00 + k**6/900 + k**4/12 + 2*k**2. Let u(f) be the second derivative of z(f). Find j such that u(j) = 0.
-1, 0, 1
Let s(a) = 7*a**2 - 5*a - 7. Let h(z) = 8*z**2 - 6*z - 8. Suppose -8*j + 6 = -7*j. Let i(f) = j*s(f) - 5*h(f). Factor i(g).
2*(g - 1)*(g + 1)
Let z = 4 - 2. Suppose 2*h + 2*h = -4*p + 12, h - z*p = 0. What is n in 7*n**5 - h*n + 9*n**4 - 5*n**3 - 9*n**2 + 0*n - 2 + 2 = 0?
-1, -2/7, 0, 1
Let r(g) be the second derivative of 5*g**7/42 - 7*g**6/30 + g**5/10 - g. Factor r(j).
j**3*(j - 1)*(5*j - 2)
Let c(n) be the first derivative of 2*n**3/33 + 3*n**2/11 - 8*n/11 - 2. Factor c(i).
2*(i - 1)*(i + 4)/11
Let b(n) = -15*n**2 - 51*n + 6. Let x(m) = 3*m**2 + 10*m - 1. Suppose i = -4*q + 16, -q = -6*q + 15. Let f(c) = i*b(c) + 21*x(c). Determine o so that f(o) = 0.
-1
Let t be (0 + (-20)/24)*(-6)/15. Let p(d) be the first derivative of d + d**2 - 2 + t*d**3. Factor p(o).
(o + 1)**2
Suppose -2 = -2*h + 2. Let -5*q**2 - 4*q + q**h + 2*q + 2*q**2 = 0. What is q?
-1, 0
Let c(h) be the third derivative of h**5/480 - h**4/96 + h**3/48 - 13*h**2. Factor c(v).
(v - 1)**2/8
Suppose 0 = -5*t - 14 - 16. Let v be 0 + 5 - (-18)/t. Determine o so that -92/9*o**3 - 2*o**5 - 20/3*o**2 - 2/9 - 22/3*o**4 - v*o = 0.
-1, -1/3
Find t such that -1/5*t**2 - 4*t - 20 = 0.
-10
Factor 1/2*q**3 - 9/2*q**2 - 8 + 12*q.
(q - 4)**2*(q - 1)/2
Let p(k) be the first derivative of 4/3*k**3 + 7/8*k**4 - 6 + 1/24*k**6 + 9/8*k**2 + 3/10*k**5 + 1/2*k. Factor p(i).
(i + 1)**4*(i + 2)/4
Let g(s) be the third derivative of -s**7/3360 - s**6/480 - s**5/160 - s**4/96 + s**3/6 + 2*s**2. Let p(o) be the first derivative of g(o). Factor p(z).
-(z + 1)**3/4
Let p(v) = v**2 + 8*v - 7. Suppose 0 = 2*o - 0*o - 4*s + 18, 0 = -3*o - s - 27. Let y be p(o). Factor -2*b**4 + 0*b**2 + 2*b - 2*b**3 + 0*b**y + 2*b**2.
-2*b*(b - 1)*(b + 1)**2
Let m = 191162939092/2849 - 67098258. Let o = 2/259 + m. Solve 18/11*v**5 + 14/11*v**2 - 34/11*v**3 - o + 16/11*v - 6/11*v**4 = 0 for v.
-1, 2/3, 1
Let t(i) be the first derivative of 250*i**6/21 - 10*i**5 - 15*i**4/7 + 88*i**3/21 - 8*i**2/7 + 2. Find c, given that t(c) = 0.
-1/2, 0, 2/5
Let r(l) = -l + 11. Let q be r(8). Factor 0*j**2 + 8*j**3 - 6*j**3 - q*j**2 - 3*j**3.
-j**2*(j + 3)
Let n(x) be the first derivative of 4 + 1/40*x**5 + 1/12*x**4 + 0*x**2 + 1/12*x**3 - 5*x. Let q(t) be the first derivative of n(t). Suppose q(u) = 0. What is u?
-1, 0
Let k be 4/1*(-3)/(-6). Let t = k - 0. Factor 0*x**t - 1/2*x + 0 + 1/2*x**3.
x*(x - 1)*(x + 1)/2
Let q(h) be the third derivative of h**7/70 + h**6/20 + h**5/20 + 7*h**2. Factor q(f).
3*f**2*(f + 1)**2
Let i = 17/14 + -23/42. Determine d so that 2/3*d - 2/9 + 2/9*d**3 - i*d**2 = 0.
1
Let k**2 + 22*k**4 + 2*k**5 + 3*k**3 - 19*k**4 - k**5 = 0. Calculate k.
-1, 0
Factor -12*l**4 + 633*l**3 - 4*l**5 + 3*l**2 - 4*l**2 - 645*l**3 - 3*l**2.
