l + 277*l**2 - 7/9*l**3. Suppose k(o) = 0. Calculate o.
-3, 7
Let l(y) be the first derivative of y**6/2 - 84*y**5/5 + 291*y**4/2 - 452*y**3 + 855*y**2/2 + 3826. Let l(r) = 0. Calculate r.
0, 1, 3, 5, 19
Factor 0 - 1970/9*q**2 - 2/3*q.
-2*q*(985*q + 3)/9
Let r(g) = 12*g + 206. Let b(d) = -7*d + 151. Let n be b(24). Let h be r(n). Find w such that -18/7 - 30/7*w + 6/7*w**3 - 6/7*w**h = 0.
-1, 3
Let a = -123 - -126. Suppose -13*f + 231 - 179 = 0. Find m, given that 18/7*m**5 - 8/7*m - 16/7*m**2 + 0 + 74/7*m**a - 68/7*m**f = 0.
-2/9, 0, 1, 2
Let r be (3/6*0)/(13 - (9 + 11)). Let k(i) be the third derivative of -1/24*i**4 + r*i - 6*i**2 + 0 - 1/120*i**5 - 1/12*i**3. Factor k(s).
-(s + 1)**2/2
Suppose -44*u + 1233 = 93*u. Suppose 9 = 6*r - 3*r + p, 5*r - 15 = -2*p. Let -35*g - 54*g**3 + 3*g**2 + 21*g**4 + 63*g**2 - r*g**5 - 4*g + u = 0. Calculate g.
1, 3
Let x(t) = -7*t**3 - 24*t**2 - 89*t - 36. Let v(y) = 13*y**3 + 48*y**2 + 174*y + 73. Let f(l) = -6*v(l) - 11*x(l). Factor f(o).
-(o + 1)*(o + 2)*(o + 21)
Let c(n) be the first derivative of -n**5/20 - n**4/3 + 5*n**3/6 - 297*n + 72. Let d(v) be the first derivative of c(v). Factor d(q).
-q*(q - 1)*(q + 5)
Let k(m) be the first derivative of -7*m**4/18 - 848*m**3/27 - 2180*m**2/3 - 800*m + 913. Solve k(x) = 0 for x.
-30, -4/7
Let g(j) = -2*j**3 - 47*j**2 - 12 + 64*j**2 + j**3 - 7*j. Let r be g(11). Suppose 6*x**2 + 634*x**4 - 3*x**3 - r*x**4 + 0*x**2 = 0. What is x?
-2, 0, 1
Suppose -12*f + 81 = -3*f. Factor -f*v**2 + 13*v - 35*v - 3*v**2 - 2*v**3 - 16 + 4.
-2*(v + 1)*(v + 2)*(v + 3)
Let w(k) be the first derivative of 386/9*k**3 + 5*k**4 + 2/15*k**5 + 512/3*k - 58 - 160*k**2. Let w(j) = 0. Calculate j.
-16, 1
Let k = 1028/7 - 138773/945. Let v(z) be the third derivative of 0*z**3 + 0*z + k*z**5 + 4*z**2 + 0 - 2/27*z**4. Factor v(j).
4*j*(j - 4)/9
Let w(i) be the second derivative of -175/12*i**4 - 49/20*i**5 - 6*i**2 + 0 + 50*i - 44/3*i**3. Factor w(s).
-(s + 3)*(7*s + 2)**2
Suppose -24 = -n + 18. Determine w so that 7*w + n + 82*w**2 - 3*w**3 - 46*w**2 + 74*w = 0.
-1, 14
Suppose -48 = -71*n + 184 - 19. Let f(c) be the third derivative of 1/48*c**4 + 0*c + 0 + 0*c**n - 1/840*c**7 + 1/80*c**5 - 12*c**2 + 0*c**6. Factor f(i).
-i*(i - 2)