
5*(c - 9)**3
Let t(z) be the third derivative of z**8/672 + z**7/210 - z**6/240 - z**5/60 - 18*z**2. Determine h, given that t(h) = 0.
-2, -1, 0, 1
Let o = -281 - -283. Factor 0 - 2/3*u - 2/3*u**3 - 4/3*u**o.
-2*u*(u + 1)**2/3
Let d be -76 + 3/((-15)/(-5)). Let n be 5*(-3)/d - -1. Factor -n*t**3 - 1/5*t**5 + 0 - 4/5*t**4 - 1/5*t - 4/5*t**2.
-t*(t + 1)**4/5
Let i(q) = 4*q**2 - 3*q + 3. Let o(h) = -h**2 - 8*h - 5. Let m be o(-5). Let d(p) = -7*p**2 + 5*p - 5. Let z(x) = m*i(x) + 6*d(x). Solve z(v) = 0.
0
Suppose t + 6 = q, 17*t - 21*t = 4. Solve 32/7*k - 2*k**4 + 2/7*k**q - 8/7 - 50/7*k**2 + 38/7*k**3 = 0 for k.
1, 2
Let z = -23907057/260 + 91950. Let p = 2/65 - z. Factor -p*a**2 + 1/2*a + 0.
-a*(a - 2)/4
Suppose -5 + 1 = -z. Find t such that -8*t**3 - 6*t**4 + 4*t**3 + z*t + 4*t**2 + 2 - 2*t**5 + 2*t = 0.
-1, 1
Let g(f) be the first derivative of -4/5*f**5 + 0*f + 0*f**4 + 1 + 0*f**2 + 0*f**3 + 1/3*f**6. Let g(k) = 0. Calculate k.
0, 2
Let b be (2/(-2))/((-3)/6). Let z(i) be the first derivative of 14*i**b + 4*i - 2 + 16/5*i**5 - 14*i**4 + 11*i**3. Determine o, given that z(o) = 0.
-1/4, 2
Let d = 8 - 12. Let l be (0 + 3 + d)*-2. Factor 0 - 4/3*k + 2/3*k**l.
2*k*(k - 2)/3
Let m be 2 - (4/2)/(-2). Let r be 1 - (0 - 2 - -1). Solve -6*d**4 + 5*d**4 - r*d**3 + 3*d**m = 0 for d.
0, 1
Let h = 0 - 3. Let c = h - -6. Let -3*z**2 + 14*z + 4 + 0 - z**2 - 14*z**c = 0. Calculate z.
-1, -2/7, 1
Let t(a) be the third derivative of a**6/20 - 2*a**5/15 - 5*a**4/12 + 2*a**3/3 + 8*a**2. Factor t(l).
2*(l - 2)*(l + 1)*(3*l - 1)
Let r(n) be the second derivative of -n**7/224 - n**6/480 - n**3/6 + n. Let l(y) be the second derivative of r(y). Factor l(o).
-3*o**2*(5*o + 1)/4
Let u(y) be the third derivative of -y**8/10080 + y**7/1260 - y**6/360 - y**5/20 + 2*y**2. Let c(h) be the third derivative of u(h). Factor c(q).
-2*(q - 1)**2
Let l(z) = z**3 + z**2 - z. Let y(o) = 4*o**3 + 12*o**2 - 10*o. Suppose -2*g + 0*g - 12 = 0. Let b(q) = g*l(q) + y(q). Factor b(n).
-2*n*(n - 2)*(n - 1)
Let t = -200 - -1802/9. Solve -2/9*h**3 - t - 2/3*h - 2/3*h**2 = 0 for h.
-1
Let i(y) be the third derivative of 1/3*y**3 + 0*y + 1/360*y**6 + 0 - 1/24*y**4 + 0*y**5 + y**2. Let v(h) be the first derivative of i(h). Solve v(o) = 0.
-1, 1
Find t, given that -2*t**2 - 17*t - 6*t**3 + 8*t + 6*t + 11*t**2 = 0.
0, 1/2, 1
Let a(r) = 3*r**5 + 8*r**4 + 2*r**3. Let g(q) = -q**4. Let x(f) = -4*a(f) - 4*g(f). Factor x(w).
-4*w**3*(w + 2)*(3*w + 1)
Let o be 6/4 - (-6)/12. Let k be o + (-2 + 1)*-1. Let 8*x**2 - 7*x + 14*x**k + 16*x**3 - x = 0. Calculate x.
-2/3, 0, 2/5
Let u(t) = 10*t + 8. Let b be u(7). Let h be (-12)/b - (-2)/13. Solve -2/5*l**2 + 2/5 + h*l = 0 for l.
-1, 1
Suppose 2*d + 2 + 1 = -i, -4*d + i = -3. Suppose 3*y + 6 = 0, d = 2*s + 5*y - 3*y. Determine g so that -g**3 + 0*g**3 + 0*g**3 - s*g**5 + 3*g**3 = 0.
