e third derivative of t(f). Let q(w) = 0. Calculate w.
-1, 0
Let o(p) = p**3 - 14*p**2 - 53*p + 37. Let z be o(17). Suppose x + 14 = 4*k, 2*x + 26 = 5*x + 5*k. Let -5/2*g + 1 - 1/2*g**z + x*g**2 = 0. Calculate g.
1, 2
Let q(f) be the second derivative of 3/10*f**2 - 1/70*f**7 + 1/10*f**6 + 0 - 3/10*f**5 - 1/2*f**3 + f + 1/2*f**4. Factor q(r).
-3*(r - 1)**5/5
Let u = 5/12 + 1/4. Find p such that -3*p**2 + 7/3*p + u = 0.
-2/9, 1
Suppose 15*h + h**2 - 6*h**2 + 2*h**2 - 12 = 0. What is h?
1, 4
Let g(h) be the third derivative of -h**5/30 + 4*h**4/3 - 64*h**3/3 - 13*h**2. Factor g(u).
-2*(u - 8)**2
Let p(l) be the first derivative of -l**8/560 + l**7/280 + l**6/120 - l**5/40 - l**3/3 - 1. Let c(y) be the third derivative of p(y). Factor c(z).
-3*z*(z - 1)**2*(z + 1)
Let b(x) be the second derivative of x**5/70 + x**4/42 - 43*x. Factor b(i).
2*i**2*(i + 1)/7
Factor 0 - 1/6*o**4 + 1/3*o**3 - 1/3*o + 1/6*o**2.
-o*(o - 2)*(o - 1)*(o + 1)/6
Let a(b) be the second derivative of -1/9*b**3 + 0*b**2 - 1/18*b**4 + 0 + 3*b. Factor a(m).
-2*m*(m + 1)/3
Let o be ((-1)/(-5))/(12/39)*4. Let 6/5*k**4 - o*k**3 - 1/5*k**5 + 0 - 4/5*k + 12/5*k**2 = 0. Calculate k.
0, 1, 2
Let m(d) = -21*d**4 + 16*d**3 + 24*d**2 - 32*d - 45. Let r(y) = -5*y**4 + 4*y**3 + 6*y**2 - 8*y - 11. Let h(f) = 6*m(f) - 26*r(f). Let h(n) = 0. Calculate n.
-1, 2
Let t(k) = k**5 - 2*k**3 + 4*k**2 + 3*k - 2. Let g(r) = r**5 + r**4 - r**3 + r**2 + r - 1. Let b(y) = -2*g(y) + t(y). Let b(s) = 0. What is s?
-1, 0, 1
Let p(n) be the third derivative of -7*n**5/15 + 3*n**4/2 - 4*n**3/3 + 2*n**2. Factor p(f).
-4*(f - 1)*(7*f - 2)
Factor 0 + 44/5*h**4 + 16/5*h**2 + 56/5*h**3 + 0*h + 2*h**5.
2*h**2*(h + 2)**2*(5*h + 2)/5
Suppose 0 = 9*q + 9 - 27. Factor -2/7*k**q - 10/7*k**4 + 16/7*k**3 + 0 - 4/7*k.
-2*k*(k - 1)**2*(5*k + 2)/7
Let o = -2/455 - -1826/1365. What is y in 0*y + 0 + o*y**4 + 1/3*y**2 + 5/3*y**3 = 0?
-1, -1/4, 0
Let t be (8 + 2)*(-1)/(-2). Factor q**3 - 5*q**4 - 2*q**2 + q**4 + q**2 - q**5 + t*q**4.
-q**2*(q - 1)**2*(q + 1)
Let q(j) be the second derivative of j**7/16380 + j**6/2340 + j**5/780 + j**4/12 - j. Let w(x) be the third derivative of q(x). Let w(t) = 0. What is t?
-1
Suppose v = 28 - 26. Determine q so that 2/15*q**v - 4/15*q + 2/15 = 0.
1
Let j(r) be the first derivative of -r**6/240 - r**5/40 + 4*r**3/3 + 4. Let n(b) be the third derivative of j(b). Factor n(t).
-3*t*(t + 2)/2
Let r(d) be the first derivative of d**2/2 + d + 11. Let g be r(-1). Solve 0 + 0*q**4 + g*q + 0*q**2 - 1/2*q**5 + 1/2*q**3 = 0.
-1, 0, 1
Let j(a) be the third derivative of 0 + 0*a + a**2 + 1/120*a**4 + 1/300*a**6 + 0*a**3 - 1/100*a**5. Suppose j(b) = 0. Calculate b.
0, 1/2, 1
Let l(j) be the third derivative of -j**8/60480 + j**6/2160 + j**5/20 - 3*j**2. Let k(y) be the third derivative of l(y). Factor k(u).
