a - 2*q, -a - 3*q + 12 = 0. Let r(p) be the first derivative of -1/10*p**2 - a + 0*p - 1/20*p**4 - 2/15*p**3. Factor r(n).
-n*(n + 1)**2/5
Suppose -7*r - 760 = -15*r. Suppose -4 - 23*p**2 - 15 - r*p + 20*p**3 - 1 - 32*p**2 = 0. Calculate p.
-1, -1/4, 4
Let j(l) be the second derivative of -l**7/42 + l**6/30 + 11*l**5/20 - 29*l**4/12 + 13*l**3/3 - 4*l**2 + 55*l. Determine a, given that j(a) = 0.
-4, 1, 2
Let j(w) be the second derivative of w**7/735 + 2*w**6/105 + w**5/30 + 24*w**2 + 2*w + 10. Let u(x) be the first derivative of j(x). What is t in u(t) = 0?
-7, -1, 0
Suppose -8/19 - 2/19*u**2 + 10/19*u = 0. Calculate u.
1, 4
Let a(d) = d**2 + 6*d + 2. Let h be a(-9). Let t = h - 24. Factor -t*j + 4*j**3 - 3*j + 4*j - 4*j + 4*j**2.
4*j*(j - 1)*(j + 2)
Let l(k) be the second derivative of -4/27*k**3 + 2/27*k**4 + 0*k**2 - 20*k + 0 - 1/90*k**5. Factor l(o).
-2*o*(o - 2)**2/9
Factor 0 - 1/5*q**2 + 18/5*q.
-q*(q - 18)/5
Factor -34/13*r**2 - 96/13 - 128/13*r - 2/13*r**3.
-2*(r + 1)*(r + 4)*(r + 12)/13
Let q = 5302 - 5299. Suppose q*z + 1/5*z**3 + 7/5 + 9/5*z**2 = 0. Calculate z.
-7, -1
Let s(j) = -j**2 + 18*j + 4. Let z be s(18). Suppose 1 + z*p - 19*p**2 + 17*p**2 - 1 = 0. Calculate p.
0, 2
Let k be 3*((-110)/270)/(-11). Let l(x) be the second derivative of -6*x + 1/36*x**4 - 1/2*x**2 + k*x**3 + 0. Factor l(p).
(p - 1)*(p + 3)/3
Solve -35/3*w**3 + 0 + 8*w - 4/3*w**4 + 5/3*w**5 - 2/3*w**2 = 0.
-2, -1, 0, 4/5, 3
Let i(h) = h**3 - 22*h**2 - 23*h + 2. Let g be i(23). Factor 6*t**3 + t**5 - g*t**4 - t**3 - 8*t**3.
t**3*(t - 3)*(t + 1)
Let b be (3 - -2) + (104/16)/(9/(-6)). Factor -2/5*l**3 + 2/15 - 2/15*l - b*l**2.
-2*(l + 1)**2*(3*l - 1)/15
Suppose 7*l + 5 - l**2 - 17 - l**2 - 21*l + 0 = 0. What is l?
-6, -1
Suppose -3*q = 2*z + 10, -22 = -3*z + 2*q + 2. Let t = -43 - -389/9. Factor -2/9*v**2 - 2/3*v**3 + 0 + 0*v - t*v**5 - 2/3*v**z.
-2*v**2*(v + 1)**3/9
Suppose -2*g = -3*y - 9 + 2, -g + y + 2 = 0. Let m(z) = -3*z**3 + 5*z**2 + 4*z + 6. Let l(f) = -f**2 + f. Let i(o) = g*m(o) - 5*l(o). Factor i(w).
3*(w - 2)*(w + 1)**2
Let w(x) be the third derivative of x**7/8820 + x**6/1260 + x**5/420 + 5*x**4/6 - 5*x**2. Let y(d) be the second derivative of w(d). Factor y(j).
2*(j + 1)**2/7
Let r(h) be the third derivative of 0*h**3 - 1/15*h**5 + 0 + 0*h + 1/6*h**4 + 12*h**2. Factor r(q).
-4*q*(q - 1)
Let r(x) = x**2 - 136*x - 127. Let b(c) = -68*c - 64. Let w(z) = -5*b(z) + 2*r(z). Factor w(k).
2*(k + 1)*(k + 33)
Let l be (-64)/(-48)*6/4 - -1. Suppose 0 = -l*b + 13 + 2. Factor 4/5*y**2 - 2/5 + 2/5*y**b + 2/5*y - 4/5*y**3 - 2/5*y**4.
2*(y - 1)**3*(y + 1)**2/5
Let u(g) be the second derivative of -g**6/180 - g**5/24 - g**4/9 - g**3/9 - 3*g + 1. Determine n so that u(n) = 0.
