ve of 5*y**6/168 + 46*y**5/21 + 181*y**4/42 + 24*y**3/7 - 27*y**2. Factor w(g).
(g + 36)*(5*g + 2)**2/7
Suppose 8 = 21*h - 37 - 60. Factor 0*p + 24/5*p**4 + 0 + 18/5*p**3 + 4/5*p**2 + 2*p**h.
2*p**2*(p + 1)**2*(5*p + 2)/5
Suppose 17*h + 758 = 146. Let p(a) = -8*a**2 + 6*a + 11. Let b(r) = -r**2 + 0 + 1 + 3*r - 2*r. Let f(c) = h*b(c) + 4*p(c). Factor f(x).
4*(x - 2)*(x - 1)
Let q(t) be the second derivative of t**5/220 - t**4/66 - 35*t**3/66 + 17*t + 8. Factor q(j).
j*(j - 7)*(j + 5)/11
Let p(h) be the third derivative of 0*h + 0 + 38*h**2 + 1/105*h**5 + 0*h**3 + 1/21*h**4. What is k in p(k) = 0?
-2, 0
Let g be (-3)/((-12)/(-16)) - 1. Let b(f) = -f**3 - 6*f**2 - 2*f + 19. Let l be b(g). Solve 44/13*h**l - 10/13*h**5 - 76/13*h**3 + 64/13*h**2 + 4/13 - 2*h = 0.
2/5, 1
Let r = 8623/3 - 2873. Factor 0*b**3 + 2*b**2 + 0 - 2/3*b**4 - r*b.
-2*b*(b - 1)**2*(b + 2)/3
Let k(t) = 1 - 1 + 31*t - 30*t. Let l be k(4). Factor -8*r**2 + 7*r**3 + 0*r**3 - 8*r**l + 2*r + 5*r**3 + 2*r**5.
2*r*(r - 1)**4
Let k(w) = w**3 - 27*w**2 + 125*w + 8. Let q be k(6). Factor 4*z**3 + q + 4/3*z**2 - 10/3*z**4 + 2/3*z**5 - 14/3*z.
2*(z - 3)*(z - 1)**3*(z + 1)/3
Solve 29*b - 49*b - b**2 + 24*b - b**2 - 70 + 20*b = 0 for b.
5, 7
Let k(a) = 6*a**2 + 10*a. Let u(y) = y**2 + y. Suppose 0 = -6*t + t - m, 4*t = 5*m + 29. Let j(h) = t*k(h) - 8*u(h). Factor j(b).
-2*b*(b - 1)
Let m(z) be the second derivative of z**4/36 - 2*z**3/9 + z**2/2 - 789*z. Factor m(i).
(i - 3)*(i - 1)/3
Let i = 891 - 888. Let s(l) be the second derivative of -l + 1/12*l**4 + 0 + 1/3*l**i + 1/2*l**2. Factor s(y).
(y + 1)**2
Let y(z) be the first derivative of -z**4/34 + 2*z**3/51 + z**2/17 - 2*z/17 + 210. Factor y(w).
-2*(w - 1)**2*(w + 1)/17
Let l(y) = -19*y**2 + 18*y - 11. Let j(w) = 12*w + 4 + 8*w**2 - 18*w - w**2. Let a(i) = 11*j(i) + 4*l(i). Factor a(k).
k*(k + 6)
Let p(h) be the second derivative of h**6/10 - 9*h**5/4 + 13*h**4/4 + 15*h**3/2 - 21*h**2 + 3*h - 2. Factor p(f).
3*(f - 14)*(f - 1)**2*(f + 1)
Suppose -2*p = -0 + 6. Let n be 84/(-36)*(p - 0). Factor 2*y**2 + 7 + y**2 - n + 3*y.
3*y*(y + 1)
Suppose -29*d + 41 = -17. Let v(x) be the first derivative of 2*x**4 - 4*x**3 + 1 + 4/5*x**5 - 8*x**d + 16*x. Solve v(a) = 0.
-2, 1
Suppose 0 = 2*d + 4*n - 1 + 3, 3*d + 23 = 4*n. Let k be (d + 3)*-2 - 2. Factor -3*r**3 - 2*r - 4*r**k + 4*r**4 - 3*r**2 - r**3.
r*(r - 2)*(2*r + 1)**2
Suppose 4*i + 16 = u, -3*u = -i - 0*i - 37. Let m be u/8*-2 + 7. Determine g, given that 16/7 + 36/7*g**2 - 88/7*g + 34*g**3 + 14*g**m = 0.
-2, -1, 2/7
Let v = -18 + 34. Factor 6561*p**4 + 5832*p**3 + 1103*p**2 + 841*p**2 + 301*p - 132*p + 119*p + v.
(9*p + 2)**4
Let f be -1 + (-1 - -3) + 1005/(-1139). Factor f*o**2 - 14/17*o + 12/17.
