h**3. Factor a(f).
2*f**2
Factor 2*d - 6*d**2 + 0 + 9/2*d**3.
d*(3*d - 2)**2/2
Let a(q) = 3*q**5 + 9*q**4 - 7*q**3 - 5*q**2 - 5. Let i(s) = 2*s**5 + 5*s**4 - 4*s**3 - 3*s**2 - 3. Let g(k) = 6*a(k) - 10*i(k). Factor g(y).
-2*y**3*(y - 1)**2
Let h(p) be the third derivative of -2/21*p**3 - 1/60*p**6 + 0 - 8/105*p**5 - 11/84*p**4 + 0*p + p**2. Factor h(n).
-2*(n + 1)**2*(7*n + 2)/7
Let w be 4 + 9/(45/(-20)). Let j(t) be the third derivative of 0*t + 1/75*t**5 + w + 0*t**4 - 1/100*t**6 + 0*t**3 - 1/105*t**7 + 2*t**2. Solve j(v) = 0 for v.
-1, 0, 2/5
Let z(l) be the third derivative of l**5/180 + l**4/36 - 2*l**2. Factor z(r).
r*(r + 2)/3
Let u(f) be the third derivative of -f**6/360 + 7*f**5/180 + 5*f**4/36 - 8*f**3/9 - 37*f**2. Determine y so that u(y) = 0.
-2, 1, 8
Let f(i) = i - 5. Let s be f(5). Let c be (-12)/(-45)*27/18. Factor -c*y**2 + s + 4/5*y.
-2*y*(y - 2)/5
Let q(h) be the second derivative of h**7/273 + 2*h**6/195 - h**5/26 - 5*h**4/39 + 4*h**3/39 + 8*h**2/13 + h. Find s such that q(s) = 0.
-2, -1, 1, 2
Solve -7*n + 2*n + 3*n**2 - 7*n + n**2 = 0.
0, 3
Factor -1/4*l + 1/2*l**2 + 1/4*l**3 - 1/2.
(l - 1)*(l + 1)*(l + 2)/4
Let l = 164 + -161. Factor -1/3*s**l + 1/3*s**2 + 0 + 0*s.
-s**2*(s - 1)/3
Let f(c) be the second derivative of c**4/12 + 4*c**3/3 + 8*c**2 - 11*c. Determine h so that f(h) = 0.
-4
Let d(y) be the second derivative of -y**6/150 + y**5/25 - y**4/20 - 2*y**3/15 + 2*y**2/5 - 3*y. Factor d(k).
-(k - 2)**2*(k - 1)*(k + 1)/5
Let x(o) = -o**3 - 11*o**2 - 8*o + 9. Let i be x(-10). Let l be -1 + (i/(-5))/1. Determine z so that 3/5*z**4 + 0 - 3*z**2 + 9/5*z**3 - 3/5*z**5 + l*z = 0.
-2, 0, 1
Find x, given that -29*x**3 + 14*x**3 + 16*x**3 - 5*x**2 + x**2 = 0.
0, 4
Let o(p) = 124*p**3 - 264*p**2 + 108*p - 32. Let j(h) = -h**3 + h**2 - h + 1. Let r(t) = -24*j(t) - o(t). Factor r(s).
-4*(s - 2)*(5*s - 1)**2
Let d(l) be the first derivative of -16*l**5/5 - 9*l**4 - 8*l**3/3 - 3. Find c such that d(c) = 0.
-2, -1/4, 0
Let p(v) = -5*v**3 + 24*v**2 + 27*v + 25. Suppose -g + 3 = 0, 0*t - 15 = t - 2*g. Let c(s) = s**3 - 6*s**2 - 7*s - 6. Let l(j) = t*c(j) - 2*p(j). Factor l(a).
(a + 1)**2*(a + 4)
Let 0*q + 0 + 1/4*q**3 + 1/2*q**2 = 0. What is q?
-2, 0
Let b(j) be the third derivative of 1/6*j**4 - 7*j**2 + 0*j - 1/30*j**6 + 0 - 4/3*j**3 - 2/105*j**7 + 1/5*j**5. Determine w so that b(w) = 0.
-2, -1, 1
Let u = 36 - 11. Suppose 0 = -9*j + 4*j + u. Let -4*t**4 - t**2 - 2*t**5 - t**3 + 0*t + 9*t**2 - 4 + j*t**3 - 2*t = 0. Calculate t.
-2, -1, 1
Let u = -4 + 3. Let r be (1 - 12/3)*u. Factor r*x - x**2 - x**2 - x.
-2*x*(x - 1)
Let l be (4/(-5))/(6/(-15)). Let p be (-1)/(-2)*l - -3. Factor o**4 - 4*o + 6*o**2 + 2*o**4 - 2*o**4 - 3*o**p.