-2, -1, 0
Let m be 2/3 + (-49)/(-21). Let -9*x**3 - 9*x**2 - 15*x - 4*x**m - 11*x**2 + 8*x**3 = 0. Calculate x.
-3, -1, 0
Determine n so that -2/7*n + 12/7 - 2/7*n**2 = 0.
-3, 2
Let y = 1131 + -7899/7. Let t be -2 - 780/(-378) - 9/((-324)/8). Suppose -12/7*r - y - t*r**2 = 0. Calculate r.
-3
Factor 2*z - 9*z**3 + 0 - 33/4*z**2 + 5/4*z**4.
z*(z - 8)*(z + 1)*(5*z - 1)/4
Let h = 318 + -315. Let l(o) be the first derivative of 4 - 6*o - 15/4*o**4 - 21/2*o**2 - 3/5*o**5 - 9*o**h. What is c in l(c) = 0?
-2, -1
Let b(c) be the first derivative of 5/4*c**4 + 0*c + 20/3*c**3 - 27 + 15/2*c**2. Solve b(p) = 0.
-3, -1, 0
Let p = 1/32 - -79/32. Let c be 0 + (3 + -1 - 0). Find j such that p*j**2 + c - 4*j - 1/2*j**3 = 0.
1, 2
Let p be -3*3/((-9)/7). Let a = p + -4. Factor n + 5*n + a*n - 8*n - n**3.
-n*(n - 1)*(n + 1)
Let g(q) = -3*q**4 - 9*q**3 + 7*q. Suppose 5*k - 24 = 1. Let u(s) = -3*s**4 - 9*s**3 + 8*s. Let l(d) = k*u(d) - 4*g(d). Find z, given that l(z) = 0.
-2, 0, 1
Let d be (-6 - (-174)/30) + (-5326)/(-30). Let a = 178 - d. Factor 1/3*i**2 - i + a.
(i - 2)*(i - 1)/3
Let n(y) be the third derivative of -9*y**7/1960 - y**6/840 - 23*y**3/6 + 18*y**2. Let p(z) be the first derivative of n(z). Factor p(c).
-3*c**2*(9*c + 1)/7
Let s(w) = w + 0 - 2 - 4 - 1. Let z be s(7). Factor -13*g**2 + 6 + 3*g + z*g + 7*g**2 - 3*g**3.
-3*(g - 1)*(g + 1)*(g + 2)
Let t(s) be the third derivative of -s**6/240 - s**5/40 + s**4/3 - s**3 - 78*s**2. Factor t(q).
-(q - 2)*(q - 1)*(q + 6)/2
Let s(b) be the third derivative of -b**6/120 + 3*b**5/20 + 27*b**4/8 - 243*b**3/2 - b**2 - 245. Find m, given that s(m) = 0.
-9, 9
Let b(q) be the first derivative of 10*q**6/3 + 16*q**5/5 - 21*q**4 - 64*q**3/3 + 8*q**2 - 303. Suppose b(n) = 0. What is n?
-2, -1, 0, 1/5, 2
Suppose -5*k = i + 2*i + 15, 15 = -5*k - 4*i. Let o(c) = 3*c**2 + 8*c - 3. Let v be o(k). Solve -1/3*s**3 + 0*s**2 + v*s**4 + 0 + 0*s + 1/3*s**5 = 0 for s.
-1, 0, 1
Suppose 71*b + 505 = 76*b. Suppose 111*c = b*c + 20. Factor -4/3 + 2/3*g + 4/3*g**c - 2/3*g**3.
-2*(g - 2)*(g - 1)*(g + 1)/3
Let k(b) be the third derivative of 4*b**2 + 1/12*b**3 + 5/192*b**4 + 0*b + 1/480*b**5 + 0. Factor k(j).
(j + 1)*(j + 4)/8
Let q be 4/10 + (-234)/(-65) + -2. Factor 2*p**3 + 3*p - 3*p + 2*p**2 - 22*p**q.
2*p**2*(p - 10)
Let u be (-28)/6*12/8. Let m be u/(-2 - (-4)/4). Suppose -4*s + 2*s**2 + m + 10 - 15 = 0. Calculate s.
1
Let t(g) = -g**2 - 3*g + 1. Let u(z) = 2*z**2 + 5*z - 3. Let a(n) = -5*t(n) - 3*u(n). Factor a(j).
-(j - 2)*(j + 2)
Suppose -252 = 649*o + 293*o - 2136. Let 0 + 1/2*n**4 + 0*n - 2*n**3 - 5/2*n**o = 0. Calculate n.
-1, 0, 5
Suppose -2*v + w - 3*w = -12, 5*w - 22 = -3*v. Factor 0 + 1/2*y**5 + y**2 - 1/2*y + 0*y**3 - y**v.
y*(y - 1)**3*(y + 1)/2
Let k(d) = -3*d**2 + 3*d - 3. Let t(n) = -n. Let b = 28 + -29. Let p(o) = b*k(o) + 3*t(o). Find r, given that p(r) = 0.
