- 2*x**3/15 + x**2/5 - 3*x - 1. Let j(b) be the first derivative of y(b). Let j(f) = 0. What is f?
1
Let z = -4 + 10. Suppose 3*p - s - 11 + 3 = 0, 5*p - 32 = -3*s. Factor f**5 - 3*f**3 + f**2 + 5*f**4 + z*f**3 - 2*f**p.
f**2*(f + 1)**3
Let c be ((-2)/7)/(81/(-42)). Let p(f) be the second derivative of 1/54*f**4 + 0 - 2*f + 4/9*f**2 + c*f**3. Factor p(k).
2*(k + 2)**2/9
Let i be (-9 + 5)*(-20)/(-14). Let d = i + 6. Factor -4/7*v + 0*v**2 - 2/7*v**4 + 4/7*v**3 + d.
-2*(v - 1)**3*(v + 1)/7
Let h be (-20)/(-9) + 20/(-90). Let a(v) be the first derivative of h + 0*v - 2/15*v**3 + 1/5*v**2. Determine w so that a(w) = 0.
0, 1
Factor 4*k**2 + 4 - 6*k**2 + 5*k**2 + 6*k - 13.
3*(k - 1)*(k + 3)
Let t(n) be the first derivative of -n**5/35 + n**4/28 - 2. Factor t(q).
-q**3*(q - 1)/7
Suppose -4*m - 4 = 0, 4*h + 3*m = 2*h + 1. What is g in g**4 + 3*g**4 + 0*g**4 + 4*g**3 - g**4 + g**h = 0?
-1, -1/3, 0
Let p(w) be the first derivative of w**4/20 - 2*w**3/15 - w**2/10 + 2*w/5 + 5. Factor p(v).
(v - 2)*(v - 1)*(v + 1)/5
Let c(b) be the first derivative of b**7/1050 - b**5/200 + b**4/120 + b**3/3 + 4. Let q(z) be the third derivative of c(z). Solve q(j) = 0 for j.
-1, 1/2
Let z(f) = 3*f**3 - 49*f**2 + 24*f - 4. Let k(q) = 2*q**3 - 24*q**2 + 12*q - 2. Let i(a) = 13*k(a) - 6*z(a). Factor i(u).
2*(u - 1)**2*(4*u - 1)
Factor -12/5*x**3 - 6/5*x - 21/5*x**2 + 3/5.
-3*(x + 1)**2*(4*x - 1)/5
Solve 0*a + 2/9*a**2 + 2/9*a**4 + 0 - 4/9*a**3 = 0 for a.
0, 1
Suppose 3*s - 21 = -8*o + 4*o, -o = s - 6. Factor 1/2*q - 1/4*q**s + 0 - 1/4*q**2.
-q*(q - 1)*(q + 2)/4
Let q(b) be the third derivative of b**10/37800 + b**9/5040 + b**8/1680 + b**7/1260 - b**5/15 + 6*b**2. Let s(d) be the third derivative of q(d). Factor s(k).
4*k*(k + 1)**3
Let h(w) = 16*w**3 - 24*w**2 + 12*w - 2. Let j(y) = -y**3 + y**2 - y. Let i = -101 - -65. Let q(n) = i*j(n) - 2*h(n). Solve q(l) = 0.
-1
Let w(n) be the first derivative of 4*n**3/3 - 10*n**2 + 16*n + 8. Determine a so that w(a) = 0.
1, 4
Let p be ((-1)/(-2))/(10/4). Let h(f) be the second derivative of -2*f + p*f**2 - 1/30*f**4 + 0 + 0*f**3. Let h(g) = 0. Calculate g.
-1, 1
Let r(q) be the third derivative of q**10/105840 + q**9/13230 + q**8/4704 + q**7/4410 + q**4/8 - q**2. Let g(t) be the second derivative of r(t). Factor g(w).
2*w**2*(w + 1)**2*(w + 2)/7
Let r(y) be the third derivative of 5*y**8/1344 + y**7/140 - y**6/120 - y**5/40 - y**4/96 + 4*y**2. Let r(x) = 0. What is x?
-1, -1/5, 0, 1
Let j = 49 + -47. Factor 1 - 3/2*t**3 + 1/2*t - j*t**2.
-(t + 1)**2*(3*t - 2)/2
Let b(c) be the third derivative of 0*c**4 - c**2 + 0*c**3 + 1/672*c**8 - 1/420*c**7 + 0*c**5 + 0*c + 0 + 0*c**6. Find l such that b(l) = 0.
0, 1
Let g(z) be the first derivative of -z**4/32 - 5*z**3/24 + 13*z**2/16 - 7*z/8 - 27. Factor g(p).
