4 - 70*g**3 - 19*g**2 + 56*g + 15. Let u(h) = h**2 - 1. Let n(z) = r(z) - u(z). Find f, given that n(f) = 0.
-2, -1, -2/7, 1, 2
Suppose -5*h - 4*h + 135 = 0. Determine q so that 3*q**5 + 19*q**4 + 10*q**4 + 4*q**2 - 17*q**4 + h*q**3 + 2*q**2 = 0.
-2, -1, 0
Let z(t) = -t**2 - 9*t - 19. Let s be z(-5). Factor 2*p**2 + 7 - s - 25 + 3 - 4*p.
2*(p - 4)*(p + 2)
Let y(l) be the first derivative of -5*l**8/168 - 2*l**7/21 - 4*l**6/45 - 5*l**3/3 + 1. Let v(j) be the third derivative of y(j). Let v(o) = 0. What is o?
-4/5, 0
Suppose -14 + 5 = 3*x. Let b be (-1 - 2)/x*4. Find y, given that 5*y**3 + 3*y**4 + 3*y**2 - 2*y**3 + 3*y**3 + 0*y**b = 0.
-1, 0
Let q(v) be the third derivative of 0*v**7 + 0*v**3 + 1/200*v**6 + 0 + 0*v**5 - 1/560*v**8 + 0*v**4 + 3*v**2 + 0*v. Factor q(b).
-3*b**3*(b - 1)*(b + 1)/5
Suppose -10 = 3*g + 5, -2*u + 24 = -4*g. Factor -u*z**2 + 17*z + 6*z**2 - 7 - z + 19.
4*(z + 1)*(z + 3)
Factor 6*a**2 + a**2 - 8*a**2.
-a**2
Let 2/7*n**3 + 4/7 + 10/7*n + 8/7*n**2 = 0. Calculate n.
-2, -1
Suppose 46*i - 47*i = 0. Let y be 1/18*(i/(-1) - -4). Factor -2/9*r**4 - 2/9*r + 2/9*r**3 + y*r**2 + 0.
-2*r*(r - 1)**2*(r + 1)/9
Suppose -2*k + p = -0*k - 25, -60 = -5*k + 2*p. Suppose 0 = -3*h + 2*h + 2*n + 2, 2*h - k = n. Factor 2*q + 1 - 2*q**2 - 7 + h.
-2*q*(q - 1)
Let g(y) be the first derivative of y**7/9 - 2*y**6/45 - 7*y**5/30 + y**4/9 + 52*y - 31. Let m(u) be the first derivative of g(u). What is d in m(d) = 0?
-1, 0, 2/7, 1
Let w(j) be the first derivative of 0*j**3 - 3*j + 1 + 0*j**2 - 1/12*j**4. Let g(r) be the first derivative of w(r). Solve g(t) = 0 for t.
0
Let m = -10 - -6. Let h(x) = 3*x**3 + 9. Let u(n) be the second derivative of n**5/20 + 2*n**2 + 603*n. Let t(z) = m*h(z) + 9*u(z). Let t(l) = 0. What is l?
0
Let r(w) = w - 17. Let a be r(-6). Let o be 12/(-60) + (-3)/(45/a). Factor o + 14/3*p - 8/3*p**2.
-2*(p - 2)*(4*p + 1)/3
Let w be (203/406)/(2/3). Determine h, given that -3/4*h + 3/4*h**3 + w - 3/4*h**2 = 0.
-1, 1
Let u(i) be the third derivative of 0*i**3 + 1/60*i**4 + 1/600*i**6 - 7*i**2 + 1/100*i**5 + 0 + 0*i. Factor u(x).
x*(x + 1)*(x + 2)/5
Let u(c) = 90*c - 720. Let f be u(8). What is s in 1/4*s**2 - 1/4*s + f = 0?
0, 1
Let i(d) be the first derivative of 2*d**5/45 - d**4 + 160*d**3/27 + 2*d**2 - 18*d + 172. Find s such that i(s) = 0.
-1, 1, 9
Let d(y) be the second derivative of -y**8/1680 + y**7/1050 + y**6/300 + 8*y**2 + 15*y. Let w(s) be the first derivative of d(s). Find k, given that w(k) = 0.
-1, 0, 2
Let a = 6243/2780 + 3/695. Let i(u) be the first derivative of -3/8*u**2 + 7 + 5/12*u**3 - a*u - 1/16*u**4. Solve i(w) = 0.
-1, 3
Let v(x) be the third derivative of x**7/280 + 17*x**6/960 - 3*x**5/160 - 17*x**4/192 + x**3/16 - 11*x**2. Determine n, given that v(n) = 0.
