0
Let n(p) be the second derivative of p**7/280 + p**6/30 + 3*p**5/40 + p**3/6 + 2*p. Let u(q) be the second derivative of n(q). Factor u(j).
3*j*(j + 1)*(j + 3)
Factor 28 - m + m**3 + 9 - 16 - 21*m**2.
(m - 21)*(m - 1)*(m + 1)
Let t be ((2 + (-64)/28)*-4)/((-6)/(-21)). Factor -16/5 - 2/5*d**t - 8*d - 36/5*d**2 - 14/5*d**3.
-2*(d + 1)*(d + 2)**3/5
Let n be 52/(-4) - (924/(-63) + 1). Determine r, given that 0 + 4/3*r**2 - n*r**3 - 2/9*r**4 + 16/9*r = 0.
-4, -1, 0, 2
Let -27947 - 4*m**2 - 6*m + 2*m**3 + 0*m + 27947 = 0. Calculate m.
-1, 0, 3
Let v(b) = b**2 - 2*b - 1. Let j be v(4). Factor -j*t**3 + 2*t**3 + 18*t - 23*t + 10*t**2.
-5*t*(t - 1)**2
Let n be (126/(-30) - -5)*1/10. Let o(i) be the first derivative of n*i**5 + 2/5*i**3 - 3/10*i**4 + 4 + 0*i - 1/5*i**2. Factor o(g).
2*g*(g - 1)**3/5
Let s(o) = o**3 - 9*o**2 + 6 - 12 + 8*o + 8 + 0. Let i be s(8). Find q, given that -4/13 + 2/13*q**i + 2/13*q = 0.
-2, 1
Suppose -4*t + 12 = 2*y, t + 7*y - 2*y = 21. Suppose 5*g - 3 = -r + 14, 0 = -5*g + 15. Factor -r*u**3 - 16*u + 6*u**2 + 3 + t + 4 + 4*u**2.
-2*(u - 2)**2*(u - 1)
Let h = -5/288 + 61/1440. Let y(p) be the third derivative of -4*p**2 - 3/20*p**5 + 0*p - 1/4*p**4 - h*p**6 + 0*p**3 + 0. What is t in y(t) = 0?
-2, -1, 0
Let y = -45 + 63. Factor 3*a**3 + 38 - y - 20 - 3*a.
3*a*(a - 1)*(a + 1)
Factor -47 + 54 - 83 + 4*l**2 + 32*l - 104*l.
4*(l - 19)*(l + 1)
Let j(r) be the second derivative of r**6/120 - r**5/20 - 3*r**4/8 - 5*r**3/6 - 7*r**2/8 - 32*r. Determine g so that j(g) = 0.
-1, 7
Suppose 4*d + 9 - 27 = -5*o, 3*o + 4 = 5*d. Factor 19*w**d - 4*w**2 - 11*w**2.
4*w**2
Suppose -44 = -14*o + 12*o - 20*o. Determine n so that 2/9*n**3 - 2/9*n + 4/9 - 4/9*n**o = 0.
-1, 1, 2
Determine r so that -3*r**4 + 167*r + 2794*r**2 + 37*r**3 - 2659*r**2 - 4*r**4 + 6*r**4 + 4*r**4 + 42 = 0.
-7, -3, -2, -1/3
Determine y so that 1936/9*y + 0 + 4/3*y**5 + 1012/3*y**2 + 284/3*y**3 - 236/9*y**4 = 0.
-4/3, -1, 0, 11
Let r be ((-18)/(9/3))/(-2). Let j = -6 + r. Let l(v) = -v**3 + 3*v. Let i(y) = y. Let u(k) = j*l(k) + 6*i(k). Find d, given that u(d) = 0.
-1, 0, 1
Let a be (-3 + 7)/((-3)/18*4). Let p(v) = -5*v**3 - 13*v**2 - v + 7. Let r(o) = 11*o**3 + 27*o**2 + 3*o - 13. Let s(n) = a*r(n) - 14*p(n). Solve s(w) = 0.
-5, -1, 1
Let v = 1051/88620 - 2/211. Let g(q) be the third derivative of v*q**6 + 4*q**2 + 0 + 1/105*q**5 + 1/84*q**4 + 0*q + 0*q**3. Let g(u) = 0. What is u?
-1, 0
Let n be (-15)/(-20) + 9/4. Let i(l) be the first derivative of -6 + 0*l + 3/2*l**2 + 9/4*l**4 - n*l**3 - 3/5*l**5. Factor i(p).
-3*p*(p - 1)**3
Factor 109*y**2 + 1927 + y**4 - 15*y**3 - 252*y - 1731 - 3*y**3.
(y - 7)**2*(y - 2)**2
Let o(y) be the third derivative of -y**7/24 + 19*y**6/72 + y**5/4 + 5*y**3/2 + 3*y**2. Let t(q) be the first derivative of o(q). Factor t(n).