-(p - 1)**2*(p + 7)/8
Let s be 12/(-15) + (-66)/(-20) + -2. Let q - 1/2 - s*q**2 = 0. Calculate q.
1
Suppose 3*k = 40 - 4. Factor -3*m**4 - 2 + 8*m + m**4 + 8*m**3 + 4*m**4 - 4*m**4 - k*m**2.
-2*(m - 1)**4
Let r(g) = -17*g**4 + 44*g**3 - 46*g**2 + 36*g - 1. Let k(a) = 11*a**4 - 29*a**3 + 31*a**2 - 24*a + 1. Let j(d) = 8*k(d) + 5*r(d). Factor j(z).
3*(z - 1)**4
Let l be (-2)/(2*2/(-6)). Let t(m) be the second derivative of -1/120*m**6 + 0*m**4 + 0 - m + 0*m**2 + 0*m**l - 1/80*m**5. Factor t(k).
-k**3*(k + 1)/4
Let v be 16/9 - (-10)/45. Let i(x) be the first derivative of -1/4*x**v + 1/5*x**5 + 0*x - 3/4*x**4 - 1 + 3/4*x**3. Factor i(z).
z*(z - 2)*(2*z - 1)**2/4
Factor 6/7*n**2 + 0 + 4/7*n + 0*n**3 - 2/7*n**4.
-2*n*(n - 2)*(n + 1)**2/7
Let p(n) be the second derivative of n**7/14 - n**6/2 + 9*n**5/10 + n**4 - 4*n**3 - 19*n. Suppose p(s) = 0. What is s?
-1, 0, 2
Let f(h) = -23*h**3 + 118*h**2 - 109*h + 14. Let n(d) = -47*d**3 + 235*d**2 - 217*d + 29. Let l(u) = -7*f(u) + 4*n(u). Determine r, given that l(r) = 0.
2/9, 1, 3
Let j be 9 - (-2)/(-4)*-2. Solve -2*q**5 - 8*q**3 + 0*q**5 + j*q**3 = 0 for q.
-1, 0, 1
Let h(l) be the third derivative of l**10/75600 - l**8/5040 + l**6/360 + l**5/30 + 3*l**2. Let k(a) be the third derivative of h(a). Factor k(t).
2*(t - 1)**2*(t + 1)**2
Let z be (-12)/(-9) + (-2)/(-3). Factor 2*k + k + 3*k**3 + 2*k**2 - 5*k**z - 2*k**3 - 1.
(k - 1)**3
Factor -3*g**2 - 17*g**2 + 97*g - 92*g.
-5*g*(4*g - 1)
Let t(s) be the third derivative of s**7/42 + s**6/6 + s**5/2 + 5*s**4/6 + 5*s**3/6 - 5*s**2. Factor t(b).
5*(b + 1)**4
Let s(i) = -2*i**4 + 2*i**3 + 4*i**2 + 10. Suppose 6*w = 2*w - 4. Let a(t) = -1. Let z(c) = w*s(c) - 10*a(c). Factor z(d).
2*d**2*(d - 2)*(d + 1)
Let p be 3/(-15)*15/(-6). Solve f**3 + 0*f - 3/2*f**4 - f**5 + 2*f**2 - p = 0 for f.
-1, 1/2, 1
Factor 73*i + 0*i**3 - 462*i - 42*i**2 - 2744 - 199*i - i**3.
-(i + 14)**3
Let u = 8 + -6. Factor 0 - 2/7*b**3 - 6/7*b**u + 0*b.
-2*b**2*(b + 3)/7
Factor -46/11*t**4 + 0 + 4/11*t - 26/11*t**2 + 14/11*t**5 + 54/11*t**3.
2*t*(t - 1)**3*(7*t - 2)/11
Let c(l) be the first derivative of l**8/4200 + l**7/700 + l**6/300 + l**5/300 - l**3/3 + 4. Let h(u) be the third derivative of c(u). Factor h(x).
2*x*(x + 1)**3/5
Factor 9/8*l**2 + 39/8*l + 3/2.
3*(l + 4)*(3*l + 1)/8
Let p(y) be the second derivative of y**5/80 + y**4/8 + y**3/2 + y**2 - 11*y. Determine b, given that p(b) = 0.
-2
Let d(c) be the second derivative of -c**8/112 + c**7/70 - 3*c**2/2 - c. Let f(t) be the first derivative of d(t). What is g in f(g) = 0?
0, 1
Let u(y) be the third derivative of 0 + 0*y - 1/12*y**3 + 1/16*y**4 + 3*y**2 + 3/40*y**5 + 1/48*y**6. Let u(q) = 0. Calculate q.