2*(o - 6)*(o - 1)/17
Let t(g) be the first derivative of -g**9/4536 - g**8/630 + 4*g**6/135 + 4*g**5/45 - g**3 - 14. Let y(j) be the third derivative of t(j). Solve y(n) = 0 for n.
-2, 0, 2
Let -4*b**5 - 800 - 106*b**2 - 46*b**2 - 303*b + 16*b**4 + 92*b**3 - 577*b = 0. Calculate b.
-2, 5
Suppose 232*b - 111*b = 115*b. Factor -35/2*c**3 + 55/2*c**2 - 25/2*c + 5/2*c**4 + b.
5*c*(c - 5)*(c - 1)**2/2
Let b(q) be the second derivative of 375*q**7/14 - 65*q**6 + 109*q**5/4 + 65*q**4/3 + 10*q**3/3 - 77*q - 7. Factor b(s).
5*s*(s - 1)**2*(15*s + 2)**2
Suppose -9*r = -15 - 0 - 3. Factor -3/2*n**3 + 27*n**r - 162*n + 324.
-3*(n - 6)**3/2
Let c(x) = -x**4 + 4*x**3 - x**2 - 2*x - 4. Let u(h) = h - 1. Let b(o) = 2*o - 2. Let j(z) = 3*b(z) - 5*u(z). Let t(q) = 5*c(q) - 20*j(q). Factor t(d).
-5*d*(d - 3)*(d - 2)*(d + 1)
Let h(k) be the third derivative of k**9/45360 - k**8/10080 + k**6/1080 - k**5/360 + 2*k**4/3 + 16*k**2. Let l(n) be the second derivative of h(n). Factor l(r).
(r - 1)**3*(r + 1)/3
Let t = 11784/11 - 1070. Let o = -31/33 + t. Factor -o*f**4 + 0 + 1/3*f**5 + 0*f + 0*f**3 + 0*f**2.
f**4*(f - 1)/3
Let v = 4857 - 4857. Let 2/5*m**3 - 6/5*m**2 + 4/5*m + v = 0. Calculate m.
0, 1, 2
Determine x so that 9*x**3 - 18*x**2 - 42 - 145*x**2 + 128*x + 6*x**3 - 2*x**4 + 33*x**3 + 31*x**2 = 0.
1, 21
Let h(q) = -q**2 - 65*q - 124. Let x be h(-63). Factor 9 + 1/4*w**x - 3*w.
(w - 6)**2/4
Suppose 16*t + 2 = 85 - 19. What is z in -2/15*z + 2/15 - 4/15*z**2 + 4/15*z**3 - 2/15*z**5 + 2/15*z**t = 0?
-1, 1
Let t(s) be the third derivative of 0 + 1/105*s**5 - 38*s**2 + 1/1176*s**8 - 1/21*s**3 + 1/84*s**4 - 1/735*s**7 - 1/210*s**6 + 0*s. Factor t(n).
2*(n - 1)**3*(n + 1)**2/7
Factor 1536/11*p - 2/11*p**4 - 4608/11 + 64/11*p**2 - 32/11*p**3.
-2*(p - 4)**2*(p + 12)**2/11
Suppose t + 3 = 5*v, v = -4*v - 3*t - 9. Suppose v = 4*n - n + 5*o - 1, 5*n - 2*o = 12. Determine a so that 2/5*a + 3/5*a**n + 1/5*a**3 + 0 = 0.
-2, -1, 0
Let h(q) be the first derivative of 2*q**5/25 - 2*q**4/5 + 2*q**3/3 - 2*q**2/5 + 62. Let h(p) = 0. What is p?
0, 1, 2
Let t(s) be the first derivative of -s**3/3 + 2*s**2 - 26. Suppose t(w) = 0. What is w?
0, 4
Suppose 100*w - 13*w = 348. Factor d**3 + 0 + 0*d + 1/6*d**w - 7/6*d**2.
d**2*(d - 1)*(d + 7)/6
Let 22*r - 14/5*r**3 + 484/5 - 486/5*r**2 + 98/5*r**4 = 0. What is r?
-2, -1, 11/7
Let h = 7476 - 37379/5. Factor -3/5*a**3 + 1/5*a**5 - 2/5*a + 0 - h*a**4 + a**2.
a*(a - 1)**3*(a + 2)/5
Let g = 2325584/16225 - 2/48675. Let b = -142 + g. Find z, given that b*z + 2/3 + 2/3*z**2 = 0.
-1
Let u(c) = -79*c - 866. Let y be u(-11). Find x such that -10/11*x**2 - 6/11 - 2/11*x**y - 14/11*x = 0.
-3, -1
Let q(s) = -s**3 - s**2 + s + 2. Let v be 3*(1 - 20/12). Let k be q(v). Solve -2*d**3 + k*d**3 + 6*d**2 + 25*d - 21*d = 0 for d.
