tive of -o**8/560 + o**7/175 - o**5/50 + o**4/40 - 18*o**2. Factor q(s).
-3*s*(s - 1)**3*(s + 1)/5
Suppose 3*x - x + 0*x**4 - 2*x**3 + 1 - x**4 = 0. What is x?
-1, 1
Let b(l) be the third derivative of l**6/200 + 7*l**5/100 + 3*l**4/20 - 5*l**2. Let b(a) = 0. Calculate a.
-6, -1, 0
Let k(b) be the second derivative of 5*b**4/12 - b**3 + b**2/2 - 15*b. Suppose k(j) = 0. Calculate j.
1/5, 1
Factor -11/8*y - 7/8*y**2 - 1/2.
-(y + 1)*(7*y + 4)/8
Let t be 6 + (-9)/(162/60). Factor -2/3*s**2 + 8/3*s - t.
-2*(s - 2)**2/3
Let c(y) be the first derivative of -y**5/10 - y**4/2 - y**3 - y**2 + y - 3. Let w(h) be the first derivative of c(h). Solve w(t) = 0 for t.
-1
Let j(c) = -c + 5. Let v be j(4). Let n = v + 1. Suppose 0 + x**3 - 1/2*x**n - 1/2*x**4 + 0*x = 0. Calculate x.
0, 1
Let p(w) = -2*w**5 - 2*w**4 - w**3 - w. Let q(m) = -m**4 + m**3 + m**2 + m. Let t(h) = 2*p(h) + 2*q(h). Suppose t(z) = 0. Calculate z.
-1, 0, 1/2
Let v be (16/(-3))/(-4) + -12 + 12. Let u be 2*(4/(-6))/(-2). What is o in 2/3*o**3 - v*o**2 + 0 + u*o = 0?
0, 1
Let b(w) be the second derivative of 0*w**2 + 1/12*w**4 + 0 + 1/20*w**5 + 0*w**3 + 3*w. Factor b(n).
n**2*(n + 1)
Factor -1/8 + 1/4*p**2 - 1/8*p**4 - 1/8*p + 1/4*p**3 - 1/8*p**5.
-(p - 1)**2*(p + 1)**3/8
Let l(f) be the second derivative of 1/90*f**5 - 3*f + 0*f**4 - 2/135*f**6 + 1/189*f**7 + 0*f**2 + 0 + 0*f**3. Factor l(w).
2*w**3*(w - 1)**2/9
Let u(x) be the first derivative of x**6/1080 - x**5/120 - x**3/3 + 4. Let k(i) be the third derivative of u(i). Factor k(t).
t*(t - 3)/3
Let h(g) be the second derivative of g**6/10 + 3*g**5/10 - 3*g**4/4 + 5*g. Let h(x) = 0. What is x?
-3, 0, 1
Find y, given that 0 - 2/13*y**4 - 4/13*y**2 + 6/13*y**3 + 0*y = 0.
0, 1, 2
Factor 30*u**2 + 11*u - 6 + 7*u**3 + 5*u + u**3.
2*(u + 1)*(u + 3)*(4*u - 1)
Let l be (-14)/(-20) - 70/350. Solve 0 - 1/4*a**2 - l*a = 0 for a.
-2, 0
Solve -452/3*x**3 + 8 + 20/3*x - 112/3*x**4 - 344/3*x**2 = 0 for x.
-3, -1, -2/7, 1/4
Factor 1/4*w - 1/4*w**2 + 1/2.
-(w - 2)*(w + 1)/4
Let p(b) be the first derivative of -b**5/5 + 5*b**4/16 + b**3/4 - 5*b**2/8 + b/4 + 7. Determine w, given that p(w) = 0.
-1, 1/4, 1
Let z be 106/120 + (-36)/48. Let t(v) be the first derivative of 0*v**2 + z*v**3 + 0*v + 2/15*v**6 - 2/25*v**5 - 1/5*v**4 - 2. Let t(d) = 0. What is d?
-1, 0, 1/2, 1
Let v(a) be the second derivative of a**6/75 + 3*a**5/50 + a**4/10 + a**3/15 + 25*a. Factor v(x).
