e of v**7/315 - v**6/45 + 2*v**5/45 - v**2 - 1. Let u(g) be the second derivative of a(g). Determine b so that u(b) = 0.
0, 2
Let g(v) = 5*v**2 + 9*v + 7. Let l(u) be the first derivative of -4*u**3/3 - 4*u**2 - 6*u - 6. Let t(c) = -2*g(c) - 3*l(c). Determine p so that t(p) = 0.
-2, -1
Let y(g) = g**2 - 11*g - 26. Let s be y(13). Solve 2/3*w + s - 2/3*w**2 = 0 for w.
0, 1
Suppose -3*o - 35 = 22. Let x = o - -19. Factor 1/2*w**2 - 1/2*w**3 + w + x.
-w*(w - 2)*(w + 1)/2
Suppose 4 = 16*g - 14*g. Let z(s) be the second derivative of 0*s**g + 1/18*s**4 + 0*s**3 + 1/15*s**5 + 0 - s + 1/45*s**6. Factor z(h).
2*h**2*(h + 1)**2/3
Let n(j) = 3*j**2 - 3*j - 21. Let g(q) = 1. Let r = 0 - -1. Let c(x) = r*n(x) + 15*g(x). Factor c(t).
3*(t - 2)*(t + 1)
Let t(w) be the third derivative of 0*w**5 + 3/70*w**7 + 0 + 0*w**3 + 5*w**2 + 1/112*w**8 + 0*w + 0*w**4 + 1/20*w**6. Determine f, given that t(f) = 0.
-2, -1, 0
Let u = -19/3 + 7. Factor 0 + 2/3*t**2 + 4/3*t - 4/3*t**3 - u*t**4.
-2*t*(t - 1)*(t + 1)*(t + 2)/3
Let j(h) be the first derivative of 5*h**3/3 - 10*h**2 + 20*h + 7. Let j(q) = 0. What is q?
2
Factor -3/2 - 2*r - 1/2*r**2.
-(r + 1)*(r + 3)/2
Let d(b) be the third derivative of -b**9/60480 + b**7/1680 + b**6/360 + b**5/20 + b**2. Let i(j) be the third derivative of d(j). Factor i(q).
-(q - 2)*(q + 1)**2
Suppose 0*o + 0*o - o = 0. Let t(u) be the second derivative of -5/42*u**4 - 2/21*u**3 + 0 + o*u**2 + 3*u. Factor t(x).
-2*x*(5*x + 2)/7
Let l(a) be the second derivative of a**6/6 - 5*a**5/2 + 55*a**4/4 - 100*a**3/3 + 40*a**2 - 21*a. Solve l(n) = 0.
1, 4
Let c(h) be the first derivative of -3*h**5/25 - 3*h**4/10 + 3*h**2/5 + 3*h/5 + 5. Determine z so that c(z) = 0.
-1, 1
Find w, given that -2*w**5 - w**5 - w**4 - 6*w**5 + 4*w**4 + 6*w**3 = 0.
-2/3, 0, 1
Solve -2/9*h + 0 + 16/9*h**3 - 2/9*h**2 + 8/3*h**4 = 0.
-1/2, 0, 1/3
Let j(o) be the second derivative of -25*o**7/42 - o**6 - o**5/4 - 14*o. Suppose j(q) = 0. Calculate q.
-1, -1/5, 0
Let b be (-3 - -6 - 0) + 0. Solve 19*p**3 - 33*p**2 + 12*p**3 - 4*p**b + 6*p = 0.
0, 2/9, 1
Suppose -f - 3*j = 2*f + 9, 3*j + 7 = -4*f. Factor -d**3 + 3*d**3 - 4*d**3 - d**f + 3*d**3.
d**2*(d - 1)
Let x(m) be the first derivative of m**6/2 - 3*m**5/5 - 6. Factor x(j).
3*j**4*(j - 1)
Let t = -5 - -9. Suppose 3*f + 9 = 3*i, -1 = 4*i - f - 10. Factor 3 - 4 + 0*p**2 - p**2 + 3*p**i - p**t.
-(p - 1)**2*(p + 1)**2
Let f(o) be the second derivative of -o**2 + 0 + 1/10*o**5 - 1/2*o**4 - 7*o + o**3. Factor f(m).
2*(m - 1)**3
Let f(q) be the first derivative of -242*q**3/3 - 88*q**2 - 32*q + 54. Factor f(v).
-2*(11*v + 4)**2
Let z = 1 - 2. Let t be -1 + (7 - z) + -1. Let i(y) = 14*y**2 + 6*y + 4. Let k(o) = 13*o**2 + 6*o + 3. Let r(x) = t*k(x) - 5*i(x). Find l such that r(l) = 0.
