0*k**3 - 1/5*k**2 + 0*k.
k**2*(k - 1)*(k + 1)/5
Factor 8/9*x**2 - 2/9*x**3 - 10/9*x + 4/9.
-2*(x - 2)*(x - 1)**2/9
Let s(r) be the first derivative of -5*r**3/3 - 5*r**2/2 + 17. Factor s(b).
-5*b*(b + 1)
Factor -4 + 18/5*a + 2/5*a**2.
2*(a - 1)*(a + 10)/5
Let q(x) be the third derivative of 4*x**7/735 - x**6/420 - 7*x**2. Factor q(b).
2*b**3*(4*b - 1)/7
Let j be 4/(-10) + ((-513)/30)/(-9). Factor -1/2*g**3 - 3/2*g**2 - j*g - 1/2.
-(g + 1)**3/2
Let p(r) be the third derivative of -r**6/240 + r**5/60 - r**4/48 + 5*r**2. Determine q, given that p(q) = 0.
0, 1
Let n(m) be the second derivative of 0*m**3 + 1/20*m**5 + 0 - 1/16*m**4 + 2*m - 1/120*m**6 + 0*m**2. Determine w, given that n(w) = 0.
0, 1, 3
Let y(o) = 4*o**5 + 8*o**4 + 6*o**3 - 2*o**2 + 2*o - 6. Let j(s) = -s**3 - s**2 - s + 1. Let t(b) = -6*j(b) - y(b). What is r in t(r) = 0?
-1, 0, 1
Let c = 18 + -22. Let u(m) = -4*m**3 - m**2 + 4*m + 1. Let j(p) = -p**3 + p. Let a(y) = c*u(y) + 18*j(y). Factor a(f).
-2*(f - 2)*(f - 1)*(f + 1)
Let j(x) be the third derivative of 0 - 2*x**2 + 0*x + 1/3*x**3 + 1/2*x**4 + 1/6*x**5. Suppose j(h) = 0. Calculate h.
-1, -1/5
Let q(i) = -3*i - 4. Let w be q(-4). Factor w - 9*l + 2*l - l + 2*l**2.
2*(l - 2)**2
Let c = -1258/7 + 180. Factor -c*q + 0 + 2/7*q**3 + 0*q**2.
2*q*(q - 1)*(q + 1)/7
Let w = 15 - 23. Let i = 8 + w. Factor 1/4*m**3 + 0 - 1/4*m**4 + 0*m**2 + i*m.
-m**3*(m - 1)/4
Let d(m) be the third derivative of m**7/42 + m**6/12 + m**5/12 - 6*m**2. Factor d(h).
5*h**2*(h + 1)**2
Suppose -4*p + 2*f = -3*p, -5*f = -5*p. Let a(b) be the first derivative of -2/3*b**3 + 1 + p*b - 1/4*b**4 - 1/2*b**2. Factor a(k).
-k*(k + 1)**2
Suppose 41*s - 70 = 12. Factor 9/2*d**s - 3/2*d + 0.
3*d*(3*d - 1)/2
Factor -8/3*t + 2/3*t**3 - 1/3*t**4 + 4/3 + t**2.
-(t - 2)*(t - 1)**2*(t + 2)/3
Suppose -3 + 110*c**2 - 112*c**2 - 3 + 8*c = 0. Calculate c.
1, 3
Let g(y) = 4*y**2 + 131*y + 251. Let d(z) = z**2 + 44*z + 84. Let p(v) = 11*d(v) - 4*g(v). Determine b so that p(b) = 0.
-4
Suppose z = -0*z - 4. Let h be 1/z - 36/(-16). Factor -4/9*a + 2/9*a**h + 2/9.
2*(a - 1)**2/9
Let a(j) = -j**2 + j - 1. Let l(w) = 9*w**2 - w + 9. Let b(z) = -5*a(z) - l(z). Let x(g) = -9*g**2 - 8*g - 9. Let q(o) = -5*b(o) + 2*x(o). Factor q(k).
2*(k + 1)**2
Let s(g) = 2*g - 5. Let f be s(4). Suppose -u + 3*a + 7 = -f*u, 3*u = -a. Factor -4*n**3 + 6*n + 3 - 2*n**5 + 4*n**2 - n**4 - 5*n**4 - u.
-2*(n - 1)*(n + 1)**4
Solve 0*x + 0 - 1/2*x**4 + 3/2*x**2 - x**3 = 0.
-3, 0, 1
Let g(b) be the second derivative of 5*b**4/48 + 5*b**3/24 - 15*b**2/4 + 10*b. Solve g(j) = 0 for j.
-3, 2
Let b be 74/(-2)*(-14)/(-6). Let t = b - -87. Factor 2/9*d**2 + 4/9 - t*d.