2*x*(x + 1)**3/5
Let g(r) be the third derivative of -49*r**6/90 + 77*r**5/45 - 16*r**4/9 + 8*r**3/9 + 3*r**2. Factor g(t).
-4*(t - 1)*(7*t - 2)**2/3
Let z(d) = -2*d**2. Let l(i) = 2*i**2 - 3*i - 3. Let s(u) = 4*u**2 - 5*u - 5. Let x(r) = -5*l(r) + 3*s(r). Let m(h) = 2*x(h) + 3*z(h). Solve m(g) = 0.
0
Factor 2/25*q**4 + 0 + 6/25*q**2 - 6/25*q**3 - 2/25*q.
2*q*(q - 1)**3/25
Let i(l) = l - 9. Let r(d) = -d**3 + d + 13. Let p be r(0). Let f be i(p). Suppose 1/3*j**f - j**5 + 0*j + 0 + 8/3*j**3 + 4/3*j**2 = 0. Calculate j.
-1, -2/3, 0, 2
Suppose 0 = 5*s - n - 3*n - 40, 3*s + 4*n = -8. Suppose 2*o = 3*l + 9, 6 = -l - l. Determine a so that 0*a**2 + 0 + o*a + 0*a**3 + 2/5*a**s = 0.
0
Let o(y) be the second derivative of y**8/1344 - y**6/480 - 3*y**2/2 + 4*y. Let c(d) be the first derivative of o(d). Let c(m) = 0. What is m?
-1, 0, 1
Let j(w) be the first derivative of 0*w - 2/25*w**5 + 1/5*w**2 + 2/15*w**3 - 1/10*w**4 + 4. What is d in j(d) = 0?
-1, 0, 1
Let g(o) be the second derivative of -o**6/60 - o**5/30 + o**4/6 + 3*o**2/2 + 6*o. Let d(w) be the first derivative of g(w). What is r in d(r) = 0?
-2, 0, 1
Let y(b) be the second derivative of -b**9/9072 + b**8/5040 + b**7/2520 - b**6/1080 + b**3/3 - 3*b. Let m(h) be the second derivative of y(h). Factor m(d).
-d**2*(d - 1)**2*(d + 1)/3
Let w be (4*-2)/(2/(-1)). Suppose -x + 12 = 5*l, -5*l - w*x - 1 = -19. Factor m**3 - l*m**4 + m**2 + 2*m**5 - 3*m**5 + m**4.
-m**2*(m - 1)*(m + 1)**2
Let v(q) = -2*q + 18. Let n be v(7). Factor 4/5*b**n - b + b**3 - 1/5 - 3/5*b**2.
(b - 1)*(b + 1)**2*(4*b + 1)/5
Let o be (-2 - 1)/12 + (-45)/(-84). Factor -o*r**2 + 0 - 2/7*r.
-2*r*(r + 1)/7
Let f(x) = -x**4 - x**2 + 1. Let d be -3*1 + 0 + 2. Let l(z) = 15*z**4 + 9*z**3 + 9*z**2 + 3*z - 18. Let t(q) = d*l(q) - 18*f(q). Determine h so that t(h) = 0.
0, 1
Suppose 0 = k + 2*k + 4*k. Factor 0*l**2 + 2/3*l**3 - 2/3*l**5 + k*l + 0 + 0*l**4.
-2*l**3*(l - 1)*(l + 1)/3
Suppose v - 13 = -3*i - 0*v, -4*v = 4*i - 28. Let 0*c**3 - 2*c**i + c + c = 0. What is c?
-1, 0, 1
Let m(r) be the first derivative of -1/6*r**3 - 1/8*r**4 - 2 + 0*r + 1/4*r**2 + 1/10*r**5. Determine t, given that m(t) = 0.
-1, 0, 1
Let r(c) be the third derivative of -c**5/60 + c**4/48 + c**3/4 + 17*c**2. Find n such that r(n) = 0.
-1, 3/2
Let z = 304 - 2126/7. Factor -2/7*r + 0 - 2/7*r**2 + 2/7*r**4 + z*r**3.
2*r*(r - 1)*(r + 1)**2/7
Let n(z) be the first derivative of z**3/7 - 3*z/7 - 1. Factor n(c).