-1, 1/4
Let w = 1867/420 + -31/7. Let u(r) be the third derivative of 0 + 4/35*r**7 - 1/30*r**5 + 0*r**4 - w*r**6 + 0*r + r**2 + 0*r**3. Determine t so that u(t) = 0.
-1/4, 0, 1/3
Find j, given that 1/4*j**2 - 5/6*j + 1/4 = 0.
1/3, 3
Suppose -3*t - 12 = -18. Let -1/2*d**t + 0 + d = 0. Calculate d.
0, 2
Let q(s) be the first derivative of -s**6/24 + s**5/20 + 3*s**4/16 - 5*s**3/12 + s**2/4 - 3. Solve q(c) = 0 for c.
-2, 0, 1
Find h, given that 1/3*h**3 - 1/3 - 1/3*h + 1/3*h**2 = 0.
-1, 1
Suppose 5*x - 3 = 3*j, x + j - 19 = -3*j. Suppose -3*m = k - 11, 27 = x*m + 5*k - 4. Solve 2*h**2 + 2*h**3 + 2*h**3 + m*h**4 + 0*h**3 = 0 for h.
-1, 0
Suppose -20*w + 0*w**3 - w**3 + 21*w = 0. Calculate w.
-1, 0, 1
Let j(p) be the second derivative of -p**7/840 + p**6/120 - p**5/48 + p**4/48 + 3*p**2/2 + 3*p. Let l(z) be the first derivative of j(z). Factor l(d).
-d*(d - 2)*(d - 1)**2/4
Let x = 442/847 - -6/121. What is b in -x*b + 2/7*b**2 - 6/7 = 0?
-1, 3
Let s(m) = 2*m + 34. Let i be s(-16). What is w in -2/5*w**5 - 8/5*w**4 - 8/5*w**3 + 4/5*w**2 + 4/5 + i*w = 0?
-2, -1, 1
Let w be ((-8)/2)/((-4)/10). Suppose -5 = -3*d + w. Factor -2*f**5 + f**3 + 0*f**3 + f**d.
-f**3*(f - 1)*(f + 1)
Let l(h) = 5*h**3 - h**2 + 3*h - 3. Let u(q) = 4*q**3 + 2*q - 2. Let t(x) = -2*l(x) + 3*u(x). Solve t(p) = 0 for p.
-1, 0
Let o be 8/(-6)*(-288)/512. Determine z, given that 3*z**2 - o + 9/4*z = 0.
-1, 1/4
Let d(i) = -3*i - 6. Let q be d(-8). Suppose -c + 4*f = -q, 0*c = 2*c + 5*f + 16. Factor y**3 + 1/2 - 3/2*y**c + 0*y.
(y - 1)**2*(2*y + 1)/2
Let g(u) be the third derivative of u**6/280 + u**5/20 + 2*u**4/7 + 6*u**3/7 - 10*u**2. Let g(s) = 0. What is s?
-3, -2
Factor 1/6*p**2 - 1/3 + 1/6*p.
(p - 1)*(p + 2)/6
Let q = -1051/4 + 263. Suppose 0*x + 1 - q*x**3 - 3/4*x**2 = 0. Calculate x.
-2, 1
Factor 3 + 3*w**3 - 18*w - 23*w**3 + 36*w**2 - 4*w**3.
-3*(2*w - 1)**3
Factor 4/3*b + 2/3*b**4 + 0 + 10/3*b**2 + 8/3*b**3.
2*b*(b + 1)**2*(b + 2)/3
Let r = -7320289/42 + 174306. Let q = r + -77/6. What is j in 2/7 + q*j + 2/7*j**2 = 0?
-1
Suppose -4*b - 2 = -j - 0, 0 = -2*b - 6. Let f be -2 + (-1 - 42/j). Factor -4/5*u**2 - 2/5 - f*u.
-2*(u + 1)*(2*u + 1)/5
Let a = 393 - 388. Factor -2/5*f + 4/5*f**2 - 4/5*f**4 + 2/5*f**a + 0*f**3 + 0.
2*f*(f - 1)**3*(f + 1)/5
Let w(q) be the second derivative of 2/3*q**3 + 1/12*q**4 + 2*q**2 + 0 - 2*q. Factor w(n).
(n + 2)**2
Let h(x) be the first derivative of 2/7*x**2 + 6 + 1/21*x**3 + 4/7*x. Factor h(w).
(w + 2)**2/7
Let l(d) be the first derivative of 1/21*d**6 + 0*d**4 - 1/7*d**2 - 2 - 4/21*d**3 + 4/35*d**5 + 0*d. Suppose l(o) = 0. Calculate o.
-1, 0, 1
Let g = -15 + 17. Suppose 3*r - 2*r**g + 4 - 8 + 3*r = 0. What is r?
1, 2
Let i(z) be the second derivative of 4*z**3 - 3*z**2 + 0 + 9/40*z**5 + z - 13/8*z**4. Factor i(a).