-4*l**2*(l + 1)**3
Let w be 5 + (-525)/119 + 2 + 4. What is n in w*n**4 + 2/17 + 146/17*n**3 + 86/17*n**2 + 32/17*n**5 + 22/17*n = 0?
-1, -1/4
Let m(l) = 4*l**3 - 4*l**2 + 3. Let u(n) = -1 + 3*n**3 - 3*n**2 + 6 - 3. Let y = -10 + 7. Let g(h) = y*u(h) + 2*m(h). Factor g(j).
-j**2*(j - 1)
Let v(r) = -25*r - 150. Let l be v(-6). Suppose -g + 5/2*g**3 + 3/2*g**2 + l = 0. What is g?
-1, 0, 2/5
Let t(n) = n**3 + n**2. Let s(a) = 7*a**3 + 10*a**2 - 2*a - 6. Let v(i) = s(i) - 6*t(i). Let q be v(-4). Factor 0*d**3 + 0*d - 1/4*d**4 + 0 + 1/4*d**q.
-d**2*(d - 1)*(d + 1)/4
Suppose -2/9*v**3 + 2/9*v - 2/9 + 2/9*v**2 = 0. Calculate v.
-1, 1
Let b(f) be the second derivative of f**7/42 - f**6/15 + f**4/6 - f**3/6 + f. Factor b(h).
h*(h - 1)**3*(h + 1)
Solve -4*y**4 - 4*y**3 - 3*y**2 + 14*y**5 - 6*y**5 - 4*y**5 + 7*y**2 = 0.
-1, 0, 1
Let x(f) = f**2 + f. Let o(n) = -n**3 - 2*n**2 + 2*n - 2. Let b be o(-3). Let l(c) = 2*c**2 + 8*c. Let a(s) = b*l(s) - 4*x(s). Factor a(u).
-2*u*(u - 2)
Suppose -3 + 18 = 5*n. Let q(f) be the first derivative of 5/6*f**6 + 23/15*f**n - 4/5*f - 11/5*f**5 - 4/5*f**2 + 1 + 19/20*f**4. Factor q(z).
(z - 1)**3*(5*z + 2)**2/5
Suppose -24 = -60*r + 54*r. Find v such that -r*v**2 + 0 - 15/4*v**3 - v = 0.
-2/3, -2/5, 0
Factor 6*p**5 - p**3 - 3*p**5 - 2*p**3.
3*p**3*(p - 1)*(p + 1)
Let z(s) = 7*s**2 - 7. Let d(a) be the first derivative of 13*a**3/3 - 13*a + 2. Let i(g) = -6*d(g) + 11*z(g). Factor i(m).
-(m - 1)*(m + 1)
Let j(o) be the second derivative of o**7/56 - o**6/20 + 3*o**5/80 - o. Find c, given that j(c) = 0.
0, 1
Solve -2 - 12*a - 4*a**2 + 18 + 0*a**2 = 0 for a.
-4, 1
Let t(z) = 5*z**3 + 9*z**2 + 3*z - 5. Let y(i) = -9*i**3 - 17*i**2 - 5*i + 9. Let c(n) = -11*t(n) - 6*y(n). Determine j, given that c(j) = 0.
1
Let d = 407/14 + -57/2. Let c = 6/7 - d. Determine a so that 2/7 + c*a - 12/7*a**2 + 10/7*a**4 + 4/7*a**3 - 6/7*a**5 = 0.
-1, -1/3, 1
Let f(k) be the second derivative of k**4/114 - 4*k**3/57 + 48*k. Factor f(g).
2*g*(g - 4)/19
Let l(s) be the third derivative of s**7/420 - s**5/40 - s**4/24 + 24*s**2. Let l(h) = 0. What is h?
-1, 0, 2
Let c(y) be the third derivative of y**7/490 - y**6/28 + 13*y**5/140 + 15*y**4/14 + 18*y**3/7 - 4*y**2. Solve c(q) = 0 for q.
-1, 6
Let t be 7*204/210 + -6. Find i such that t*i - 8/5 + 4/5*i**2 = 0.
-2, 1
Let b(m) be the first derivative of -m**3/12 - 3*m**2/8 - 3. Factor b(c).
-c*(c + 3)/4
Let c = 979 - 977. Factor 9/4*y**3 + 0*y**4 + 3/2*y**c - 3/4*y**5 + 0 + 0*y.
-3*y**2*(y - 2)*(y + 1)**2/4
Find z such that 6*z**2 + 3/4*z**4 - 27/4 + 9/2*z**3 - 9/2*z = 0.
-3, -1, 1
Let d(f) be the second derivative of f**7/8820 - f**6/1260 + f**5/420 + f**4/12 + 6*f. Let g(y) be the third derivative of d(y). Find p, given that g(p) = 0.