-1, 0, 1
Let z(p) be the third derivative of -p**7/105 - 2*p**6/75 - p**5/150 + p**4/30 - 2*p**2. Factor z(n).
-2*n*(n + 1)**2*(5*n - 2)/5
Let t = 16 - 10. Determine c, given that 4 - 2*c**2 + 0*c - t*c + 4*c**2 + 0*c = 0.
1, 2
Let b(t) be the second derivative of 0*t**2 + 0*t**3 + 1/4*t**4 + 3/10*t**6 + 0 - 9/20*t**5 + t - 1/14*t**7. Factor b(m).
-3*m**2*(m - 1)**3
Let l(b) be the second derivative of -b**6/150 - b**5/50 + b**4/20 + 2*b**3/15 - 2*b**2/5 + 29*b. Let l(i) = 0. Calculate i.
-2, 1
Let x be 5 - (-9 + 5 - -6). Let n(y) be the second derivative of 1/4*y**2 + 1/8*y**4 - 1/40*y**5 - 1/4*y**3 - x*y + 0. Factor n(o).
-(o - 1)**3/2
Let p(a) be the third derivative of 5*a**8/336 - 5*a**7/21 + 25*a**6/24 + 5*a**5/3 - 50*a**4/3 - 160*a**3/3 + 14*a**2. Factor p(b).
5*(b - 4)**3*(b + 1)**2
Suppose 13*i - 4 = 9*i. Factor 3/4*f**2 - i - 1/4*f**3 + 0*f.
-(f - 2)**2*(f + 1)/4
Suppose i - 6 = -0. Let l = -3 + i. Factor 2*g**4 - g**l - 3*g**3 + 10*g**2 - 4*g - 4*g**3.
2*g*(g - 2)*(g - 1)**2
Let j be (1 + -5)*(3 - 15/4). Solve 3/2 + j*p + 3/2*p**2 = 0.
-1
Suppose 2*x = -4*z - 8, -x - z - 7 = 2*z. Let w be 10/(-15) + 84/99. Factor -w*u**x + 0 + 4/11*u.
-2*u*(u - 2)/11
Let k(l) = -2*l + 2. Let f be k(-2). Suppose -f = -h - 2. Factor 4/3*p**h + 0*p + 2/3*p**3 + 0 + 0*p**2 + 2/3*p**5.
2*p**3*(p + 1)**2/3
Let x(u) be the third derivative of -u**7/210 + u**6/60 + u**5/20 - u**4/6 - 2*u**3/3 + 4*u**2. Suppose x(o) = 0. What is o?
-1, 2
Let f(q) = q**4 - q**3 + 1. Let j(h) = 5*h**4 - 6*h**3 + h**2 + 6. Let k be -3*(-3)/9*1. Let n(i) = k*j(i) - 6*f(i). Factor n(s).
-s**2*(s - 1)*(s + 1)
Let l = 599/447 + -1/149. Suppose 4/3*y**4 + 0 + 10/3*y**3 - l*y**2 - 10/3*y**5 + 0*y = 0. What is y?
-1, 0, 2/5, 1
Let t(h) = h**3 + h + 4. Suppose 0*c = 4*c. Let z be t(c). Factor -2/5*q**z - 2/5*q**3 + 4/5 + 6/5*q**2 + 2*q.
-2*(q - 2)*(q + 1)**3/5
Let c(k) be the second derivative of k**4/30 - 8*k**3/15 + 16*k**2/5 - 23*k. Determine h so that c(h) = 0.
4
Let r = 295 - 294. Factor 1/2*p**2 + r - 3/2*p.
(p - 2)*(p - 1)/2
Let a be (8 + 4)/(-4) + 3. Solve a + 1/2*b**2 + b = 0 for b.
-2, 0
Suppose 3*h = 4*h + 2, -3*l - 2*h = 4. Let 2/3*a + 0*a**2 + l - 2/3*a**3 = 0. Calculate a.
-1, 0, 1
Let r be 1/99*(1 - 0). Let w = r - -493/198. Factor -1 - w*h**3 + h**2 + 5/2*h.
-(h - 1)*(h + 1)*(5*h - 2)/2
Let w(r) be the second derivative of -1/9*r**4 + 0 - 1/9*r**3 + r - 1/30*r**5 + 0*r**2. Factor w(f).
-2*f*(f + 1)**2/3
Find q, given that 1/4*q + 1/4 - 1/4*q**3 - 1/4*q**2 = 0.
-1, 1
Let m be (-6482)/(-90) + (-3)/(-15). Solve -2/9 - 212/9*f**2 + 250/9*f**5 + 580/9*f**3 - m*f**4 + 34/9*f = 0 for f.