3*(a - 2)**2*(3*a - 1)/2
Suppose 3*i - 77 = -68. Find n such that 2/3*n - 3*n**2 + 0 + 7/3*n**i = 0.
0, 2/7, 1
Let s(i) be the third derivative of -i**9/13608 - i**8/2520 - i**7/1260 - i**6/1620 + i**3/6 + i**2. Let r(d) be the first derivative of s(d). Factor r(l).
-2*l**2*(l + 1)**3/9
Suppose 3*p = 2*p + 2. Factor -2*l**3 + 6*l**p + 2*l - 5*l - l.
-2*l*(l - 2)*(l - 1)
Let v(r) = -r**3 - 4*r**2 + 5*r. Let f be v(-5). Let q(z) be the second derivative of 1/90*z**5 + 0*z**3 + f + 0*z**2 - 1/54*z**4 + z. Solve q(m) = 0.
0, 1
Let q be 26/65 + (0 - 0). Factor q*p**2 - 1/5*p**5 - 2/5*p**3 - 3/5*p**4 + 1/5 + 3/5*p.
-(p - 1)*(p + 1)**4/5
Let a(i) be the second derivative of -i**4/3 - 4*i**3/3 + 6*i**2 + 47*i. Let a(o) = 0. What is o?
-3, 1
Suppose 4*u = 9*u + 2*f - 13, 0 = 2*u + 5*f - 22. Factor -u + 0*l**2 - 3/2*l + 1/2*l**3.
(l - 2)*(l + 1)**2/2
Suppose 6 = -2*p, -d + 4*p = -4 - 11. Factor -m + 0*m**2 + d*m**2 - 8*m + 6.
3*(m - 2)*(m - 1)
Let k = -762 - -764. Factor 34/11*b**k + 32/11*b**4 + 0 + 80/11*b**3 + 4/11*b.
2*b*(b + 2)*(4*b + 1)**2/11
Suppose 0 = -7*v + 67 + 143. Let p = v - 27. Factor 2/3*x**2 - 2/3*x + 2/9 - 2/9*x**p.
-2*(x - 1)**3/9
Factor 0 - 12/7*f + 4/7*f**2.
4*f*(f - 3)/7
Let w = 250 - 250. Suppose -2/9*x**4 + 0 + 4/9*x**3 + 0*x**2 + w*x = 0. Calculate x.
0, 2
Let a(z) = 35*z - 1. Let k be a(-1). Let j = k - -57. Factor 10*y**2 - 4*y**2 - j*y**4 + 11*y**3 + 3*y**3 + y**3.
-3*y**2*(y - 1)*(7*y + 2)
Let l(s) be the first derivative of -s**6/4 - 3*s**5/10 + 3*s**4/8 + s**3/2 - 9. Solve l(f) = 0 for f.
-1, 0, 1
Let b(i) = -44*i**3 + 64*i**2 + 20*i - 16. Let d(p) = -9*p**3 + 13*p**2 + 4*p - 3. Let l(m) = 5*b(m) - 24*d(m). Factor l(r).
-4*(r - 2)*(r - 1)*(r + 1)
Let g(v) be the second derivative of -14*v**6/45 + 16*v**5/15 - 11*v**4/9 + 4*v**3/9 + 10*v. Factor g(t).
-4*t*(t - 1)**2*(7*t - 2)/3
Let q(m) be the third derivative of m**8/90720 + m**7/5670 + m**6/810 + m**5/15 + 4*m**2. Let a(w) be the third derivative of q(w). Factor a(r).
2*(r + 2)**2/9
Let q(i) = -4*i**3 - 8*i**2 - 2*i. Let t(z) = 0*z + 20*z**2 - z + 5*z**2 + 6*z + 13*z**3. Let c(x) = -7*q(x) - 2*t(x). Factor c(p).
2*p*(p + 1)*(p + 2)
Let v = 305/396 - 2/99. Factor 0 - 1/4*b**3 + v*b**2 - 1/2*b.
-b*(b - 2)*(b - 1)/4
Let x(b) be the second derivative of 1/480*b**6 + 0*b**2 + 0 - 1/80*b**5 - 2*b + 1/6*b**3 + 0*b**4. Let w(z) be the second derivative of x(z). Factor w(n).
3*n*(n - 2)/4
Let y be (-34)/(-9) + (-20)/(-90). Let z be (0/(-1))/(-2 + y). Factor 5/2*a**2 + a + 1/2*a**4 + 2*a**3 + z.
a*(a + 1)**2*(a + 2)/2
Find j, given that 0*j + 2/7*j**2 - 2/7 = 0.
-1, 1
Suppose 4*z - 5 = -4*q + 19, 16 = z + 3*q. Let g = 3 - z. Factor -f**4 - g*f + f**2 - f**5 + 2 + 5*f**3 - 6*f +