-2, -1, 0
Let c(y) be the third derivative of -y**6/90 - 41*y**5/360 - 53*y**4/144 - y**3/6 + 834*y**2. Factor c(b).
-(b + 2)*(b + 3)*(8*b + 1)/6
Suppose 3*o - 4 = 4*t, 0 = -5*o - 3*t + 8*t + 10. Let l be (-3 - -8)*(9 - 669/75). Factor 0*j + 0*j**2 + 0 + l*j**3 - 2/5*j**5 + 0*j**o.
-2*j**3*(j - 1)*(j + 1)/5
Factor 0 - 65/3*x + 5/3*x**2.
5*x*(x - 13)/3
Let f(n) be the third derivative of 1/560*n**8 + 6*n**2 + 3/350*n**7 + 0*n + 0 + 0*n**3 - 1/20*n**4 - 3/100*n**5 + 1/200*n**6. Determine i so that f(i) = 0.
-2, -1, 0, 1
Let d be (-128)/448*2/(2/(-7)). Let t(m) be the first derivative of -4 + 4/33*m**3 + 1/11*m**d - 4/55*m**5 + 0*m**4 - 1/33*m**6 + 0*m. What is y in t(y) = 0?
-1, 0, 1
Factor 0 + 18/7*p**2 + 2/7*p**3 + 0*p.
2*p**2*(p + 9)/7
Let y = -3314 + 2386081/720. Let f(o) be the third derivative of 0*o + 0*o**3 + 0 + 0*o**4 - 6*o**2 - y*o**6 - 1/360*o**5. Factor f(t).
-t**2*(t + 1)/6
Let w(x) be the first derivative of x**4/15 - 7*x - 3. Let q(s) be the first derivative of w(s). Solve q(d) = 0 for d.
0
Let g(t) be the first derivative of 24*t**5 + 0*t**2 + 10/3*t**3 + 0*t - 15 + 75/4*t**4 - 40/3*t**6. Factor g(b).
-5*b**2*(b - 2)*(4*b + 1)**2
Let k(i) be the second derivative of 0*i**2 + 5/6*i**4 + 9*i - 1/4*i**5 + 0 + 0*i**3. What is r in k(r) = 0?
0, 2
Let j be (-9)/(-18) + 27/(-90) - 0. Let w = -353/5 + 71. Factor -j*i + 1/5*i**2 - w.
(i - 2)*(i + 1)/5
Let i(p) = p**3 - p. Let o(f) = 3*f**3 + f**2 + 6*f - 4. Let s(m) = -6*i(m) + o(m). Determine h so that s(h) = 0.
-2, 1/3, 2
Let y be -1 - ((-7)/27)/((-13)/11193). Let i = -224 - y. Factor 2/9*a**2 + 2/9*a - i*a**3 - 2/9.
-2*(a - 1)**2*(a + 1)/9
Let p be (6/(-180))/(6/(-5)). Let v(y) be the third derivative of 0 + 0*y**3 + 0*y**5 - y**2 + p*y**4 + 0*y - 1/180*y**6. Factor v(a).
-2*a*(a - 1)*(a + 1)/3
Let a = 13 + -9. Let d(h) = h**3 + 3*h**2 - 4*h + 3. Let j be d(-4). Factor -4*i**a + i**5 - 2*i**3 + i**j + i**2 + 3*i**4.
i**2*(i - 1)**2*(i + 1)
Factor 77*z - 24*z + 3*z**2 + 0*z**2 + 2*z - 8*z**2.
-5*z*(z - 11)
Let f(x) be the second derivative of -x**6/240 + x**5/60 + x**4/12 + 7*x**3/3 + 19*x. Let d(y) be the second derivative of f(y). Suppose d(z) = 0. Calculate z.
-2/3, 2
Suppose 158*p - 40 = 150*p. Determine c, given that 4/5 + 74/5*c**2 + 6*c + 82/5*c**3 + 8/5*c**p + 42/5*c**4 = 0.
-2, -1, -1/4
Let a(b) = 10*b**2 - 15*b - 10. Let u(d) = d**2 - 2*d. Let n(h) = a(h) - 15*u(h). Determine q so that n(q) = 0.
1, 2
Factor -6*i**2 - 4*i**2 + 14*i**2 - 27*i - 7*i**2 + 17 + 13.
-3*(i - 1)*(i + 10)
Let u be 2 - (-597)/(-369) - 238/4879. Factor -u*a**2 + 1/3*a**4 + 0 + 2/3*a - 2/3*a**3.
a*(a - 2)*(a - 1)*(a + 1)/3
Let v(i) be the second derivative of 0*i**2 + 12*i - 1/4*i**4 - 9/80*i**5 - 1/8*i**3 + 0. Suppose v(w) = 0. Calculate w.
-1, -