1
Let l be ((-4)/(-5))/(20/50). Suppose l*w + q = 4, w - 2*q + 3*q = 0. Let -6/5 + 9/5*v + 3/5*v**2 + 3/5*v**w - 9/5*v**3 = 0. Calculate v.
-1, 1, 2
Suppose 2*f = -3*f + 4*b + 172, -3*f + 110 = b. Suppose p - 14 = 2*t, 4*t + f = 4*p - 0*p. Factor 2*g**2 - 2*g**3 + 2*g**2 + g**p - 3*g**2.
g**2*(g - 1)**2
Let w = 11292/6265 - 3/1253. Let 2/5 + z**3 + 1/5*z**4 + w*z**2 + 7/5*z = 0. What is z?
-2, -1
Let n be ((-6)/(-16))/((-10)/8 + 2). Let l(j) be the first derivative of -4 - 1/2*j**2 + 0*j**5 + 0*j + 0*j**3 - 1/6*j**6 + n*j**4. Factor l(w).
-w*(w - 1)**2*(w + 1)**2
Let k = 396 + -394. Let q(x) be the second derivative of 2*x**k + 0 - 7/3*x**3 + 5/6*x**4 + 3*x. Factor q(u).
2*(u - 1)*(5*u - 2)
Factor 24/5 - 28/5*l**2 - 2*l**3 + 14/5*l.
-2*(l - 1)*(l + 3)*(5*l + 4)/5
Let z be 7764/24 + 1*1/2. Factor 364*g**3 - 188*g**4 - z*g**2 + 45*g**5 + 122*g - 17*g + 23*g - 9*g**5 - 16.
4*(g - 2)*(g - 1)**3*(9*g - 2)
Let k(r) be the second derivative of 15*r - 1/36*r**4 + 5/3*r**2 + 0 + 1/6*r**3. Factor k(z).
-(z - 5)*(z + 2)/3
Let p(l) be the second derivative of l**5/40 - 11*l**4/4 + 363*l**3/4 - 245*l. Let p(o) = 0. Calculate o.
0, 33
Let i be ((-16)/320)/(1*(-1)/5). Let n(t) be the first derivative of -i*t**4 - 1/3*t**3 - 7 + 1/2*t**2 + 1/5*t**5 + 0*t. Find f such that n(f) = 0.
-1, 0, 1
Let g(y) be the third derivative of y**5/60 + 3*y**4/8 + 27*y**3/8 + 284*y**2 + 2. Determine d so that g(d) = 0.
-9/2
Factor 256*b**3 + 101*b**2 + 347*b**2 + 16 - 26 + 2*b**5 + 10 + 44*b**4.
2*b**2*(b + 4)**2*(b + 14)
Let y(z) = 2*z**3 - z + 1. Let g(j) = 17*j**3 + 6*j**2 - 8*j + 3. Let p(b) = 4*g(b) - 36*y(b). Suppose p(c) = 0. Calculate c.
-1, 1, 6
Suppose -3*m = 9, 2*t - 2*m = t + 18. Let -474*r + 2*r**3 + 474*r - 5*r**4 - 5*r**2 - t*r**3 = 0. Calculate r.
-1, 0
Let g(r) be the first derivative of r**4/18 - r**3/3 + 2*r**2/3 + 8*r + 16. Let d(n) be the first derivative of g(n). Factor d(h).
2*(h - 2)*(h - 1)/3
Let m(h) be the second derivative of -12*h**2 - 24*h - 2*h**3 + 1/2*h**4 + 3/20*h**5 + 0. Factor m(l).
3*(l - 2)*(l + 2)**2
Let n(y) be the second derivative of -y**5/170 - 2*y**4/51 + 4*y**3/17 + y + 14. Suppose n(l) = 0. Calculate l.
-6, 0, 2
Suppose -l = 3 - 5. Suppose -8 - 4 = -l*t. Find a such that 11*a**2 - 15*a**2 + t*a**2 + 2*a**4 + 4*a**3 = 0.
-1, 0
Let j be (2/(-4)*0)/(-1). Factor -2*d + 4 + j*d**2 + 1 - d**2 - 2.
-(d - 1)*(d + 3)
Suppose -8 = y - 5*f, 2*y - f = 4*f - 6. Let o(w) = -w + 7. Let p be o(y). Factor -30*k**3 + 14*k**5 + p*k**2 + 5*k**2 - 15*k**3 + 60*k**4 - 39*k**5.
-5*k**2*(k - 1)**2*(5*k - 2)
Let s(b) = 3997*b**5 - 36397*b**4 + 65080*b**3 + 79317*b**2 + 25917*b + 2703. Let m(h) = h**5 - h**4 - 3*h**2 + h - 1. 