erivative of d(g). Factor f(m).
-2*m*(m + 1)*(m + 2)/5
Let i(x) be the second derivative of x**6/30 + x**5/20 + x**2/2 + 3*x. Let m(b) = -12*b**4 - 6*b**3 + 5*b**2 - b - 3. Let a(u) = 3*i(u) + m(u). Factor a(f).
-f*(f + 1)*(3*f - 1)**2
Factor 0 + 4*o - 2/3*o**4 + 2/3*o**2 - 4*o**3.
-2*o*(o - 1)*(o + 1)*(o + 6)/3
Let i(h) be the first derivative of -2*h**3/15 - 2*h**2/15 - 13. Determine m so that i(m) = 0.
-2/3, 0
Let f be (13 + -1)*(-8)/(-16). Let v(l) be the second derivative of -1/36*l**4 + 1/90*l**f + 0*l**2 + 0*l**3 + 1/126*l**7 - 2*l + 0 - 1/60*l**5. Factor v(x).
x**2*(x - 1)*(x + 1)**2/3
Let w(i) = -2*i - 3. Let k(h) = h**2 + h + 1. Let j(d) = -2*k(d) - 2*w(d). Factor j(g).
-2*(g - 2)*(g + 1)
Let u(p) be the third derivative of -p**8/13440 + p**7/5040 + p**4/8 + p**2. Let t(z) be the second derivative of u(z). Determine o so that t(o) = 0.
0, 1
Let i(t) be the second derivative of t**4/24 - t**2 + 8*t. Factor i(m).
(m - 2)*(m + 2)/2
Suppose 16/7*o**3 - 8/7 - 16/7*o + 6/7*o**4 + 2/7*o**2 = 0. Calculate o.
-2, -1, -2/3, 1
Let r(z) = -z**2 + 5*z + 14. Let l be r(7). Factor -6/5*p**3 + 6/5*p + l*p**2 + 3/5*p**4 - 3/5.
3*(p - 1)**3*(p + 1)/5
Let x(j) be the second derivative of j**5/45 - 2*j**4/27 + 2*j**3/27 - 23*j. Factor x(g).
4*g*(g - 1)**2/9
Let x(r) be the third derivative of r**5/330 - r**4/6 + 11*r**3/3 - 40*r**2. Determine m, given that x(m) = 0.
11
Let l(p) be the third derivative of p**6/360 + p**5/120 - p**4/12 - p**3/2 + 5*p**2. Let n(k) be the first derivative of l(k). Factor n(c).
(c - 1)*(c + 2)
Let u(k) be the first derivative of -k**4/2 + 2*k**3/3 + 5. Factor u(d).
-2*d**2*(d - 1)
Let d(t) = -26*t**3 + 9*t**2 + 26*t - 26. Let y(k) = -9*k**3 + 3*k**2 + 9*k - 9. Let u(j) = -6*d(j) + 17*y(j). Solve u(f) = 0 for f.
-1, 1
Suppose 2*m - 7 = 1. Let f = -79 - -241/3. Find v, given that 14/3*v**2 - f*v + 0 + 4/3*v**3 - 14/3*v**m = 0.
-1, 0, 2/7, 1
Let p(v) be the second derivative of -1/3*v**3 + v**2 + 1/10*v**5 - 9*v + 0 - 1/6*v**4. Find z such that p(z) = 0.
-1, 1
Let v = -10 + 15. Let o(h) be the first derivative of 3/8*h**4 - h - 3/4*h**2 - 1/2*h**v + 7/6*h**3 - 1. Find l, given that o(l) = 0.
-1, -2/5, 1
Let m(h) be the third derivative of h**10/3780 - h**9/1512 + h**8/3360 + h**4/24 - 3*h**2. Let k(t) be the second derivative of m(t). Factor k(b).
2*b**3*(b - 1)*(4*b - 1)
Let c be (8/14)/((-40)/(-28)). Let l = 654/805 - 2/161. Solve c*j + 2*j**3 - l + 16/5*j**2 = 0 for j.
-1, 2/5
Let z(y) = 13*y**2 - 60*y + 50. Let a(t) = -12*t**2 + 60*t - 50. Let r(b) = -5*a(b) - 6*z(b). Factor r(i).
-2*(3*i - 5)**2
Let t be (-6)/14*(-52)/39. Factor 2/7*c**2 + 0 - 4/7*c + t*c**3 - 2/7*c**4.
-2*c*(c - 2)*(c - 1)*(c + 1)/7
Let l be ((-8)/(-12))/(2/6). Let 6*c + 6 + l*c**2 + 2/9*c**3 = 0. What is c?