2*(d - 2)*(d - 1)/9
Let h = -1/384 - -775/2688. Solve 2/7 - h*a**2 + 0*a = 0 for a.
-1, 1
Suppose 3*s - t - 6 = 2*t, 3*s + 3*t - 12 = 0. Let o(n) be the third derivative of n**2 - 1/240*n**6 + 0*n + 0*n**s + 0 + 1/48*n**4 + 0*n**5. Factor o(g).
-g*(g - 1)*(g + 1)/2
Let p(y) = y**3 + 5*y**2 + 3. Let o be p(-5). Let g(d) be the first derivative of -3*d**2 - 5/2*d**4 + d + 4*d**o + 3/5*d**5 + 1. Suppose g(j) = 0. What is j?
1/3, 1
Let d(r) be the third derivative of r**6/360 - 7*r**5/60 + 49*r**4/24 - 343*r**3/18 + 36*r**2. Suppose d(n) = 0. What is n?
7
Let r(f) be the second derivative of -f**5/270 - f**4/36 - 2*f**3/27 - 3*f**2/2 - 3*f. Let j(q) be the first derivative of r(q). Factor j(h).
-2*(h + 1)*(h + 2)/9
Suppose -2/5*v**3 + 54/5 + 18/5*v**2 - 54/5*v = 0. Calculate v.
3
Solve 7/2*w**2 + 0 + 5/2*w**4 + 1/2*w**5 + 9/2*w**3 + w = 0 for w.
-2, -1, 0
Let a(t) be the third derivative of t**6/80 + t**5/40 - t**4/16 - t**3/4 - t**2. Let a(d) = 0. What is d?
-1, 1
Let -15*p**2 + 3/2*p**5 - 3/2 + 15/2*p + 15*p**3 - 15/2*p**4 = 0. Calculate p.
1
Let v(s) = s + 7. Let a be v(-7). Let u = 6 + -2. What is n in -2*n**4 + n + u*n**3 - n**3 + n**4 - 3*n**2 + a*n = 0?
0, 1
Let o be (2/2)/(-5 - -4). Let d be (3 + o)*(-2)/(-2). Solve -x**2 + 5*x**2 - 2*x + 6*x**3 + d*x**2 + 2*x**3 = 0 for x.
-1, 0, 1/4
Let t(u) = 6*u**3 - 4*u**2 - 2*u. Let c(n) = -7*n**3 + 3*n**2 - 4*n - 1 + 2*n**3 + 7*n + 2. Let f(d) = 4*c(d) + 3*t(d). Factor f(i).
-2*(i - 2)*(i + 1)**2
Let y be (-12)/(-150)*(7 - 2). Let d(w) be the first derivative of y*w**2 - 2/5*w - 1 - 2/15*w**3. Let d(i) = 0. Calculate i.
1
Let c = -42 - -45. Let a(b) be the first derivative of 0*b**4 + 4/35*b**5 + 1/7*b**2 + 1 - 1/21*b**6 - 4/21*b**c + 0*b. Determine v so that a(v) = 0.
-1, 0, 1
Let y(c) = 5*c**5 - 9*c**4 + 4*c**3 + 10*c**2 - 15*c + 11. Let t(f) = -5*f**5 + 10*f**4 - 5*f**3 - 10*f**2 + 15*f - 10. Let h(n) = 6*t(n) + 5*y(n). Factor h(i).
-5*(i - 1)**4*(i + 1)
Let s(t) be the second derivative of -t**4/8 + 3*t**3/4 + 25*t. Let s(g) = 0. What is g?
0, 3
Let 52/7*g - 10/7 + 8/7*g**3 - 50/7*g**2 = 0. What is g?
1/4, 1, 5
Factor -18 - 771*i**2 + 99*i**3 + 23*i**4 + 888*i**2 - 2*i**4 + 21*i.
3*(i + 1)**2*(i + 3)*(7*i - 2)
Let d be (-7)/(-35) + 1 + 18/(-15). What is t in d - 2*t**2 - 3*t**3 - 1/2*t**5 - 2*t**4 - 1/2*t = 0?
-1, 0
Let m(c) be the first derivative of c**7/14 + c**6/10 - 5*c - 1. Let s(h) be the first derivative of m(h). Let s(f) = 0. Calculate f.
-1, 0
Let u(c) be the second derivative of c**3 + 0 + 1/6*c**4 + 2*c + 2*c**2. Factor u(t).
2*(t + 1)*(t + 2)
Let t(h) be the first derivative of 3*h**4/8 + 3*h**3 + 33*h**2/4 + 9*h + 34. Find s, given that t(s) = 0.
-3, -2, -1
Suppose -u + 9 = 2*u. Let k be (2 - (-26)/(-6)) + u. Factor 2/3*z**4 - 2/3*z**2 + 0 + 2/3*z - k*z**3.