-5*n*(n - 3)*(7*n + 2)
Let s(c) = c**2 + c - 1. Let q(v) = -3*v - 3*v + 5*v - v**3 + 3*v. Let k(m) = q(m) - s(m). Determine i, given that k(i) = 0.
-1, 1
What is w in -2/13*w**5 - 2/13*w**4 - 60/13*w - 22/13*w**2 + 0 + 38/13*w**3 = 0?
-5, -1, 0, 2, 3
Let n(y) be the third derivative of y**7/525 + y**6/30 - 23*y**5/150 + y**4/5 + 37*y**2 + 2. Factor n(h).
2*h*(h - 1)**2*(h + 12)/5
Let c = -169 + 174. Suppose p + 4 = 4*o - p, c*p = -o + 12. Let 3/2*g**3 + 45/2*g - 21/2*g**o - 27/2 = 0. What is g?
1, 3
Suppose 5*i = 2*x + x - 26, -2*x + 16 = -3*i. Suppose -u + 0 + x = 0. Factor 4*z**2 + 3 + z**u + 7*z - 2*z**3 + 3*z**3.
(z + 1)**2*(z + 3)
Factor 309 + c**2 - 625 + 311 + 4*c.
(c - 1)*(c + 5)
Factor 64/3 - 4/3*r**3 - 44*r + 24*r**2.
-4*(r - 16)*(r - 1)**2/3
Let t(k) = k**2 - 14*k - 92. Let o be t(-5). Let i(v) be the third derivative of 0*v**4 + 1/60*v**5 + 0*v + 0*v**o + 0 - 5*v**2. Find x, given that i(x) = 0.
0
Let m(j) be the first derivative of j**5/10 - 3*j**3/2 + j**2 + 6*j + 166. Factor m(p).
(p - 2)**2*(p + 1)*(p + 3)/2
Let i be (4/6 - 1) + (-794)/(-204). Let k = i + -1/17. Factor 1/3 + k*y**3 + 4/3*y**2 - 11/6*y.
(y + 1)*(3*y - 1)*(7*y - 2)/6
Suppose -322 = -2*y + 4*x - 332, -11 = 3*y - 5*x. Factor -y*b**2 - 2/5*b + 0 + 16/5*b**4 - 24/5*b**3.
b*(b - 2)*(4*b + 1)**2/5
Let d be -3*(-348)/54 + -18. Find b such that 20/3*b**2 + 4*b - 12 + d*b**3 = 0.
-3, 1
Let 2/3*x**5 + 2/3*x - 4/3 + 8/3*x**2 - 4/3*x**3 - 4/3*x**4 = 0. What is x?
-1, 1, 2
Let l = 722 - 722. Let m(n) be the first derivative of 1/22*n**4 + 4/33*n**3 + 0*n + l*n**2 - 4. Determine u, given that m(u) = 0.
-2, 0
Suppose -5*b - 2*m = -24, 4*b - 24*m - 6 = -19*m. Let h(v) be the first derivative of 5/8*v**2 + 1/3*v**3 + 1/2*v - 4 + 1/16*v**b. Factor h(c).
(c + 1)**2*(c + 2)/4
Factor -882 + 32*p**3 - 201*p - 10*p**3 - 156*p + 40*p**2 - 11*p**3 - 12*p**3.
-(p - 21)**2*(p + 2)
Let t(f) = f**2 - f + 2. Let i be t(0). Let x be 23/i - 2/(-4). Suppose -12*h**3 - 2*h**5 - 4*h**5 + 3*h**2 + x*h**4 + 3*h**4 + 0*h**4 = 0. Calculate h.
0, 1/2, 1
Let h = 21788/3395 - 12/679. Factor -2/5*v**2 - 16/5*v - h.
-2*(v + 4)**2/5
Let o be (-1)/(1/4) - (93 - 101). Let a(j) be the first derivative of 10 + 1/2*j**o + 0*j + j**2 - 4/3*j**3. Determine m, given that a(m) = 0.
0, 1
Let h(p) be the third derivative of p**7/840 - p**6/36 + 3*p**5/40 - p**3/6 - 5*p**2. Let c(m) be the first derivative of h(m). What is t in c(t) = 0?
0, 1, 9
Let z = -86569/23 + 3767. Factor -252/23*t**3 + 8/23 - z*t + 218/23*t**2 + 98/23*t**4.
2*(t - 1)**2*(7*t - 2)**2/23
Let q(z) be the third derivative of -1/180*z**5 + 0 + 5/72*z**4 - 15*z**2 + 0*z**3 + 0*z. Factor q(n).