-1, 1/5
Let r(x) = -x**2 + 17*x - 11. Let v be r(16). Let s(y) be the first derivative of 0*y**v - 1/3*y**6 + 0*y - y**2 + 0*y**3 + y**4 + 3. Factor s(k).
-2*k*(k - 1)**2*(k + 1)**2
Let r(n) be the third derivative of -n**8/168 + n**6/20 - n**5/15 - 6*n**2. Factor r(z).
-2*z**2*(z - 1)**2*(z + 2)
Let v(m) be the first derivative of -1/14*m**4 + 2/7*m**3 - 8/7*m - 1 + 0*m**2. Determine d so that v(d) = 0.
-1, 2
Factor -26*s - 15 - 5*s**2 + 0*s + 6*s.
-5*(s + 1)*(s + 3)
Determine n, given that -7*n**3 + 16*n**3 + n**2 - 10*n**3 = 0.
0, 1
Factor -1/4 + 0*r + 1/4*r**2.
(r - 1)*(r + 1)/4
Let w(k) be the third derivative of k**6/540 - k**5/135 + k**4/108 - 4*k**2. Factor w(r).
2*r*(r - 1)**2/9
Let k be (36/12 + 5/(-2))*6. Factor -8/7*q**2 - 2/7*q**k - 8/7*q + 0.
-2*q*(q + 2)**2/7
Let w(z) be the third derivative of z**7/21 + z**6/30 - z**5/2 - 4*z**4/3 - 4*z**3/3 + 8*z**2. Let w(c) = 0. Calculate c.
-1, -2/5, 2
Suppose 0 = i - 3. Let w(f) be the third derivative of 0*f + 1/12*f**4 + 7/30*f**6 + 2*f**2 + 17/30*f**5 - 2/3*f**i + 0. Solve w(d) = 0.
-1, -1/2, 2/7
Let p(u) be the first derivative of u**4/12 - 2*u**3/3 + 2*u**2 - 7*u - 7. Let s(h) be the first derivative of p(h). Solve s(n) = 0 for n.
2
Let w(t) = -3*t**3 - t**2. Let k be w(-1). Let -2*o**4 - o**4 - 2*o**3 + o**4 + k*o**2 + 2*o**5 = 0. Calculate o.
-1, 0, 1
Let l be 10/(-55) + (-84)/(-99). Let m(b) be the first derivative of 1 + 2/15*b**5 + 1/3*b**4 - 2/3*b - l*b**2 + 0*b**3. Let m(n) = 0. What is n?
-1, 1
Let o = 36 + -36. Let t(d) be the third derivative of 1/240*d**6 + 0*d + 0*d**4 + 2*d**2 + 0 + 0*d**5 + o*d**3. Factor t(v).
v**3/2
Let j = -106 - -109. Let d(x) be the second derivative of -3*x - 4/7*x**2 + 0 - 4/21*x**j - 1/42*x**4. Find u, given that d(u) = 0.
-2
Let d(r) = -5*r**2 + 36*r - 7. Let s be d(7). Factor 3/5*g**4 + s + 9/5*g**2 + 9/5*g**3 + 3/5*g.
3*g*(g + 1)**3/5
Let k(i) be the first derivative of -i**5/90 + i**4/27 - i**3/27 - i + 2. Let l(t) be the first derivative of k(t). What is o in l(o) = 0?
0, 1
Factor -5/3*j**2 - 1/6*j**5 - 1/6 - 5/3*j**3 - 5/6*j**4 - 5/6*j.
-(j + 1)**5/6
Let p be 1*(2 + -2 + -2). Let u(w) = -8*w**2 - 13*w + 4. Let c(v) = -v**2 - v. Let d(t) = p*u(t) + 18*c(t). Factor d(f).
-2*(f - 2)**2
Let j(t) be the second derivative of 3*t**5/40 - 3*t**4/4 + 3*t**3 - 6*t**2 - 33*t. Let j(v) = 0. What is v?
2
Let k(u) be the first derivative of 1/3*u**3 + 0*u**2 - 1/6*u**6 + 0*u + 3/5*u**5 - 3/4*u**4 + 9. Let k(b) = 0. Calculate b.
0, 1
Let n(y) be the second derivative of y**7/8820 + y**6/1260 + y**4/3 + 4*y. Let p(h) be the third derivative of n(h). Solve p(s) = 0.
-2, 0
Let h(o) = -o**4 - o**3 + o. Let s(t) = -11*t**4 - 7*t**3 + 2*t**2 + 7*t. Let v(r) = 18*h(r) - 2*s(r). Solve v(b) = 0.
-1, 0, 1
Suppose 0 = -i + 2. Determine w so that