-3, -1, 1/6, 1
Let s = 45 - 45. What is c in -c + s*c**2 + c**5 - 5*c**2 + 3*c**2 + 2*c**4 = 0?
-1, 0, 1
Determine w, given that 5/3*w**3 + 0 + 0*w - 200/3*w**2 = 0.
0, 40
Let v = -3/160 - -169/480. Let u(j) be the first derivative of -4/5*j**5 + 5 + 4/3*j**3 + 0*j**2 + 0*j - v*j**6 + 1/2*j**4. Let u(q) = 0. What is q?
-2, -1, 0, 1
Let s(f) be the first derivative of 3*f**4/28 - 2*f**3 - 21*f**2/2 - 102*f/7 - 481. Factor s(z).
3*(z - 17)*(z + 1)*(z + 2)/7
Let z(f) be the third derivative of -f**6/540 - 19*f**5/45 - 361*f**4/9 - 54872*f**3/27 + f**2 + 147. Suppose z(b) = 0. Calculate b.
-38
Let w(m) be the second derivative of m**4/54 + 44*m**3/27 + 484*m**2/9 - 41*m. Factor w(j).
2*(j + 22)**2/9
Let n = -19431 + 19433. Factor 0*b + 0 - 2/7*b**n.
-2*b**2/7
Let a(v) be the first derivative of 0*v**4 - 1/35*v**5 + 1/21*v**3 + 0*v**2 + 15 + 0*v. Let a(h) = 0. What is h?
-1, 0, 1
Let m = -21 - -30. Let j be 37/3 + (-3)/m. Find p, given that -p - 2*p**2 + j*p**3 - 3*p - 5*p**2 - 8*p**5 + 4*p**4 + 3*p**2 = 0.
-1, -1/2, 0, 1
Let u = -899 + 901. Let q(x) be the second derivative of 3/10*x**5 - 2/3*x**4 + 0*x**u + 0 - 7*x + 1/3*x**3. Factor q(c).
2*c*(c - 1)*(3*c - 1)
Let j(v) be the third derivative of 1/84*v**4 - 40*v**2 + 0 + 3/245*v**7 + 0*v + 1/28*v**6 + 0*v**3 + 1/30*v**5. Factor j(m).
2*m*(m + 1)*(3*m + 1)**2/7
Let x(b) be the second derivative of -b**5/4 + 5*b**4/4 + 15*b**3/2 + 25*b**2/2 + 70*b. Determine a, given that x(a) = 0.
-1, 5
Let h(q) be the second derivative of -5*q**4/12 - 5*q**3/6 + 30*q**2 + 470*q. Find z, given that h(z) = 0.
-4, 3
Let b(s) be the third derivative of -s**10/75600 - s**9/10080 + s**7/630 + 3*s**5/20 + 2*s**2. Let z(g) be the third derivative of b(g). Factor z(h).
-2*h*(h - 1)*(h + 2)**2
Let o = 18 + -16. Let w = 2 + 1. Factor -11*l**o + 2*l**2 + w*l**3 + 0 - 3 + 0 + 9*l.
3*(l - 1)**3
Let f be 1/((2/36)/(90/(-27))). Let n be (119/42)/(-17) + (-22)/f. Suppose 27/5*h - 27/5*h**2 + 0 + 9/5*h**3 - n*h**4 = 0. What is h?
0, 3
Let g be (3*6/81)/(2/18). Determine t so that -15*t**g + 2682*t - 3*t**3 - 2706*t + 9 - 21 = 0.
-2, -1
Let g(d) be the third derivative of -12/7*d**3 + 23/210*d**6 + 0 + 19/14*d**4 - 59/105*d**5 - 2/245*d**7 + 13*d**2 + 0*d. Solve g(l) = 0 for l.
2/3, 1, 3
Factor -180 + 5*f**2 - 19*f + 21*f + 34*f + 9*f.
5*(f - 3)*(f + 12)
Suppose -3*r + 1 + 8 = 0. Factor 2 - 9 + 31 - 3*k**2 - r*k**2 + 12*k - 3*k**3.
-3*(k - 2)*(k + 2)**2
Suppose 51 = 3*w - 3*x + 18, -5*w + 15 = 3*x. Suppose 16 = 4*m - 4*a, -4 + w = 4*m + 3*a. Suppose -9/4*v**m + 3 + 0*v + 3/4*v**3 = 0. What is v?
-1, 2
Let y(g) be the second derivative of -3*g**5/20 - 21*g**4/4 + g**3/2 + 63*g**2/2 - 188*g. Let y(k) = 0. What is k?
-21, -1, 1
Let g(f) = 5*f**2 + 45*f + 30. Let l(w) be the first derivative of -w**2/2 + w - 26. Let s(t) = -g(t) - 15*l(t). Factor s(h).