-n*(n - 5)/3
Suppose -3 = 4*v - 5*v. What is w in -9*w**4 + 2*w**5 - 3*w**2 + w**5 - 6*w**3 + 15*w**v = 0?
0, 1
Let d be 1/(-6) - 68/24. Let s be 3/(-4*d/16). Determine b so that -4*b**2 + s*b**2 + 2 + b**2 - 2*b - 1 = 0.
1
Let r(o) be the first derivative of o**4/22 + 18*o**3/11 - 90*o**2/11 - 501. Factor r(g).
2*g*(g - 3)*(g + 30)/11
Suppose -2*u + u = -6. Let v be (6/(-12))/(u/(-3)). Factor -1/4*z**2 + 1/2*z - v.
-(z - 1)**2/4
Let g(m) be the second derivative of -5/2*m**3 - 6*m - 9/2*m**2 - 7/12*m**4 - 1/20*m**5 + 0. What is d in g(d) = 0?
-3, -1
Let b(c) be the first derivative of 2*c**3/3 + c**2 - 4*c - 101. Suppose b(o) = 0. Calculate o.
-2, 1
Factor 118 - 164 - d**2 + 86 + 3*d.
-(d - 8)*(d + 5)
Let i = 8353/24 + -348. Let d(u) be the third derivative of 1/6*u**3 - 4*u**2 + 0 - 1/60*u**5 + 0*u - 1/120*u**6 + i*u**4. Solve d(l) = 0.
-1, 1
Let u be 4*(16 - 17) - 2*(-56)/12. Determine g so that -204*g**3 - 150*g**5 + 0 - 56*g**2 - 910/3*g**4 - u*g = 0.
-1, -2/5, -2/9, 0
Let l(f) be the first derivative of -f**3/3 + 2*f**2 - 4*f - 27. Factor l(k).
-(k - 2)**2
Suppose b = -30*b + 31. Let o(j) be the first derivative of -b - 2/11*j + 0*j**2 + 2/33*j**3. Find n such that o(n) = 0.
-1, 1
Let m be 1*((-8)/18)/(2/72*-4). Factor -2/15*g**m + 2/15*g**5 + 0 + 0*g + 0*g**2 + 0*g**3.
2*g**4*(g - 1)/15
Suppose 0 = 5*y - 2*d + 334, 30 = -y - 3*d - 30. Let r = y - -200/3. Factor 4/3*p + r*p**2 + 2/3.
2*(p + 1)**2/3
Let k(n) be the first derivative of 0*n - 8/21*n**3 - 2/7*n**5 - 12 + 25/21*n**6 - 8/7*n**4 + 0*n**2. Factor k(w).
2*w**2*(w - 1)*(5*w + 2)**2/7
Let v(f) be the second derivative of -f**6/33 + 9*f**5/55 - 7*f**4/66 - 2*f**3/11 - 18*f. What is g in v(g) = 0?
-2/5, 0, 1, 3
Let b be 4*(1 - 486/496). Let r = 13/31 + b. Factor 0*y**2 + r + 1/4*y**3 - 3/4*y.
(y - 1)**2*(y + 2)/4
Let g(r) be the third derivative of 0*r + 1/210*r**7 + 0 - 33*r**2 + 1/10*r**4 + 0*r**3 - 7/75*r**5 - 7/600*r**6. Factor g(n).
n*(n - 3)*(n + 2)*(5*n - 2)/5
Let r(c) be the first derivative of 6*c + c**3 - 14 + 9/2*c**2. What is q in r(q) = 0?
-2, -1
Let j(k) = -k**3 + k**2 - 2*k + 2. Let g(d) = -8*d**3 - 247*d**2 + 509*d - 254. Let x(h) = g(h) - 3*j(h). Factor x(b).
-5*(b - 1)**2*(b + 52)
Let b(k) be the first derivative of -k**3/18 + 55*k**2/6 - 3025*k/6 - 95. Factor b(q).
-(q - 55)**2/6
Factor -129*o + 67*o**2 + 3 + 31*o - 16*o**3 + 39*o**3 + 5.
(o - 1)*(o + 4)*(23*o - 2)
Let o(n) = 8*n**3 + 23*n**2 + 33*n + 23. Let b(t) = -9*t**3 - 24*t**2 - 33*t - 24. Let h(u) = 5*b(u) + 6*o(u). Factor h(q).
3*(q + 1)*(q + 2)*(q + 3)
Determine i so that 5/3*i**4 - i**3 + 0 + 4/3*i - 1/3*i**5 - 5/3*i**2 = 0.
-1, 0, 1, 4
Factor -n**3 + 5*n**3 + 89*n + n**3 + 16*n**2 - 160 - n**3 - 237*n.
4*(n - 5)*(n + 1)*(n + 8)
Let l be (32/(-132))/(10/(-15)). Factor 0 + 2/11*d**5 - 2/11*d + l*d**