- 23. Suppose 4*v - 4*z - o = 0, -v + 4*z + 11 = 3. What is m in -1/2*m + 1/2*m**2 + v = 0?
0, 1
Let g = -2 - -6. Let z(m) be the second derivative of -1/48*m**g + 0 + 1/8*m**2 - m + 0*m**3. Factor z(u).
-(u - 1)*(u + 1)/4
Let i = 7 - 6. Let a = -1 + i. Determine w so that -1/3*w**3 + a*w - 4/3 + w**2 = 0.
-1, 2
Let l = 67 + -60. Let d(v) be the third derivative of -1/5*v**5 + 3*v**2 - 1/15*v**6 - 1/105*v**l + 0*v - 1/3*v**4 - 1/3*v**3 + 0. Factor d(m).
-2*(m + 1)**4
Let c(t) = -18*t**2 + 8*t - 18. Let d(n) = n**2 + 1. Let o(f) = -c(f) - 12*d(f). Let m(g) = -g**2 + g - 1. Let b(y) = -4*m(y) - o(y). Solve b(x) = 0 for x.
1
Let v(p) be the second derivative of -p**8/10920 - p**7/5460 + p**6/2340 + p**5/780 + p**3/6 - 4*p. Let m(h) be the second derivative of v(h). Factor m(i).
-2*i*(i - 1)*(i + 1)**2/13
Factor 2/3*g**4 - 8/3*g**3 + 2/3 - 8/3*g + 4*g**2.
2*(g - 1)**4/3
Let t(a) = a**2 - 3*a + 2. Let m(k) = -k**2 + 4*k - 3. Suppose -3*b = 23 - 8. Let u(n) = b*t(n) - 4*m(n). Suppose u(y) = 0. Calculate y.
-2, 1
Factor 1/7*b**4 + 1/7*b**3 + 0*b - 2/7*b**2 + 0.
b**2*(b - 1)*(b + 2)/7
Let r = 37/66 - 5/22. Suppose 0 + 0*h - 1/3*h**4 - r*h**2 - 2/3*h**3 = 0. What is h?
-1, 0
Let z(y) be the first derivative of -y**5/5 + y**4/12 + 2*y**3/3 - y**2/2 + 2*y + 2. Let i(j) be the first derivative of z(j). Factor i(m).
-(m - 1)*(m + 1)*(4*m - 1)
Let v(d) be the third derivative of -d**6/140 + d**5/42 - d**4/84 - d**3/21 - 9*d**2. What is g in v(g) = 0?
-1/3, 1
Suppose -2*k - 4*s = 0, -3*k - 5*s = 2*k - 10. Factor 1/2*f + 0 + 1/2*f**5 - f**3 + 0*f**k + 0*f**2.
f*(f - 1)**2*(f + 1)**2/2
Let d(z) = 2*z - 3. Let j(o) = o - 2. Let u(i) = -2*d(i) + 3*j(i). Let h be u(-2). Determine q so that -4/7 - 2/7*q**h + 6/7*q = 0.
1, 2
Factor -5/9*y**2 + 2/9*y**4 - 1/9*y**3 + 1/3 + 1/9*y.
(y - 1)*(y + 1)**2*(2*y - 3)/9
Let l(c) be the first derivative of -c**6/900 + c**5/300 + c**4/30 - c**3/3 - 1. Let g(k) be the third derivative of l(k). Factor g(z).
-2*(z - 2)*(z + 1)/5
Let y = -2 - -2. Factor 1/3*w**2 + 0 - 1/3*w**3 + y*w.
-w**2*(w - 1)/3
Let h(d) be the second derivative of -2*d**7/21 - 2*d**6/5 + 4*d**4/3 + 6*d. Determine f, given that h(f) = 0.
-2, 0, 1
Let w(p) = p**2 - p - 1. Let y(u) = -5*u**2 + 13*u - 9. Let k(z) = 6*w(z) + 2*y(z). Suppose k(s) = 0. What is s?
2, 3
Let o(k) be the third derivative of k**8/112 + 2*k**7/35 + k**6/10 + 15*k**2. Let o(q) = 0. What is q?
-2, 0
Let l(i) = i**3 + 5*i**2 + 4*i - 1. Let d be l(-4). Let n be (d + (-9)/(-8))*2. Factor p**3 + 0 + 3/4*p**4 + 0*p + n*p**2.
p**2*(p + 1)*(3*p + 1)/4
Let c be (10/(-6))/(2/48). Let a be (-26)/c - 2/5. Solve -a + 3/4*o + 1/4*o**3 - 3/4*o**2 = 0 for o.
1
Let y(w) be the third derivative of -w**7/40 - 19*w**6/160 - 3*w**5/16 - w**4/32 + w**3/4 - 4*w**2. Factor y(v).