-5*(h + 3)**2
Let n = 44118/5 + -8823. Let 0 - n*g**2 - g**3 + 2/5*g = 0. What is g?
-1, 0, 2/5
Suppose 4*j + 5*l - 35 = 0, 2 - 14 = -4*l. Suppose -5*d + d = b - j, 3*b + 3*d - 6 = 0. Factor -z**2 - b + 8 - z - 7.
-z*(z + 1)
Let v(y) be the first derivative of -y**6/6 - 5*y**5/4 - 10*y**4/3 - 10*y**3/3 - y - 18. Let n(d) be the first derivative of v(d). Determine o so that n(o) = 0.
-2, -1, 0
Let i(j) = -155*j**3 + 340*j**2 - 375*j + 35. Let f(o) = 9*o**3 - 20*o**2 + 22*o - 2. Let v(n) = -35*f(n) - 2*i(n). Let v(x) = 0. Calculate x.
0, 2
What is p in 2/5*p**4 + 16/5*p**3 - 16/5*p**2 + 288/5 - 192/5*p = 0?
-6, 2
Let g(c) = -c**2 + 16. Let l(s) = 2*s**2 + s - 28. Let n(x) = -11*g(x) - 6*l(x). Factor n(a).
-(a + 2)*(a + 4)
Let q = -73 - -81. Let t be (4 - 35/q)/(-3)*2. Suppose 1/4*j**5 + t*j**3 + 0*j**2 + 0 - 1/2*j**4 + 0*j = 0. What is j?
0, 1
Let c(d) be the third derivative of 0 - 1/3*d**6 - 2/21*d**7 - d**2 + 5/3*d**3 + 0*d + 3/2*d**5 + 5/112*d**8 - 55/24*d**4. Factor c(y).
5*(y - 1)**3*(y + 2)*(3*y - 1)
Factor 60*r**2 - 11*r + 11*r**3 - 121/2 + 1/2*r**4.
(r - 1)*(r + 1)*(r + 11)**2/2
Let v(z) be the second derivative of -5*z**4/12 + 85*z**3/3 - 7*z - 19. Solve v(s) = 0 for s.
0, 34
Let t be 4/1 - 8981/196. Let y = 169/4 + t. Solve y*a**2 + 3/7*a + 0 = 0.
-1, 0
Let l(w) be the first derivative of w**7/840 - w**5/240 + 6*w**2 + 3. Let s(y) be the second derivative of l(y). Factor s(p).
p**2*(p - 1)*(p + 1)/4
Let y(a) = -a**2 + 1 - 6*a - 3 - 3*a**2 + 3*a**2. Let v be y(-5). Factor v*r**2 - r**2 - 9*r**3 - 3*r + 13*r**2 - 3.
-3*(r - 1)**2*(3*r + 1)
Let t(g) be the second derivative of -6*g**5/25 - 7*g**4/20 + g**3/10 + 37*g - 2. Let t(d) = 0. Calculate d.
-1, 0, 1/8
Suppose x = -5*o + 2*o + 5, 5*o - 9 = -x. Factor -6 + 1 - o*q**2 - 11 + 6*q**2.
4*(q - 2)*(q + 2)
Let s(n) be the third derivative of n**9/3780 - n**8/1050 + n**6/225 - n**5/150 + 2*n**3 + 11*n**2. Let v(g) be the first derivative of s(g). Factor v(f).
4*f*(f - 1)**3*(f + 1)/5
Let z be 36/(-45) - 47/(-40). Let j(t) be the second derivative of -3*t + 0 + 3/80*t**5 - z*t**3 + 0*t**4 - 3/4*t**2. Factor j(v).
3*(v - 2)*(v + 1)**2/4
Suppose -4 - 1/6*t**2 + 11/6*t = 0. What is t?
3, 8
Let l = -2138/5 - -8597/20. Solve l*o + 0 + 3/4*o**3 - 3*o**2 = 0 for o.
0, 1, 3
Let p(m) be the first derivative of -m**6/27 + 22*m**5/45 - 43*m**4/18 + 146*m**3/27 - 56*m**2/9 + 32*m/9 - 130. Factor p(g).
-2*(g - 4)**2*(g - 1)**3/9
Let x(v) = -v**5 + v**3 + v**2 + v + 1. Let b(w) = 28*w**5 - 88*w**3 + 128*w**2 - 156*w + 16. Let g(c) = b(c) + 24*x(c). Factor g(p).
4*(p - 2)*(p - 1)**3*(p + 5)
Suppose 35*q + 136*q - 684 = 0. Factor 0*s - 1/6*s**3 + 0 - 1/6*