5/80 - h**4/16 + h + 5. Let n(z) be the first derivative of d(z). Factor n(j).
-3*j**2*(j - 1)**2*(j + 1)/4
Suppose -5*r + 10 = -3*r. Solve 39*d**2 + 0*d - 4*d - r - 1 - 37*d**2 = 0.
-1, 3
Let k(m) be the second derivative of -4*m**2 - 2/3*m**3 + 5*m + 0 + 1/5*m**5 + 2/3*m**4. Solve k(h) = 0.
-2, -1, 1
Factor -2*p**2 - 2*p + 52*p**3 + 2 + 4*p - 54*p**3.
-2*(p - 1)*(p + 1)**2
Solve -6*p**3 + 16*p**3 - 2*p**2 + 18*p**2 - 8*p = 0 for p.
-2, 0, 2/5
Let r(l) be the first derivative of 2/21*l**3 + 0*l + 4 + 0*l**2. Factor r(g).
2*g**2/7
Let u(j) be the first derivative of 16*j**5/25 + 3*j**4/5 - j**2/10 + 6. What is w in u(w) = 0?
-1/2, 0, 1/4
Suppose 68 = -7*w + 24*w. Determine d so that -4/9*d - 2/9*d**5 - 2*d**3 + 0 - 14/9*d**2 - 10/9*d**w = 0.
-2, -1, 0
Let k(w) be the second derivative of w**6/60 + 3*w**5/40 + w**4/24 - w**3/4 - w**2/2 + 7*w. Factor k(b).
(b - 1)*(b + 1)**2*(b + 2)/2
Let o be 478/126 - 12/54. Find q such that -6/7*q**2 + o*q**4 + 4*q - 55/7*q**3 + 8/7 = 0.
-2/5, 1, 2
Solve 6*y + 0*y**3 + y**2 + 4*y**2 - 2*y**2 - 3*y**3 = 0.
-1, 0, 2
Let n(u) be the second derivative of u**4/84 - 10*u**3/21 + 50*u**2/7 + 51*u. Factor n(j).
(j - 10)**2/7
Let b(d) be the second derivative of -d**10/37800 - d**9/18900 - d**8/33600 - d**4/3 - 4*d. Let x(v) be the third derivative of b(v). Let x(a) = 0. Calculate a.
-1/2, 0
Let d = -12 + 19. Suppose 5*f = -20, i + 4*i = -2*f + d. Factor -2*j**3 + 3*j**2 + 11*j**i + 7*j**4 - j**2.
j**2*(j + 1)*(7*j + 2)
Let w(j) be the third derivative of -1/150*j**6 + 0*j**5 + 0*j - 1/15*j**3 + j**2 + 1/525*j**7 + 1/30*j**4 + 0. Determine z, given that w(z) = 0.
-1, 1
Let m(n) = -n**3 + 3*n**2 + 3. Let p be m(3). Determine t so that p*t**4 - t - 2*t**3 + 3*t**2 - 2*t**4 - t**3 = 0.
0, 1
Let y = -1/131 + 143/1572. Let t(s) be the second derivative of 0*s**2 - y*s**3 - 1/80*s**5 + 0 - 2*s + 1/16*s**4. Factor t(d).
-d*(d - 2)*(d - 1)/4
Let s be 1 - (-5)/(-7 + 2). Let r(x) be the second derivative of 1/36*x**4 + 1/6*x**2 + 1/9*x**3 + s - x. Find c, given that r(c) = 0.
-1
Let i(m) be the second derivative of -1/90*m**5 - 8/27*m**3 + 0 - 5/54*m**4 - 2*m - 4/9*m**2. Find b such that i(b) = 0.
-2, -1
Let n(i) = -9*i**2 - 4*i + 13. Let b(s) = 4*s**2 + 2*s - 6. Let r(v) = -5*b(v) - 2*n(v). Factor r(m).
-2*(m - 1)*(m + 2)
Let n(s) be the second derivative of s**9/52920 + s**8/23520 - s**4/4 - s. Let j(i) be the third derivative of n(i). Suppose j(c) = 0. What is c?
-1, 0
Let g(u) = -u. Let y be g(-1). Let x(j) be the first derivative of -2/9*j**2 - y + 2/27*j**3 + 0*j. Solve x(n) = 0.
0, 2
Suppose -26/5*j**2 - 2/5*j**5 + 0 + 14/5*j**3 + 2/5*j**4 + 12/5*j = 0. Calculate j.
-3, 0, 1, 2
Let u(c) = c**2 - 1. Let o be u(-2). Factor -4*x**5 - 2*x**3 - x - x - 1 + o*x + 5*x**5 + 2*x**2 - x**4.