-3*(v + 1)**3*(7*v - 2)/4
Let w(o) be the first derivative of o**6/6 + o**5/5 - o**4/4 - o**3/3 - 8. Factor w(t).
t**2*(t - 1)*(t + 1)**2
Find q, given that -4*q**4 - 9*q**2 + 18*q**3 - 10*q**4 + 5*q**2 = 0.
0, 2/7, 1
Let a(f) be the third derivative of 5*f**8/336 - f**7/14 + f**6/12 + f**5/6 - 5*f**4/8 + 5*f**3/6 + 15*f**2. Let a(u) = 0. What is u?
-1, 1
Find x, given that 12 - 9/5*x**2 - 84/5*x = 0.
-10, 2/3
Suppose -7*x = -3*c - 3*x + 28, -2*c + 5*x + 21 = 0. Let s = 10 - c. Factor -s*h**3 + h + 4*h + 0*h**3 + h**2 + 2.
-(h - 2)*(h + 1)*(2*h + 1)
Let u(o) be the third derivative of 0*o**5 + 1/3*o**3 - 1/105*o**7 - 1/6*o**4 + 1/30*o**6 + 0*o + 3*o**2 + 0. Factor u(m).
-2*(m - 1)**3*(m + 1)
Let u(l) be the third derivative of l**7/13860 + 7*l**4/24 + l**2. Let m(z) be the second derivative of u(z). What is x in m(x) = 0?
0
Let i = 99/190 - -3/38. Factor i*w - 3/5*w**3 - 1/5*w**2 + 2/5*w**4 - 1/5.
(w - 1)**2*(w + 1)*(2*w - 1)/5
Let i(s) be the third derivative of s**10/35280 + s**9/13230 + s**8/23520 - s**4/24 + 6*s**2. Let m(l) be the second derivative of i(l). Factor m(h).
2*h**3*(h + 1)*(3*h + 1)/7
Let d be 5/(-3)*(1 + -4). Find v such that 2*v**3 + v**d - 3*v**3 - v**4 + v**4 = 0.
-1, 0, 1
Let r(k) be the first derivative of -4*k**5 + 65*k**4/4 - 5*k**3 - 40*k**2 + 20*k + 14. Suppose r(v) = 0. What is v?
-1, 1/4, 2
Let u(g) be the first derivative of g**7/2940 + 4*g**3/3 + 4. Let b(m) be the third derivative of u(m). What is f in b(f) = 0?
0
Let n = -86/3 - -29. Let z = -1 + 5. Factor -n*y**z - 1/3*y + 0 - y**2 - y**3.
-y*(y + 1)**3/3
Let t(q) = q + 18. Let x be t(-15). Suppose -3*z - 4*m - 8 = -5*z, 2*m + 12 = 5*z. Factor 2/3 + z*g + 2/3*g**x + 2*g**2.
2*(g + 1)**3/3
Let x(o) = 4*o + 1. Let j be x(-1). Let y be ((-4)/j)/(-2)*-6. Factor 3*k**3 + 3*k - k**y - 2*k**3 - 4*k + k**2.
-k*(k - 1)**2*(k + 1)
Suppose -5*o - 16 = 2*k, -3*k + 5*o + 17 + 9 = 0. Solve -2*h**2 - h**3 - 2*h**k - 5*h + 4*h + 6*h**2 = 0 for h.
0, 1
Let r(j) be the second derivative of j**7/210 - j**6/50 + j**5/50 + 14*j. Factor r(z).
z**3*(z - 2)*(z - 1)/5
Let n(v) be the third derivative of -v**7/1260 - v**6/540 - v**3/2 - 2*v**2. Let p(k) be the first derivative of n(k). Suppose p(j) = 0. Calculate j.
-1, 0
Let k(u) be the third derivative of 0*u + 1/90*u**5 + 1/18*u**4 + u**2 + 0 + 1/9*u**3. Factor k(h).
2*(h + 1)**2/3
Suppose -5*z + 16 + 34 = 0. Suppose -z = 3*a - 8*a. Factor -l**2 - a*l**3 + 2*l + 1 + 3*l - 3*l.
-(l - 1)*(l + 1)*(2*l + 1)
Let i be (-76)/(-209)*(-22)/(-4). Determine q so that -2/7*q + 0 + 2/7*q**3 + 2/7*q**i - 2/7*q**4 = 0.
-1, 0, 1
Suppose 4*x - 40 = -0. Let w = x - 8. Suppose -300*z**2 - 153*z**3 - 375*z**4 + 24*z**w + 978*z**3 + 204*z - 24 - 354*z**2 = 0. Calculate z.
