et i(d) be the second derivative of d**7/5040 + d**6/1440 - d**4/4 - d. Let j(n) be the third derivative of i(n). Factor j(p).
p*(p + 1)/2
Let d be 1 - (1 - 9/6). Factor 0 + 2*c**3 + d*c**4 - 1/2*c**2 - c.
c*(c + 1)**2*(3*c - 2)/2
Suppose -28*p**4 - p**3 + 4*p**5 + 11*p**4 - 3*p**2 + 17*p**3 = 0. What is p?
0, 1/4, 1, 3
Let j(p) be the second derivative of -p**8/8960 - p**7/1680 - p**6/960 + p**4/12 - p. Let g(y) be the third derivative of j(y). Let g(d) = 0. What is d?
-1, 0
Let r be (-3)/(6/(-22)) + 1. Suppose 4*s - r = -2*g, -3*g - 2*g - 14 = -s. Suppose 4*h**s + 2*h - 17*h**4 - 9*h**3 + 4*h**2 - 5*h**5 - 3*h**2 = 0. What is h?
-1, 0, 2/5
Let j be (-6)/(1 + -3) - -2. Let l(h) be the third derivative of -1/240*h**j + 0 + 1/480*h**6 + 2*h**2 + 0*h + 0*h**3 + 0*h**4. Factor l(o).
o**2*(o - 1)/4
Let w = -38 + 65. Factor -29*j + 2*j**3 - 3*j**3 + w*j - 3*j**2.
-j*(j + 1)*(j + 2)
Factor -2/9*k - 2/9*k**2 + 4/9.
-2*(k - 1)*(k + 2)/9
Suppose 0 = 5*r - 9*v + 4*v + 10, -2 = -v. Let c be 28/30*4/((-8)/(-6)). Determine n, given that -4/5*n**4 - c*n**5 + 42/5*n**3 + 8*n**2 + 8/5*n + r = 0.
-1, -2/7, 0, 2
Let b(o) = -o + 1. Let w(s) = 2*s**2 + 4*s - 10. Let c(h) = -6*b(h) - w(h). Factor c(z).
-2*(z - 2)*(z + 1)
Let n(h) be the third derivative of 10*h**2 - 2/15*h**5 + 0*h**3 + 0*h + 1/12*h**4 + 0 + 1/20*h**6. Factor n(b).
2*b*(b - 1)*(3*b - 1)
Let h(t) be the second derivative of t**6/540 - t**5/90 - 5*t**3/6 + 4*t. Let f(k) be the second derivative of h(k). What is s in f(s) = 0?
0, 2
Let k(i) be the first derivative of -3*i**5/5 + 3*i**3 - 3*i**2 + 4. Suppose k(a) = 0. What is a?
-2, 0, 1
Let x(f) be the first derivative of -f**6/2 + 9*f**4/4 + 2*f**3 + 9. Factor x(b).
-3*b**2*(b - 2)*(b + 1)**2
Let p(v) = -v**3 + 5*v**2 + 2*v - 5. Let x be p(5). Suppose 0 = -0*l + 3*l - 3. What is m in -2*m**2 - x*m + l - 3 + m = 0?
-1
Let a(y) = 5*y**2 + 7*y - 3. Let b be ((-1)/(-3))/((-2)/(-18)). Let h(x) = 5*x**2 - 1 + 10*x - b*x - 3. Let t(u) = 6*a(u) - 5*h(u). Find z, given that t(z) = 0.
-1, -2/5
Let o be (0*(-7)/(-21))/(-1 + -1). Find t, given that o*t + 0 + 2/5*t**3 - 2/5*t**5 + 0*t**2 + 0*t**4 = 0.
-1, 0, 1
Suppose 24 = 6*j - 9*j. Let v be (-9)/(-6)*j/(-6). Factor 0*y**v - 4/5*y + 4/5*y**3 - 2/5 + 2/5*y**4.
2*(y - 1)*(y + 1)**3/5
Let z(h) be the second derivative of -h**6/165 - 3*h**5/55 - 13*h**4/66 - 4*h**3/11 - 4*h**2/11 + 4*h. Determine r so that z(r) = 0.
-2, -1
Let r be 2/36*(-18)/(-12). Let k(u) be the second derivative of -1/16*u**4 - u - r*u**3 + 1/8*u**2 + 0. Solve k(q) = 0 for q.
-1, 1/3
Let w(x) be the first derivative of x**4/4 + x**3 - 9*x**2/2 + 5*x - 25. Factor w(c).
(c - 1)**2*(c + 5)
Suppose -2*d - 6 = 0, d = 4*t - 2*d - 17. Factor t - 2*r**3 - 2*r - 4*r - 3*r**2 + 9*r**2.
-2*(r - 1)**3
Let h(d) be the third derivative of d**5/240 - d**4/32 + d**3/12 + 8*d**2. Suppose h(k) = 0. What is k?