(x - 1)**3*(x + 1)**2
Let c(y) be the second derivative of 2*y**6/45 + y**5/15 - 2*y**4/9 - 3*y - 1. Factor c(r).
4*r**2*(r - 1)*(r + 2)/3
Let v(i) be the first derivative of i**7/840 - i**6/120 + i**5/40 - i**4/24 + i**3 + 2. Let u(f) be the third derivative of v(f). Suppose u(l) = 0. Calculate l.
1
Let h(b) = -b**3 - 7*b**2 + 2*b. Let o(j) = 2*j**3 - 2*j - 1. Let f be o(-1). Let g = f - 0. Let w(n) = n**2 - n. Let z(t) = g*h(t) - 4*w(t). Factor z(i).
i*(i + 1)*(i + 2)
Suppose 4*g + 3*a + 3 = 0, -9 = 2*g + a + 2*a. Let v(q) be the second derivative of 0*q**5 + 2/15*q**3 - 1/75*q**6 + 1/10*q**4 + 0 + 0*q**2 + g*q. Factor v(j).
-2*j*(j - 2)*(j + 1)**2/5
Let q(i) be the second derivative of i**5/4 - 5*i**4/12 - 5*i**3/3 + 43*i. Factor q(x).
5*x*(x - 2)*(x + 1)
Let b = -205 + 1847/9. Determine i so that 2/9*i + b*i**4 - 2/9*i**3 + 4/9 - 2/3*i**2 = 0.
-1, 1, 2
Let k = -17 - -17. Let n(o) be the first derivative of k*o - 2/5*o**5 - 2*o**3 - o**2 - 2 - 3/2*o**4. Factor n(j).
-2*j*(j + 1)**3
Let k(u) be the third derivative of -u**8/560 - u**7/140 - u**6/120 - 4*u**3/3 - 8*u**2. Let c(x) be the first derivative of k(x). Factor c(y).
-3*y**2*(y + 1)**2
Let v(d) be the first derivative of -d**5/90 - d**4/9 - 4*d**3/9 + d**2 - 1. Let w(u) be the second derivative of v(u). Solve w(o) = 0.
-2
Let j(u) be the second derivative of 12*u**2 - 25/2*u**7 + 321/20*u**5 + 0 + 3*u + 91/2*u**4 + 34*u**3 - 19*u**6. Find f such that j(f) = 0.
-1, -2/5, -2/7, 1
Let h be (-3*9/45)/(6/(-20)). Factor -24/5*p**h + 18/5*p**3 + 8/5*p + 0.
2*p*(3*p - 2)**2/5
Let u(o) = -o + 4. Let n be u(2). Factor t**2 + 2*t**2 - n*t**2 - t**4 + t**5 - t**3.
t**2*(t - 1)**2*(t + 1)
Let a(s) = 20*s**3 - 2*s**2 - 11*s - 7. Let p(q) = q**2 - 1. Let b(j) = a(j) - 5*p(j). Factor b(d).
(d - 1)*(4*d + 1)*(5*d + 2)
Let o(m) = -2*m**2 + 2*m. Let n be o(1). Let i(q) be the second derivative of 1/21*q**3 + 0 + 0*q**4 - 1/70*q**5 + n*q**2 + q. Factor i(l).
-2*l*(l - 1)*(l + 1)/7
Let q = 39/2 + -19. Let b = -37/2 + 19. Factor -q*k + 1/2*k**3 - b + 1/2*k**2.
(k - 1)*(k + 1)**2/2
Let x(j) = j**3 + 7*j**2 + 4*j - 9. Let l be x(-6). Factor 8/5 - 2/5*w**l - 6/5*w**2 + 0*w.
-2*(w - 1)*(w + 2)**2/5
Let w(h) be the third derivative of h**8/3360 - h**7/840 + h**5/120 + h**4/8 - 5*h**2. Let q(b) be the second derivative of w(b). Factor q(r).
(r - 1)**2*(2*r + 1)
Let c = 5149/36 + -143. Let a(q) be the third derivative of 0*q**5 + 0*q + 0 - 1/90*q**6 + c*q**4 + 1/504*q**8 + 0*q**7 + 4*q**2 + 0*q**3. Factor a(t).
2*t*(t - 1)**2*(t + 1)**2/3
Let i be 4/60*-4*(-2)/88. Let u(l) be the second derivative of 0*l**2 + 1/110*l**5 + i*l**6 + 0*l**4 + l + 0*l**3 + 0. Factor u(h).
2*h**3*(h + 1)/11
Let k be (-21)/28 + (-46)/(-8). Factor 12*v**4 - 2*v**k - 7*v**4 - 4*v**3 + v**4.
-2*v**3*(v - 2)*(v - 1)
Let w(u) be the third derivative of -u**6/120 + u**4/24 - 8*u**2. Factor w(t).