-2*o*(o - 1)**2*(o + 2)
Let p(v) be the third derivative of v**8/504 - v**7/90 + v**6/45 - v**5/90 - v**4/36 + v**3/18 - 5*v**2. Determine u so that p(u) = 0.
-1/2, 1
Let f = 82/9 + -137/18. Factor -3*h**3 + 3/2*h**2 + 0*h + 0 + f*h**4.
3*h**2*(h - 1)**2/2
Suppose 2*a**4 - 3*a**4 - 1 + 13*a**3 + 2*a**2 - 13*a**3 = 0. Calculate a.
-1, 1
Let o(j) be the second derivative of j**7/630 - j**6/30 + 3*j**5/10 + j**4/3 - 5*j. Let q(d) be the third derivative of o(d). Find v, given that q(v) = 0.
3
Find a, given that -15*a**4 - 24*a**3 - 3 + 11 - 5*a**4 + 2*a**4 + 10*a**2 + 24*a = 0.
-1, -2/3, 1
Let v(u) = u**3 - 8*u**2 + 13*u - 2. Let w be v(6). Let m be 2/(-42)*(w - 10). Factor 2/7*c + 6/7*c**3 + 0 - m*c**4 - 6/7*c**2.
-2*c*(c - 1)**3/7
Let b(v) be the first derivative of 4*v**6/75 + 9*v**5/50 + v**4/5 + v**3/15 - v - 2. Let p(i) be the first derivative of b(i). Factor p(u).
2*u*(u + 1)**2*(4*u + 1)/5
Let z = 4889/9 + -543. Find l such that z + 2/3*l**2 - 2/9*l**3 - 2/3*l = 0.
1
Let y(p) be the first derivative of 4*p**5/5 - 4*p**3 - 4*p**2 + 4. Determine l, given that y(l) = 0.
-1, 0, 2
Let j(b) be the second derivative of -b**6/21 + 13*b**5/70 - 3*b**4/14 - b**3/21 + 2*b**2/7 + 3*b. Solve j(v) = 0 for v.
-2/5, 1
Let d(c) = 2*c**2 - 9*c. Let z(y) = -y**2 + 5*y. Let a(w) = 3*d(w) + 5*z(w). Suppose a(s) = 0. Calculate s.
0, 2
Let f = 26 - 23. Let g(x) be the third derivative of 0 + 4*x**2 + 0*x**4 + 0*x - 1/840*x**7 + 0*x**f - 1/240*x**6 - 1/240*x**5. Factor g(c).
-c**2*(c + 1)**2/4
Let k(s) = -s**4 + 4*s**3 - 3*s**2 + s - 1. Let t(p) = -p + 1. Let v(h) = k(h) + 5*t(h). Solve v(o) = 0 for o.
-1, 1, 2
Let b = 56 + -55. Suppose -b - 1/2*f**2 - 3/2*f = 0. What is f?
-2, -1
Suppose 0 = i + 4*i. Let k(f) be the first derivative of 1/4*f**2 - 1/8*f**4 + 0*f + i*f**3 + 2. Factor k(u).
-u*(u - 1)*(u + 1)/2
Solve 1/2*v**2 - 1/2*v**4 - 1/2*v + 1/2*v**3 + 0 = 0.
-1, 0, 1
Let 8*d - d**4 - 5*d - 2*d - d**3 + d**2 = 0. What is d?
-1, 0, 1
Let r(k) = k**5 + k**4 + k**3 - k + 1. Let d(v) = -v**5 - 17*v**4 + 7*v**3 - 4*v**2 + 5*v - 5. Let w(i) = -d(i) - 5*r(i). Let w(m) = 0. Calculate m.
0, 1
Factor 0*t**3 - 68 + 5*t**3 - 15*t**2 + 15*t + 63.
5*(t - 1)**3
Let g be (-2)/(-8) + 6/8. Factor 24*a + g - 25*a - 3 - 20*a**3 + 23*a**2.
-(a - 1)*(4*a + 1)*(5*a - 2)
Solve -1/5*n**2 - 4/5 + 4/5*n = 0.
2
Let i(u) be the first derivative of 1/54*u**4 + 3*u + 3 + 1/27*u**3 + 0*u**2. Let v(g) be the first derivative of i(g). Solve v(l) = 0.
-1, 0
Let v(w) be the third derivative of -w**8/168 + w**7/105 + w**6/30 - 7*w**2. Factor v(a).
-2*a**3*(a - 2)*(a + 1)
Let j(w) be the first derivative of w**3/3 + 3*w**2/2 + 1. Let q be j(-4). Factor 3*a**3 + 2 + 0*a - 2*a**4 + q*a + 0*a**4 - 7*a**3.
-2*(a - 1)*(a + 1)**3
Let c(h) be the first derivative of 1/2*h**4 + 0*h**3 - 1/3*h**6 + 0*h**2 + 4 + 0*h**5 + 0*h. Factor c(b).