2*z*(z - 1)**2*(z + 1)/3
Let u(g) = 16*g - 94. Let k be u(6). What is o in -1/3*o + o**k - o**3 + 0 + 1/3*o**4 = 0?
0, 1
Let k(b) be the second derivative of -b**10/15120 + b**8/3360 + b**4/6 - 4*b. Let h(t) be the third derivative of k(t). Suppose h(y) = 0. What is y?
-1, 0, 1
Factor 6 - 8*x + 6*x + 2*x**2 - 6*x.
2*(x - 3)*(x - 1)
Let n(o) be the first derivative of 9*o**5/5 + 21*o**4/4 - 38*o**3/3 - 34*o**2 - 24*o - 36. Factor n(v).
(v - 2)*(v + 3)*(3*v + 2)**2
Factor -2/11*i**2 + 2/11*i + 0.
-2*i*(i - 1)/11
Let t(g) be the first derivative of -g**7/189 - g**6/135 + g**5/90 + g**4/54 + 2*g + 4. Let s(k) be the first derivative of t(k). Factor s(p).
-2*p**2*(p - 1)*(p + 1)**2/9
Let x(c) be the second derivative of -c**8/1260 - c**7/630 + c**6/270 + c**5/90 - c**3/2 - 5*c. Let i(w) be the second derivative of x(w). Factor i(m).
-4*m*(m - 1)*(m + 1)**2/3
Let d(g) = -4*g**3 + 2*g + 2. Let v(t) = -5*t**3 - 6*t - 7. Let i(s) = -11*s**3 - 13*s - 15. Let j(x) = 6*i(x) - 13*v(x). Let k(n) = d(n) - 2*j(n). Factor k(m).
-2*m*(m - 1)*(m + 1)
Suppose -9*r**5 + 4*r**3 + 0*r - 10*r**2 + 3*r - 6*r**2 + 24*r**4 + 10*r**3 = 0. What is r?
-1, 0, 1/3, 3
Let w(b) be the third derivative of -b**8/672 + b**7/420 + b**6/240 - b**5/120 + 2*b**2. Factor w(r).
-r**2*(r - 1)**2*(r + 1)/2
Let z = 24/5 + -43/10. Let r(f) be the second derivative of 0 - 3*f + z*f**3 + 0*f**2 - 3/4*f**4. Factor r(i).
-3*i*(3*i - 1)
Suppose 2*i - 14 = 2. Let d be (1 + (-12)/i)*-9. Factor d*v**3 - 9/2*v - 3/2*v**2 + 3/2.
3*(v - 1)*(v + 1)*(3*v - 1)/2
Let k = 1951/30 + -65. Let a(n) be the third derivative of k*n**5 - 2/3*n**3 + 0*n + 1/4*n**4 + 1/105*n**7 + 0 - 1/20*n**6 + 2*n**2. Find f such that a(f) = 0.
-1, 1, 2
Let j(f) = f**2 + 9*f - 7. Let z be j(-5). Let y be -4 - (-2 - z/(-12)). Solve 0*b - 1/2*b**4 + 0*b**2 - y*b**3 + 0 = 0.
-1/2, 0
Let k = -3/82 + 191/738. Let v(w) be the first derivative of 0*w**3 - 2/9*w + 2 - 1/9*w**4 + k*w**2 + 2/45*w**5. Factor v(b).
2*(b - 1)**3*(b + 1)/9
Let p = -803/2 + 402. Factor 0*l + p*l**2 - 2.
(l - 2)*(l + 2)/2
Let i(n) be the third derivative of -n**7/11340 - n**6/1620 - n**5/540 + n**4/6 - 4*n**2. Let q(g) be the second derivative of i(g). Solve q(h) = 0 for h.
-1
Let r(z) = -7*z**4 + 22*z**3 - 40*z**2 + 28*z. Let y(c) = -6*c**4 + 21*c**3 - 39*c**2 + 27*c. Let x(k) = -3*r(k) + 4*y(k). Factor x(o).
-3*o*(o - 2)**3
Let z(y) be the first derivative of 1/24*y**6 + 3/20*y**5 + 1/12*y**3 + 0*y + 2 + 3/16*y**4 + 0*y**2. Suppose z(k) = 0. Calculate k.
-1, 0
Let r = -126 + 126. Let w(p) be the second derivative of 0 + 1/54*p**4 + 1/90*p**5 + r*p**2 - 2/27*p**3 - 3*p. Determine a, given that w(a) = 0.
-2, 0, 1
Let p(d) = -d**4 + d**2 + d - 1. Let q(t) = -16*t**4 - 4*t**3 + 16*t**2 + 16*t - 12. Let i(c) = -12*p(c) + q(c). Suppose i(b) = 0. Calculate b.
-