-t*(t - 1)*(t + 1)
Let u(w) = w**2 + 1. Let v(y) = 28*y**3 + 214*y**2 + 384*y - 130. Let d(p) = -2*u(p) - v(p). Let d(l) = 0. What is l?
-4, 2/7
Find v, given that -101*v**5 - 9*v**2 - 7*v**2 + 156*v**4 + 241*v**5 = 0.
-1, -2/5, 0, 2/7
Suppose -4*x + 4*v + 44 = 0, 4*v = -3*x - v - 7. Suppose -b = -4*h - 2*b + 22, -2*h + b = -14. Factor 2 - x*o**2 - 4*o**2 - h*o + 2*o**2.
-2*(o + 1)*(4*o - 1)
Suppose -22 = -2*g + 2*u, 8 = -4*u - 0. Suppose -15 = 4*a - g*a. Let 8*h**2 - 2*h**a - 4*h - 4*h + 0*h**2 = 0. Calculate h.
0, 2
Suppose 3*q - 37 = -q + 5*y, -4*y = 20. Let i = 5 - q. Let 4*t**2 - i*t + 5*t**2 - 4*t**2 = 0. What is t?
0, 2/5
Let l be 2/5 + (-2)/5. Suppose -12*m = -8*m. Factor -2/5*y**2 + l*y + m.
-2*y**2/5
Let j(v) = -v**2 - 1. Let p(q) = -q**2 + q - 4. Suppose 5*u - 2*u = 12. Let w(i) = u*j(i) - p(i). Solve w(y) = 0.
-1/3, 0
Factor -4/3*r + 0 + 26/3*r**2.
2*r*(13*r - 2)/3
Factor 0 + 0*f + 0*f**3 + 0*f**2 + 2/11*f**4.
2*f**4/11
Solve -7/8*r - 9/8*r**2 - 1/8*r**4 - 1/4 - 5/8*r**3 = 0.
-2, -1
Let c = 1 + 0. Suppose 3*h - 5*w = 37, -c = 2*h - h + w. Find k such that 1 + 3*k**3 - k**h + 2*k**2 - 2 - 3*k**3 = 0.
-1, 1
Let y(d) = 6*d**2 + 16*d - 6. Let v(z) = z**2 - 5*z + 2. Let o(a) = a**2. Let w(s) = -3*o(s) + v(s). Let q(f) = 16*w(f) + 5*y(f). Factor q(p).
-2*(p - 1)*(p + 1)
Let w(a) = a**3 + a**2. Suppose 7*b - 6 = 1. Let k(r) = -3*r**3 - r. Let s(x) = b*k(x) + 2*w(x). Solve s(f) = 0.
0, 1
Determine f so that 10*f**5 + 2*f**5 - 8*f**4 - 8*f**2 - 12*f**3 + 16*f**4 = 0.
-1, -2/3, 0, 1
Suppose 2 + 3 = h. Suppose h*y - 15 = 0, 2*g - 27 = -2*y + 3. Factor 13*j**5 - 4*j + g*j**2 - 5*j**3 - 6*j**4 - 6*j**4 - 4*j**5.
j*(j - 1)*(j + 1)*(3*j - 2)**2
Let r(x) be the first derivative of x**3/5 - 21*x**2/5 + 147*x/5 - 14. Factor r(t).
3*(t - 7)**2/5
Suppose 2*v + 8 = 4*v. Let a = 6 - v. Suppose 2*s**3 - s**2 + 4 - 2 - 2*s - s**a = 0. Calculate s.
-1, 1
Let f(d) be the second derivative of -d**7/1260 - d**6/270 + d**5/180 + d**4/18 - 5*d**3/6 - d. Let r(h) be the second derivative of f(h). Factor r(g).
-2*(g - 1)*(g + 1)*(g + 2)/3
Let h = -12 + 8. Let s(j) = -j**3 + j**2 - 7*j**2 + 7*j - 1 + j**2. Let k(f) = 2*f**3 + 4*f**2 - 6*f. Let c(q) = h*s(q) - 3*k(q). Factor c(l).
-2*(l - 2)*(l - 1)**2
Let f(x) be the second derivative of -3/5*x**5 + 0*x**2 - 2/15*x**6 + 0*x**3 - 2/3*x**4 + 0 + 8*x. Factor f(k).
-4*k**2*(k + 1)*(k + 2)
Let h(i) = i**2 - 11*i + 28. Let k be h(8). Let p(d) be the second derivative of 1/6*d**k + 3*d + d**2 - 2/3*d**3 + 0. Factor p(o).
2*(o - 1)**2
Factor 2/9*g**4 - 8/3*g - 4/9*g**2 + 8/9*g**3 + 2.
2*(g - 1)**2*(g + 3)**2/9
Let h(j) = -j*