-(u - 1)*(u + 1)/3
Suppose 5*x - 141 = 3*h, -2*h - 90 = -2*x - 0*x. Let g be (36/h)/((-8)/14). Find j, given that g*j**2 + 3/2 + 3*j = 0.
-1
Let g(s) = s**2 + 11*s + 2. Let h be g(-11). Determine c so that -12*c**2 + 24*c - 12 + 8*c**h + 19*c**2 = 0.
-2, 2/5
Let x(d) = -d**3 - d - 1. Let n(z) = -3*z**3 + 6*z**2 + 7*z + 2. Let b(s) = -n(s) + 4*x(s). Factor b(h).
-(h + 1)*(h + 2)*(h + 3)
Solve 4/7*v**3 - 8/7*v**2 + 4/7*v + 0 = 0 for v.
0, 1
Let s(y) = 2*y - 6. Let n be s(4). Factor n*a**3 + a**3 + a**5 - a**4 - 4*a**3 - a**2 + 2*a**2.
a**2*(a - 1)**2*(a + 1)
Solve 2*a**3 - 8*a**3 + 3*a**5 + a**5 + 4*a - 2*a**3 = 0 for a.
-1, 0, 1
Let d = 8152/7 + -1164. Factor -4/7*g**4 - 2/7*g + 2/7*g**5 + d*g**2 + 0 + 0*g**3.
2*g*(g - 1)**3*(g + 1)/7
Let k(v) be the third derivative of v**9/241920 + v**8/80640 - v**7/20160 - v**6/2880 + v**5/20 - v**2. Let h(b) be the third derivative of k(b). Factor h(o).
(o - 1)*(o + 1)**2/4
Let c(z) be the first derivative of 8*z**2 + 32*z - 8/3*z**3 - 8 - z**4. Factor c(t).
-4*(t - 2)*(t + 2)**2
Let j(g) be the third derivative of -1/30*g**5 + 0*g**3 + 1/24*g**4 + 1/105*g**7 + 0*g + 0*g**6 - 1/336*g**8 - 4*g**2 + 0. Factor j(u).
-u*(u - 1)**3*(u + 1)
Factor 0 + 2/5*a**2 - 4/5*a.
2*a*(a - 2)/5
Let r(k) = k**4 + k. Let u(t) = t**4 - 20*t**3 - 36*t**2 - 23*t - 8. Let v(x) = -5*r(x) + u(x). Factor v(f).
-4*(f + 1)**3*(f + 2)
Let v = 10 - 6. Let p(f) be the first derivative of -1/21*f**6 - 8/35*f**5 - 4/21*f**3 + 0*f + 0*f**2 - 5/14*f**v - 2. Solve p(c) = 0.
-2, -1, 0
Let g(r) be the second derivative of r**6/1260 + r**5/420 - r**3/2 + r. Let v(i) be the second derivative of g(i). Factor v(m).
2*m*(m + 1)/7
Let d be (2/(-3))/(4/(-12)). Suppose d*s = -3*s + 20. Let -2/5*c - 2/5*c**5 - 2/5*c**s - 2/5 + 4/5*c**3 + 4/5*c**2 = 0. What is c?
-1, 1
Let j(w) = -w. Let f be j(-2). Let 7 - 3 - 6*g**2 - f - g + 5*g = 0. What is g?
-1/3, 1
Let c be 1/(-2 - (-21)/9). Factor 3*t**2 - c*t**3 + 4 + 0 - 4.
-3*t**2*(t - 1)
Find a, given that -2/3*a**2 + 2/3*a**3 + 2/3*a**4 + 0 - 2/3*a = 0.
-1, 0, 1
Let g(k) be the second derivative of -2*k**6/15 + 2*k**5/5 - k**4/3 - 51*k. Factor g(n).
-4*n**2*(n - 1)**2
Let m(f) be the third derivative of -1/360*f**6 + 0*f + 1/36*f**5 - 1/9*f**3 + 1/72*f**4 - 1/210*f**7 + f**2 + 0. Let m(s) = 0. What is s?
-1, 2/3, 1
Let j(d) be the first derivative of -3 - 1/15*d**5 + 0*d + 1/12*d**4 + 0*d**2 + 0*d**3. Suppose j(b) = 0. What is b?
0, 1
Let p(o) be the first derivative of -3*o**4/4 - 5*o**3 - 12*o**2 - 12*o + 42. Solve p(m) = 0 for m.
-2, -1
Let g = 3 + 2. Suppose -g*x + 4*x + 3 = 0. Factor 0*z**3 + 3*z**x - 2*z**5 - z**3.
-2*z**3*(z - 1)*(z + 1)
Let z be (-550)/(-45) - 4/18. Factor 2*b - z*b**3 + 15*b**2 + 0 - b**2 - 4.