-3
Let j(i) be the second derivative of 2*i - 3/2*i**2 + 1/42*i**4 + 0*i**3 + 0 - 3/70*i**5. Let q(s) be the first derivative of j(s). Factor q(a).
-2*a*(9*a - 2)/7
Let h be (4/6)/((48/27)/8). Factor -1/4*t**4 + 0*t**h + 0*t + 0*t**2 + 0.
-t**4/4
Suppose -3*l - 6 = 2*d, -4*l - 12 - 19 = -5*d. Suppose 5*v = d*a + 12 + 13, a - 3*v = -15. Solve 0 + 1/5*f**2 + 1/5*f**5 + a*f - 1/5*f**3 - 1/5*f**4 = 0 for f.
-1, 0, 1
What is t in 53*t**3 - 12*t**2 - 10*t**5 - 37*t**4 + 31*t**5 + 7*t**3 - 32*t**4 = 0?
0, 2/7, 1, 2
Let s(m) = 10*m**3 - 20*m**2 + 14*m - 6. Let x(w) = w**4 + 20*w**3 - 41*w**2 + 28*w - 13. Let l be ((-12)/8)/(3/(-4)). Let u(o) = l*x(o) - 5*s(o). Factor u(d).
2*(d - 2)*(d - 1)**3
Let y(a) be the second derivative of a**4/18 + a**3/3 - 10*a**2/3 - 31*a. Solve y(s) = 0 for s.
-5, 2
Let m(w) = 5*w + 0*w + 4*w**2 + 2*w + 1 + 6*w. Let q(f) = -f**2 - 3*f. Let u(t) = 4*m(t) + 18*q(t). Suppose u(p) = 0. What is p?
-2, 1
Find x such that 11*x - 9*x**2 + 4 - 20 + 5*x**2 + 9*x = 0.
1, 4
Let n(p) be the first derivative of -p**4/4 + p**3 - 3*p**2/2 + 4*p - 4. Let m(v) be the first derivative of n(v). Factor m(h).
-3*(h - 1)**2
Suppose -4*u - 20 = 0, -u - 5 = f + 2*u. Let z = f + -7. Factor 2*m**2 + z*m**3 - 5*m**3 + m**4 - m**2 + 0*m**4.
m**2*(m - 1)**2
Let x be (-4)/18*(-77 - -75). Suppose -46/9*g**4 - 26/9*g**2 + 0 - 6*g**3 - 14/9*g**5 - x*g = 0. Calculate g.
-1, -2/7, 0
Factor 2/3*q + 2/3 + 1/6*q**2.
(q + 2)**2/6
Factor 1/3*u**2 + 3 + 2*u.
(u + 3)**2/3
Let k(w) be the second derivative of w**8/840 + w**3/6 + 3*w. Let p(t) be the second derivative of k(t). Factor p(u).
2*u**4
Let u = 11 - 8. Let o**5 + 12*o**3 + 2*o**5 - 3*o**2 - 15*o**3 + u*o**4 = 0. Calculate o.
-1, 0, 1
Let j(v) be the third derivative of 2*v**7/525 - v**6/150 - v**5/25 + v**4/30 + 4*v**3/15 + 7*v**2. Factor j(a).
4*(a - 2)*(a - 1)*(a + 1)**2/5
Suppose 5*s + 5 = 0, -3*s - 10 = -o - 3. Let t(l) = -l**2 + 5*l + 3. Let f be t(5). Factor 1/4*y + 1/4*y**2 - 1/4*y**o - 1/4*y**f + 0.
-y*(y - 1)*(y + 1)**2/4
Let l(v) = -7*v**3 + 29*v**2 - 68*v - 112. Let m(z) = -6*z**3 + 30*z**2 - 69*z - 111. Let q(c) = 3*l(c) - 4*m(c). Suppose q(p) = 0. Calculate p.
-1, 6
Let s(d) be the third derivative of -d**8/3528 + d**7/735 - 32*d**2. Factor s(f).
-2*f**4*(f - 3)/21
Let z(j) be the third derivative of -j**5/80 - 3*j**4/32 - 39*j**2. Factor z(m).
-3*m*(m + 3)/4
Factor 3/2*s**4 - 6*s**3 + 15/2*s**2 - 3*s + 0.
3*s*(s - 2)*(s - 1)**2/2
Let y(c) be the third derivative of c**7/1680 - c**5/240 - c**3/6 - 4*c**2. Let o(a) be the first derivative of y(a). Factor o(f).
f*(f - 1)*(f + 1)/2
Let i = 365/63 + -39/7. Solve -10/9*w**2 + i*w**3 - 8/9 + 16/9*w = 0 for w.
1, 2
Let d be (-8)/(-6) - 1/3. Let o(y) = 3*y**3 - 2*y**2 + 2*y - 1. Let k be o(d). Factor -2*b**k + 3 - 4 + 3.