1/5, 1
Suppose 2*z + 2*z = 12. Let n be 55/88*4/10. Factor 1/4*d**z - n*d**2 + 1/4 - 1/4*d.
(d - 1)**2*(d + 1)/4
Find h such that -1/9*h**4 - 2/3*h**3 - 4/9 - 4/3*h - 13/9*h**2 = 0.
-2, -1
Let s(q) be the first derivative of -2*q**6/3 - 28*q**5/5 - 15*q**4 - 12*q**3 - 12. Factor s(u).
-4*u**2*(u + 1)*(u + 3)**2
Let b(i) = 3*i**2 - i - 2. Let k(u) = 2*u**2 - 2. Let n(h) = -4*b(h) + 5*k(h). Suppose n(j) = 0. What is j?
1
Let z(v) be the first derivative of -1/12*v**6 + 3 + 0*v**4 + 1/4*v**2 - 1/5*v**5 + 0*v + 1/3*v**3. Factor z(o).
-o*(o - 1)*(o + 1)**3/2
Let 4*o**2 - 8/3*o**3 + 2/3*o - 4/3 + 2*o**5 - 8/3*o**4 = 0. Calculate o.
-1, -2/3, 1
Let a(g) be the third derivative of -2*g**7/105 + g**6/30 + g**5/15 - g**4/6 - 10*g**2. Suppose a(q) = 0. What is q?
-1, 0, 1
Let o(r) be the second derivative of 0 + 2/5*r**6 + 0*r**2 + r**4 - 8/5*r**5 - 6*r + 4/3*r**3. Factor o(n).
4*n*(n - 2)*(n - 1)*(3*n + 1)
Suppose 0*y + 5*y + 56 = -m, -2*y + 5*m - 44 = 0. Let c be (y/(-18))/((-8)/(-6)). Suppose 1/2*w**3 + c*w**2 - 1/2 - 1/2*w = 0. Calculate w.
-1, 1
Suppose 11*k**2 - 6*k**2 - 2*k**3 - 7*k**2 + 8*k + 8 = 0. What is k?
-2, -1, 2
Suppose -h + 20 = 4*h. Let b(m) = -9*m - 151. Let w be b(-17). Suppose 0*r**w - 1/6*r + 0*r**h + 0 + 1/3*r**3 - 1/6*r**5 = 0. What is r?
-1, 0, 1
Let n be 6/(-24) + (-22)/(-40). Let a(o) be the second derivative of 0 + 2/5*o**2 + n*o**4 - 2*o - 11/15*o**3. Let a(w) = 0. What is w?
2/9, 1
Let p be 4/(-20) + 3/(2 + 13). Let m(l) be the second derivative of -1/20*l**5 + 0*l**4 + 1/28*l**7 + 0*l**2 + 0*l**3 - 1/60*l**6 + 4*l + p. Factor m(d).
d**3*(d - 1)*(3*d + 2)/2
Let t = 52 - 49. Let w(g) be the second derivative of 1/3*g**3 - g**2 - 1/5*g**5 - t*g + 1/3*g**4 + 0 - 1/15*g**6 + 1/21*g**7. Factor w(a).
2*(a - 1)**3*(a + 1)**2
Let z(j) be the second derivative of -j**5/40 - j**4/4 + 5*j**3/4 - 2*j**2 + 4*j. Let z(g) = 0. Calculate g.
-8, 1
Factor -4*x**2 - 2*x + 5*x - 4 + 5*x.
-4*(x - 1)**2
Let d(r) be the second derivative of 2*r**2 + 0 - 1/15*r**6 + 3/10*r**5 - 7*r - r**3 - 1/6*r**4. Determine s so that d(s) = 0.
-1, 1, 2
Let k(x) be the second derivative of -5*x**7/14 + 3*x**6/10 + 51*x**5/20 + x**4/4 - 6*x**3 - 6*x**2 + x. Solve k(v) = 0.
-1, -2/5, 1, 2
Let b(c) be the third derivative of -c**6/660 - c**5/330 + c**4/132 + c**3/33 - 9*c**2. Factor b(j).
-2*(j - 1)*(j + 1)**2/11
Let c(m) be the first derivative of m**6/30 - m**5/25 - 3*m**4/20 + m**3/15 + m**2/5 - 8. Factor c(a).
a*(a - 2)*(a - 1)*(a + 1)**2/5
Let n(z) be the second derivative of -z**5/5 + 2*z**4/3 - 2*z**3/3 - 7*z. Determine u, given that n(u) = 0.
0, 1
Let x(j) be the third derivative of -j**7/945 + j**6/108 - j**5/30 + 7*j**4/108 - 2*j**3/27 - 9*j**2. Factor x(c).
-2*(c - 2)*(c - 1)**3/9
Let o(u) be the first derivative of u**4/4 - u**3 + 4*u + 