-2*(b - 1)*(2*b + 1)*(3*b - 2)
Suppose -4*c - 65 = -205. Let y be 60/c - 4/(-14). Suppose -2*p**2 - 5*p**2 - 5 + 3 - 4*p + 5*p**y = 0. What is p?
-1
Factor 0 - 2/7*a**3 + 2/7*a + 0*a**2.
-2*a*(a - 1)*(a + 1)/7
Suppose 0 = i + 3*i + 28. Let j = i - -7. Suppose 4/5*d**4 + 14/5*d**5 + j*d + 0 - 4/5*d**2 - 14/5*d**3 = 0. What is d?
-1, -2/7, 0, 1
Let u be (-3)/(-2)*(-16)/(-12). Let i**2 + 0 + 0 + 2*i + u - 5*i = 0. Calculate i.
1, 2
Let s(u) be the third derivative of -u**5/330 + u**4/66 + 3*u**2. Factor s(o).
-2*o*(o - 2)/11
Let a(q) be the second derivative of -q**6/15 + q**4/2 + 2*q**3/3 + 16*q. Factor a(p).
-2*p*(p - 2)*(p + 1)**2
Let v be 1/(-2*(-1)/6). Suppose -19 = 3*g + 5*l, -v*g - 3*l - 14 = l. Factor -2 + 5*j - 4*j - 3*j - g*j - 2*j**2.
-2*(j + 1)**2
Let o be (-20)/(-35)*(-2 + 16). Factor 14/3*a**4 + 2*a**2 + 0 + o*a**3 - 4/3*a.
2*a*(a + 1)**2*(7*a - 2)/3
Find a, given that 0*a**4 - 1/3*a**5 + 0 + 0*a + 0*a**2 + 1/3*a**3 = 0.
-1, 0, 1
Let n(f) be the first derivative of -f**7/1470 + f**6/210 - f**5/105 - 4*f**2 + 4. Let q(m) be the second derivative of n(m). Factor q(a).
-a**2*(a - 2)**2/7
What is r in -2/11*r**4 - 12/11*r**3 - 18/11*r**2 + 0*r + 0 = 0?
-3, 0
Let r = 1/2 + 5/22. Factor -2/11 - 2/11*x**4 - 12/11*x**2 - 8/11*x**3 - r*x.
-2*(x + 1)**4/11
Let v(x) be the third derivative of -x**5/480 - x**4/24 - 24*x**2. Factor v(l).
-l*(l + 8)/8
Let i(y) be the second derivative of -2*y**7/63 + 7*y**6/90 - y**5/30 - y**4/36 - 20*y. Factor i(s).
-s**2*(s - 1)**2*(4*s + 1)/3
Suppose -10 = -4*z - 2. Find i, given that -2*i - 2*i - 1 - 1 - 3*i**z + i**2 = 0.
-1
Let w = -14 + 17. Suppose 6/5*d**2 + 6/5*d + 2/5*d**w + 2/5 = 0. What is d?
-1
Let z(h) be the first derivative of 0*h**4 + 1 + 0*h**5 + 0*h + 0*h**3 + 0*h**2 + 1/12*h**6. Factor z(d).
d**5/2
Factor 2*w**2 - 7*w**3 - 3*w**2 - 3*w**2 + 3*w**3.
-4*w**2*(w + 1)
Let l(j) be the second derivative of j**7/420 - j**6/240 - j**5/60 + j**2/2 - 2*j. Let v(z) be the first derivative of l(z). Determine s, given that v(s) = 0.
-1, 0, 2
Let r = 85/9 + 35/9. Let g = -10 + r. Solve 10/3*u - g*u**3 - 2/3 - 2*u**2 + 8/3*u**4 = 0.
-1, 1/4, 1
Determine j, given that 0 - 2/11*j**2 - 6/11*j = 0.
-3, 0
Let t be ((-99)/(-231))/((-6)/(-21)). Factor 0 + 0*w + t*w**3 + 0*w**2 - 1/2*w**4.
-w**3*(w - 3)/2
Suppose 0 = -0*x + 4*x - 440. Let b = x - 766/7. Factor -2/7*c**4 - 2/7 - 2/7*c**5 + b*c**2 - 2/7*c + 4/7*c**3.
-2*(c - 1)**2*(c + 1)**3/7
Let -1/3*h**2 - 75 + 10*h = 0. What is h?
15
Let t(z) = 5*z**2 + 12*z + 8. Suppose 2*s = -0*f + f - 5, 3*f + 15 = 0. Let y(m) = 3*m**2 + 8*m + 5. Let u(d) = s*t(d) + 8*y(d). Determine l so that u(l) = 0.
0, 4
Let c(a) = a**2 - 5*a - 3. Let n be c(6). Let k = 20 - 17. Factor 3*u**2 + 6*u 