1, 2
Let y(q) be the second derivative of -q**4/132 - q**3/11 - 9*q**2/22 + 3*q. Suppose y(a) = 0. What is a?
-3
Let u(q) be the second derivative of -q**7/840 + q**5/120 + q**3/3 - q. Let v(b) be the second derivative of u(b). Factor v(x).
-x*(x - 1)*(x + 1)
Let u(g) = g**2 + 5*g + 2. Let r be (3/1 + -2)*-7. Let v(w) = -5*w - 4 + w**2 - 4*w + 1 - 3*w**2. Let d(k) = r*u(k) - 4*v(k). Solve d(a) = 0 for a.
-2, 1
Let q be (0/((-2)/1))/(-2). Suppose 4*j - 5*j + 2 = 4*g, 0 = -j + 3*g + 2. Factor b**2 + 2 + q*b**j - 3.
(b - 1)*(b + 1)
Determine f, given that f**2 + 1/3*f**4 + f**3 + 0 + 1/3*f = 0.
-1, 0
Let f = -34 + 31. Let x be f/(-42) + (-12)/(-28). Suppose 1/4*j - 1/4*j**2 + x = 0. What is j?
-1, 2
Let l(w) = 2*w**4 - 3*w**3 + 5*w**2 - 5*w - 5. Let p(c) = -2*c**4 + 4*c**3 - 4*c**2 + 4*c + 4. Let r(u) = 4*l(u) + 5*p(u). Factor r(z).
-2*z**3*(z - 4)
Let d(f) be the second derivative of 7*f**4/54 + f**3/3 + 14*f. Factor d(p).
2*p*(7*p + 9)/9
Suppose -5*g**4 - 43*g**3 - 3*g**5 + 4*g**5 + 47*g**3 = 0. Calculate g.
0, 1, 4
Suppose 3*w - 2*c = -36, -4*w + 5*c + 8 = 63. Let m be 6/15 + (-1)/w. Factor 0*d + 0 + 3/2*d**4 - 3/2*d**3 + 1/2*d**2 - m*d**5.
-d**2*(d - 1)**3/2
Let w(q) = q**3 + 4*q**2 + 3*q. Let t be w(-3). Let h(i) be the first derivative of t*i**2 - 1/9*i**3 + 1/4*i**4 - 1 + 0*i + 1/18*i**6 - 1/5*i**5. Factor h(m).
m**2*(m - 1)**3/3
Let -24*a + 20 + 3*a**4 - 12 - 2*a**4 + a**4 - 12*a**3 + 26*a**2 = 0. What is a?
1, 2
Let j(v) = -v**3 + v**2. Let o(r) = r + 3. Let k be o(-5). Let b(g) = -g**3 + g**2 - g + 1. Let t(f) = k*j(f) + b(f). Factor t(u).
(u - 1)**2*(u + 1)
Suppose 5*p - 6 = -1. Let w be (-8 + 12)/(p - -1). What is i in 2/9 + 8/9*i**3 + 8/9*i + 2/9*i**4 + 4/3*i**w = 0?
-1
Let f(d) be the third derivative of -5*d**8/336 + d**7/21 - d**6/24 + 11*d**2. Solve f(s) = 0.
0, 1
Factor 1/3*i**2 - 2/3*i - 1.
(i - 3)*(i + 1)/3
Let h(u) = u**2 + 8*u - 1. Let o(z) = -4*z**2 - 33*z + 5. Let q(y) = -9*h(y) - 2*o(y). Let j be q(-5). Factor 4*i + 3*i**2 - i - j*i - 2*i**2.
i*(i - 1)
Suppose 11*g**2 + 11*g**2 - 24*g**2 + g + g = 0. What is g?
0, 1
Let s be (-58)/120 + 7/2 + -3. Let c(m) be the second derivative of -1/18*m**4 + 1/3*m**2 + 0 + 1/18*m**3 - m - s*m**5. Solve c(i) = 0 for i.
-2, -1, 1
Let z(s) = -2*s**3 - 4*s**2 - 2*s + 1. Let a be z(-2). Suppose 4*b = d + 14, -a*d = -8*b + 3*b + 25. Factor -9*q - 2 - 4*q + b*q - 8*q**2.
-2*(q + 1)*(4*q + 1)
Let q = 25 - 23. Factor 0*b + 0 - 2/5*b**q + 2/5*b**4 + 0*b**3.
2*b**2*(b - 1)*(b + 1)/5
Suppose 4*d - 59 = -3*v, 4*d + 0*v + 5*v - 69 = 0. Let z = d - 11. Factor z + 0*i + 10/9*i**3 - 2/3*i**2.