1
Suppose -3*t = t. Suppose t = -4*z + 2*z. Factor 0*d - 2/9*d**3 + 0 + z*d**2.
-2*d**3/9
Let v(s) = s**3 + s**2. Let j be v(-1). Suppose -4 = -j*n - n - w, -n + w + 2 = 0. Factor 5*m**4 - 7*m**3 + m**4 + 8*m**2 - 9*m**n - 2 + 4*m**2.
2*(m - 1)**3*(3*m + 1)
Let v be -7 + (-482)/(-96) + 2*1. Let s(y) be the second derivative of v*y**4 - 1/8*y**3 + 0 - y + 1/4*y**2. Determine p so that s(p) = 0.
1, 2
Let l = -16 + 22. Let d(m) be the third derivative of 0 + 0*m**3 + 0*m - 1/105*m**7 - 1/20*m**l - 1/10*m**5 - m**2 - 1/12*m**4. Solve d(w) = 0 for w.
-1, 0
Suppose -5*o - 1 + 6 = -u, o - 1 = -2*u. Let j = 4 - u. Factor 0*i + 0*i**2 + 1/2*i**5 + 0*i**j - 1/2*i**3 + 0.
i**3*(i - 1)*(i + 1)/2
Let k be 6 - (15/(-3) + 77/11). Factor 0*o**2 + 0 + 0*o + 1/6*o**3 - 1/6*o**k.
-o**3*(o - 1)/6
Let m(s) be the first derivative of s**4/4 + 5*s**3/3 + 26. Suppose m(b) = 0. What is b?
-5, 0
Let w = -965 + 967. What is m in 0 - 2/7*m - 4/7*m**3 + 5/7*m**w + 1/7*m**4 = 0?
0, 1, 2
Let c = 329/60 + -27/5. Let m(h) be the third derivative of 0*h + 1/16*h**4 + 1/120*h**5 - 1/80*h**6 - 2*h**2 - c*h**3 + 0. Suppose m(f) = 0. Calculate f.
-1, 1/3, 1
Determine u, given that 5*u + 4 + 3*u - 14*u**3 - 4*u**4 + 6*u**3 = 0.
-1, 1
Let x(i) = -2*i - 4. Let c be x(-4). Factor -9*o + o**4 - o**4 - 12 + 15*o**2 - 3*o**c + 9*o**3.
-3*(o - 4)*(o - 1)*(o + 1)**2
Factor -2/5*k**2 + k**3 - 3/5*k**4 + 0*k + 0.
-k**2*(k - 1)*(3*k - 2)/5
Suppose 0 = -4*y + 4*s - 7 - 5, -4*s + 14 = -5*y. Let p(c) = c**2 - c + 2. Let a(t) = -t**2 + t. Let i(j) = y*a(j) - p(j). Factor i(b).
(b - 2)*(b + 1)
Let f = 35 + 70. Let -f*m + m**3 + 2*m**3 + 93*m = 0. Calculate m.
-2, 0, 2
Let m(p) = -3*p**4 - p**3 - 2*p**2 + 2*p + 2. Let f(l) = -19*l**4 - 5*l**3 - 13*l**2 + 11*l + 13. Let h(t) = 6*f(t) - 39*m(t). Factor h(y).
3*y*(y - 1)*(y + 2)**2
Let r = 301 + -1203/4. Factor 1/2 + h**2 - r*h**3 - 5/4*h.
-(h - 2)*(h - 1)**2/4
Let m = -343 + 1385/4. Find p such that m*p**3 + 3*p**2 + 0 + 1/4*p**5 + 3/2*p**4 + p = 0.
-2, -1, 0
Let q(r) be the second derivative of -r**4/30 + 2*r**3/15 - r**2/5 + r. Factor q(c).
-2*(c - 1)**2/5
Let d be (6/9)/((-4)/(-18)). Suppose 0 = -d*z + 7*z - 8. Factor 3*v**z - 4*v + 6*v - v**2.
2*v*(v + 1)
Let x(s) = -s**3 - s + 1. Let n(v) = -6*v**3 - 4*v + 5. Let z(j) = -j**3 - 4*j**2 + 4*j - 4. Let i be z(-5). Let u(g) = i*n(g) - 5*x(g). What is a in u(a) = 0?
-1, 0, 1
Let u(m) be the third derivative of -m**8/840 + m**6/180 + m**3 - 5*m**2. Let n(c) be the first derivative of u(c). Factor n(p).
-2*p**2*(p - 1)*(p + 1)
Let u(c) be the third derivative of -c**8/1344 - c**7/840 + c**6/240 + c**5/120 - c**4/96 - c**3/24 + 16*c**2. Determine o so that u(o) = 0.
-1, 1