-2*b**3*(b - 1)*(b + 1)
Let d(c) = 23*c**4 - 11*c**3 - 72*c**2 - 24*c - 7. Let y(n) = 2*n + 9 + 48*n**2 - 15*n**4 + 14*n + 8 + 7*n**3 - 12. Let m(z) = -5*d(z) - 7*y(z). Solve m(v) = 0.
-1, -2/5, 0, 2
Let u = 0 - -2. Let d be (4/5)/2 + -5 + 5. Factor -2/5*j**u + d + 0*j.
-2*(j - 1)*(j + 1)/5
Let a = -153 - -419. Let t be 4/(-18) + a/63. Determine z, given that 3*z**5 - 3*z**2 + 3*z**t - 9*z**4 + 6*z**2 - 3*z + 3*z**2 = 0.
-1, 0, 1
Suppose 3*l + l - 8 = 0. Solve -5*u**3 - u**4 + 3*u**4 - 2*u**l + 5*u**3 = 0.
-1, 0, 1
Let c(s) be the second derivative of s**6/360 - s**5/120 - s**4/12 - s**3/6 - 3*s. Let b(p) be the second derivative of c(p). Factor b(i).
(i - 2)*(i + 1)
Factor -3/4 - 3/8*s**3 + 3/4*s**2 + 3/8*s.
-3*(s - 2)*(s - 1)*(s + 1)/8
Suppose 0 = -3*l + 7*l + 16. Let v be l/10 + 12/5. What is u in -v*u + 0*u**2 - 3*u**3 + 0*u**2 + 5*u**3 = 0?
-1, 0, 1
Suppose w + 10 = 3*w, 31 = 3*o + 5*w. Suppose 3*z - 24 = -3*t, 3*z - o - 2 = 2*t. Factor -3/2*s**3 + 0 + 0*s - 1/2*s**5 + 1/2*s**2 + 3/2*s**z.
-s**2*(s - 1)**3/2
Let a(z) be the second derivative of z**6/180 - z**4/12 - 2*z**3/9 + 3*z**2 - 4*z. Let p(c) be the first derivative of a(c). Factor p(r).
2*(r - 2)*(r + 1)**2/3
Suppose -5*x + 0 + 5/3*x**2 = 0. Calculate x.
0, 3
Suppose -5*c = -0*a + 4*a + 21, c = -4*a - 1. Let u be 2 - (40/a)/(-2). Suppose 8/5*f - u*f**2 + 8/5 - 40*f**3 = 0. What is f?
-2/5, 1/4
Let g(q) be the first derivative of -q**2 + 3 + 6/5*q**5 + 0*q - 4/3*q**6 - 2*q**3 + 5/2*q**4. Suppose g(d) = 0. What is d?
-1, -1/4, 0, 1
Let o(v) be the second derivative of -v**6/6 - v**5 - 5*v**4/2 - 10*v**3/3 - 5*v**2/2 + 5*v. Let o(z) = 0. What is z?
-1
Let y(c) be the third derivative of c**8/840 + c**7/525 - c**6/300 - c**5/150 + 13*c**2. Determine r so that y(r) = 0.
-1, 0, 1
Let h(u) be the second derivative of -u**6/225 - u**5/50 - u**4/30 - u**3/45 - 4*u. Determine w, given that h(w) = 0.
-1, 0
Let q(p) be the third derivative of 0 + 1/120*p**6 + 0*p**3 + 3*p**2 - 1/210*p**7 + 1/30*p**5 + 0*p + 0*p**4. Factor q(b).
-b**2*(b - 2)*(b + 1)
Let f = 152 + -303/2. Factor -f*w**2 + 0*w + 0 + 1/2*w**3.
w**2*(w - 1)/2
Let k be (-4)/8 + (-33)/(-6). Factor -4/5*b**3 + 16/5*b**2 - 4/5*b**4 + 4/5 - 14/5*b + 2/5*b**k.
2*(b - 1)**4*(b + 2)/5
Let v = 5 + -3. Suppose 4*r - 10 - v = -k, -2*k = 3*r - 14. Factor -2*d**2 + k*d**5 - 5*d**3 + 4*d**2 + d + d**2 - 6*d**2 + 3*d**4.
d*(d - 1)*(d + 1)**2*(4*d - 1)
Let z = 123/238 + -2/119. Factor 0*n**2 + 0 + z*n - 1/2*n**3.
-n*(n - 1)*(n + 1)/2
Let k(b) = -4. Let c(i) = i**2 + 9. Let v(l) = 4*c(l) + 10*k(l). Factor v(a).
4*(a - 1)*(a + 1)
Let p(y) = y**3 - 4*y**2 + 6*y - 4. Let l be p(4). Let o be 2/(-4)*l/(-35). Factor o*b**2 + 0 - 4/7*b.
2*b*(b - 2)/