2*i**2*(5*i - 3)/9
Let o(c) be the third derivative of 0 - 7/120*c**6 + 2*c**2 + 7/24*c**4 + 1/70*c**7 - 1/3*c**3 + 0*c - 1/60*c**5. Solve o(g) = 0.
-1, 1/3, 1, 2
Let m(c) be the third derivative of -c**11/110880 + c**10/16800 - c**8/1680 + 2*c**5/15 + 3*c**2. Let l(p) be the third derivative of m(p). Factor l(z).
-3*z**2*(z - 2)**2*(z + 1)
Let p(l) be the third derivative of l**8/1344 - l**6/480 - 11*l**2. Solve p(g) = 0.
-1, 0, 1
Let k(t) = -t**3 - 4*t**2 - 4*t + 1. Let g be k(-4). Find p such that g*p**2 + 2*p**4 + p**4 - 14*p**2 + 6*p**3 = 0.
-1, 0
Determine c so that -7*c**3 - 3*c**3 - 12*c**2 + 2*c**3 + 17*c**4 + 158*c**5 - 163*c**5 = 0.
-3/5, 0, 2
Suppose o - 25 = -x - 19, x = -5*o + 18. Factor 1/6*z + 19/6*z**o - 1/3 + 7/6*z**4 + 5/2*z**2.
(z + 1)**3*(7*z - 2)/6
Let f(y) = -1 + 5*y - 4*y + 3. Let c be f(0). Determine t so that t**5 - 6*t**3 + t**5 + 0*t**2 + 4*t**c = 0.
-2, 0, 1
Let k(r) be the third derivative of -r**8/588 + r**6/105 - r**4/42 + 7*r**2. Solve k(g) = 0.
-1, 0, 1
Let u(l) be the second derivative of -l**6/45 + l**5/15 - 2*l**3/9 + l**2/3 - 7*l. Find n, given that u(n) = 0.
-1, 1
Let d = 12 + -8. Let i be 18/20 + d/(-10). Factor -7/2*k**2 + i - k - 2*k**3.
-(k + 1)**2*(4*k - 1)/2
Let z(p) = 2*p**4 + 2 + 1 - 6 - p**2 - 4*p**4. Let u(m) = 3*m**4 - m**3 + 2*m**2 + 4. Let s(n) = 3*u(n) + 4*z(n). Factor s(c).
c**2*(c - 2)*(c - 1)
Let s(x) be the third derivative of x**8/2016 + x**7/252 + x**6/72 + x**5/36 + 5*x**4/144 + x**3/36 + 17*x**2. Factor s(q).
(q + 1)**5/6
Factor -2*p**2 + 78*p - 12 - 62*p - 2*p**2.
-4*(p - 3)*(p - 1)
Factor 0*b - 3/7*b**4 + 3/7*b**3 + 6/7*b**2 + 0.
-3*b**2*(b - 2)*(b + 1)/7
Suppose -3*q = 4*i - 20, 26 = -4*i - q + 38. Factor 2/5*y**i + 0*y + 2/5*y**4 - 4/5*y**3 + 0.
2*y**2*(y - 1)**2/5
Let i(n) = -n**2 - 5*n - 2. Let f be i(-5). Let x = f - -5. Factor 2 + t**3 + 0*t - 2*t**2 + 2*t - x*t.
(t - 2)*(t - 1)*(t + 1)
Let z(a) be the third derivative of a**6/720 - a**5/360 - a**4/72 - 6*a**2. Find j, given that z(j) = 0.
-1, 0, 2
Let r(s) be the third derivative of -s**7/210 + s**5/30 - s**3/6 + 5*s**2. Factor r(b).
-(b - 1)**2*(b + 1)**2
Let k(r) = 30*r**2 - 30*r + 18. Let o(b) = -15*b**2 + 14*b - 9. Let q(c) = 5*k(c) + 9*o(c). Factor q(s).
3*(s - 1)*(5*s - 3)
Suppose -g = -8*g. Factor g - 2*f**3 + 4/9*f**2 + 0*f.
-2*f**2*(9*f - 2)/9
Let n = 18 - 12. Let w(j) = 2*j**3 + 12*j**2 + 8. Let s(y) = 0*y + 1 - y + y**2 + 0*y. Let v(u) = n*s(u) - w(u). Factor v(b).
-2*(b + 1)**3
Let v(m) = -2*m**3 + 4*m**2 - 9*m. Let q(l) = -2*l**3 + 4*l**2 - 8*l. Let h = -9 + 0. Let u = h - -16. Let x(f) = u*q(f) - 6*v(f). Factor x(w).
-2*w*(w - 1)**2
Let t(o) = o**3 + o**2 - o. Suppose -20 = -4*j + x - 4, 5*j - x = 20. Suppose -j*g + g + 6 = 0. Let n(f) = -2. Let m(z) = g*t(z) + n(z). Factor m(u).
2*(u - 1)