2/5, 1
Let n(i) = -7*i**4 + 82*i**3 - 448*i**2 + 1002*i - 627. Let r(z) = z**4 - z**3 - z**2 - z + 1. Let h(s) = -n(s) - 2*r(s). Factor h(u).
5*(u - 5)**3*(u - 1)
Let z(q) be the first derivative of -q**3/3 - 3. Solve z(o) = 0.
0
Factor -4/5*s**2 + 16/5*s + 0.
-4*s*(s - 4)/5
Suppose h = -5*n + 2*n + 27, 5*h = -4*n + 80. Suppose -7*x + h = -x. Factor -4/3*b - 2/3*b**x - 2/3.
-2*(b + 1)**2/3
Let z(n) be the third derivative of -n**8/1120 - n**7/210 - n**6/90 + n**5/20 - 9*n**2. Let l(q) be the third derivative of z(q). Suppose l(y) = 0. What is y?
-2/3
Factor 8/5*d**3 + 2/5 + 12/5*d + 18/5*d**2.
2*(d + 1)**2*(4*d + 1)/5
Let p = 2 - -2. Suppose -5*v + 9 = -i, -2*i + 2 - p = -2*v. Find h, given that -3*h**2 + h**v - 1 + 4*h + 3 + 4*h**2 = 0.
-1
Let p(q) be the third derivative of q**5/15 - q**4/3 + 2*q**3/3 + 18*q**2. Factor p(c).
4*(c - 1)**2
Let k(b) be the first derivative of 17*b**3/3 - 21*b**2/2 + 4*b + 1. Let f = -3 - 3. Let g(z) = 4*z**2 - 5*z + 1. Let x(y) = f*k(y) + 26*g(y). Factor x(p).
2*(p - 1)**2
What is a in -7*a + a**4 + 998*a**3 + a - 2*a - 993*a**3 - 4 - a**2 - a**5 = 0?
-1, 2
Let y = -3 + 1. Let g = 0 - y. Factor 2*h**g + 2*h**3 - 3*h**3 - h**3.
-2*h**2*(h - 1)
Suppose n = q + 7, 3*n + 2*q + 7 = 3. Suppose v = -0*v + n. Determine k, given that -3*k - k + 5*k**2 - 3*k**v = 0.
0, 2
Find g, given that 48*g**3 + 38*g**3 + 47*g**3 - 134*g**3 - 12*g - 8 - 6*g**2 = 0.
-2
Let j = -3 + 9. Let -h**2 + 2*h**2 + 2*h**2 - 3 + 6*h - j*h**2 = 0. Calculate h.
1
Let w(s) be the third derivative of 2/105*s**6 + 0 - 1/336*s**8 + 0*s**4 - 7*s**2 + 0*s - 1/105*s**5 - 1/294*s**7 + 0*s**3. Solve w(a) = 0.
-2, 0, 2/7, 1
Factor 5*i**2 - 2*i**2 + 11*i**3 + i**4 - 7*i**3.
i**2*(i + 1)*(i + 3)
Let p(b) be the first derivative of b**4/21 - 2*b**3/7 + 7*b - 9. Let s(g) be the first derivative of p(g). Factor s(v).
4*v*(v - 3)/7
Suppose -2*l + 2*t + 17 = 7*t, 0 = 2*l + 2*t - 8. Let s(b) be the first derivative of 10/21*b**3 + l - 2/7*b**2 + 0*b. Factor s(o).
2*o*(5*o - 2)/7
Let c(l) be the third derivative of -1/70*l**7 + 0*l**3 + 1/20*l**5 - 2*l**2 + 1/224*l**8 + 0 + 0*l + 0*l**6 - 1/16*l**4. Factor c(u).
3*u*(u - 1)**3*(u + 1)/2
Let b(x) be the second derivative of x**7/840 - x**6/360 - x**5/60 - x**3/6 + 4*x. Let o(y) be the second derivative of b(y). Factor o(k).
k*(k - 2)*(k + 1)
Factor 4 - 5 + 8*t - 4*t**2 - 2 - 1.
-4*(t - 1)**2
Let i be 8/(-12)*(0 - 2). Let x(s) be the first derivative of 3/2*s**2 - s + i*s**3 - 1. Determine u so that x(u) = 0.
-1, 1/4
Let d(j) be the third derivative of j**8/84 + j**7/210 - j**6/30 - j**5/60 + 8*j**2. Factor d(m).
m**2*(m - 1)*(m + 1)*(4*m + 1)
Let d = -208 + 1042/5. Factor -1/5*w**5 + 0*w**2 + 0*w + 1/5*w**4 + d*w**3 + 0.
-w**3*(w - 2)*(w + 1)/5
Let f(