-2*(b - 1)*(b + 1)
Let z(g) be the second derivative of -g**5/90 + g**4/6 - g**3 - g**2/2 + 4*g. Let s(c) be the first derivative of z(c). Suppose s(t) = 0. Calculate t.
3
Determine g, given that -12/7*g + 0 - 12/7*g**3 + 22/7*g**2 + 2/7*g**4 = 0.
0, 1, 2, 3
Let z(x) be the first derivative of 8*x**3/3 + 5*x**2 + 2*x + 8. Suppose z(q) = 0. Calculate q.
-1, -1/4
Let i(l) be the third derivative of 0*l + 0*l**3 - 1/210*l**7 + 0*l**4 - 3*l**2 - 1/60*l**5 + 0 - 1/60*l**6. Factor i(w).
-w**2*(w + 1)**2
Suppose -w + 3*w = 0. Let z(m) = m**3 + 4*m**2. Let d be z(-4). Factor -k**2 + d*k**2 + w + 1.
-(k - 1)*(k + 1)
Let t(j) = -j**5 + 5*j**4 + 9*j**3 - j**2 - 6*j + 2. Let w(x) = -3*x**5 + 21*x**4 + 36*x**3 - 3*x**2 - 24*x + 9. Let y(d) = -9*t(d) + 2*w(d). Factor y(z).
3*z*(z - 2)*(z - 1)*(z + 1)**2
Let m(t) be the second derivative of 1/135*t**6 + 1/90*t**5 + 0*t**3 - 1/27*t**4 - 5*t + 0 + 0*t**2. Suppose m(l) = 0. Calculate l.
-2, 0, 1
Factor -w**2 + 5/2*w**3 - 2*w**4 + 0*w + 0 + 1/2*w**5.
w**2*(w - 2)*(w - 1)**2/2
Let g(c) be the second derivative of 5/42*c**4 + 0 + 1/7*c**3 - 2/7*c**2 + 9*c. What is z in g(z) = 0?
-1, 2/5
Solve 1446*y**3 + 79*y**3 - 85*y**3 + 405*y**4 + 80 - 640*y + 920*y**2 = 0 for y.
-2, 2/9
Factor 4*u + 5*u - 4*u + 0*u**3 + 5*u**3 - 10*u**2.
5*u*(u - 1)**2
Let i be 11/(-12) + -6 + 7. Let r(f) be the third derivative of -i*f**4 + 0 - 1/60*f**5 + 0*f**3 + 2*f**2 + 0*f. Determine b so that r(b) = 0.
-2, 0
Let q be ((-7)/(-35))/(3 + -2). Solve 1/5*a**2 - 1/5 - 1/5*a + q*a**3 = 0.
-1, 1
Let h(t) be the second derivative of 0 + 1/8*t**2 - 4*t + 1/48*t**4 - 1/12*t**3. Find m such that h(m) = 0.
1
Let g(y) be the second derivative of -y**6/135 + y**5/90 + 5*y**4/54 + y**3/9 - 31*y. Let g(m) = 0. Calculate m.
-1, 0, 3
Let f = -5 - -8. Let o**4 + o**4 + 4*o + 10*o**2 + 10*o**3 - 2*o**f = 0. What is o?
-2, -1, 0
Suppose -2*h = -0*h - 0*h. Solve 0*y - 4/7*y**2 + 2/7*y**4 + h*y**3 + 2/7 = 0 for y.
-1, 1
Let v(d) be the third derivative of d**8/3528 - 2*d**7/2205 + d**6/1260 - 7*d**2. Solve v(q) = 0.
0, 1
Let b(m) = -m**2 - 3*m + 1. Let u be b(-2). Determine j so that 32*j**u + 0*j + 8 - 14*j**3 - 6*j**2 - 16*j = 0.
-1, 2/3
Let b(d) be the third derivative of d**6/120 - d**5/30 + d**4/24 + d**3/6 - 4*d**2. Let h be b(2). Determine j so that 0*j + 2/5*j**h + 0 - 2/5*j**2 = 0.
0, 1
Suppose 2*j = 4*n + 42, n = -3*j + 3*n + 43. Find a, given that -32*a**2 - 5 - 12*a**3 - 11*a - j*a + 1 - 2*a**3 = 0.
-1, -2/7
Let a(t) be the third derivative of t**7/735 - t**6/420 - t**5/70 + t**4/84 + 2*t**3/21 + 12*t**2. Solve a(i) = 0.
-1, 1, 2
Let o = -29 - -29. Suppose o + 0*p**2 + 0*p + 1/2*p**4 + 1/2*p**3 = 0. What is p?
-1, 0
Solve j**2 - 1/4*j**3 + 3/2