3*(c - 1)*(c + 1)/7
Factor 0*k + 0 - 2/9*k**3 + 4/9*k**2.
-2*k**2*(k - 2)/9
Let n be ((-2)/(-8))/((-9)/(-24)). Let c = -218/3 + 74. Solve -n*o**2 - c + 2*o = 0 for o.
1, 2
Let d be ((-27)/18)/(-4 + 1). Let j(x) be the second derivative of -1/20*x**5 + 0 - 1/12*x**4 + d*x**2 + 1/6*x**3 - 2*x. Let j(g) = 0. What is g?
-1, 1
Suppose -2/7*h**2 + 0 + 2/7*h**3 + 0*h = 0. What is h?
0, 1
Let y = 13 - 12. Let p be y + ((-6)/(-9) - 1). Let -1/3*d**3 + p*d**2 + 0*d + 0 = 0. Calculate d.
0, 2
Let d be (0 - (1 - 0))*0. Let d*s**2 + 6*s**2 - s**2 - 3*s**2 = 0. Calculate s.
0
Let q(u) be the third derivative of u**5/90 + u**4/18 + u**3/9 - 4*u**2. Factor q(f).
2*(f + 1)**2/3
Determine y so that -45/8*y - 27/8*y**2 + 75/8 - 3/8*y**3 = 0.
-5, 1
Let w(r) = r**3 + 7*r**2 + 6*r + 4. Let d be w(-6). Let z be 1/d - (-63)/36. Suppose 2/5*y - 2/5*y**3 - 2/5*y**z + 2/5 = 0. Calculate y.
-1, 1
Let z(p) be the third derivative of p**7/525 - p**6/300 - p**5/150 + p**4/60 + 7*p**2. Factor z(g).
2*g*(g - 1)**2*(g + 1)/5
Let s = 5 + -1. Factor 7*l**5 + 0*l**2 - 12*l**s - 2*l**2 + 3*l**3 + 4*l**2.
l**2*(l - 1)**2*(7*l + 2)
Let j(y) be the third derivative of -y**6/180 - y**5/45 + y**4/12 - 4*y**2. Factor j(t).
-2*t*(t - 1)*(t + 3)/3
Let y(p) be the first derivative of -p**3/15 - p**2/2 - 6*p/5 + 27. Determine h so that y(h) = 0.
-3, -2
Let s(a) be the first derivative of 1/4*a**2 - 7/20*a**5 + 2 + 7/12*a**3 - 1/8*a**4 + 0*a. Let s(q) = 0. Calculate q.
-1, -2/7, 0, 1
Find w, given that 2 + 3 + 2*w + 2*w**2 - 2*w**3 - 7 = 0.
-1, 1
Let d(q) be the third derivative of q**6/180 + q**5/35 - q**4/21 + q**3/2 + 2*q**2. Let w(r) be the first derivative of d(r). Solve w(c) = 0.
-2, 2/7
Let r = 12 - 0. Factor 41 + r*z - 28*z - 9 + 2*z**2.
2*(z - 4)**2
Suppose -10 + 4 = -3*t. Let o(s) be the second derivative of 0*s**3 - s + 1/21*s**7 - 2/15*s**6 + 0*s**t + 0 + 0*s**4 + 1/10*s**5. Let o(i) = 0. Calculate i.
0, 1
Let t(i) be the first derivative of -i**4/8 - i**3/3 - i**2/4 + 10. Factor t(o).
-o*(o + 1)**2/2
Let p = -20 - -17. Let d = -1 - p. Factor 0 - 1/4*l - 1/4*l**d.
-l*(l + 1)/4
Factor 1/2*o**4 + 7*o**3 + 49/2*o**2 + 0*o + 0.
o**2*(o + 7)**2/2
Let p(m) = 3*m**3 - m**2 + 2*m - 4. Let g(c) = 8*c**3 - 2*c**2 + 5*c - 11. Let j(z) = -4*g(z) + 11*p(z). Determine f, given that j(f) = 0.
0, 1, 2
Suppose -12*g = -8*g + 560. Let m be 40/g + 62/21. Find w such that -5*w**4 - 82/3*w**2 + 44/3*w + 61/3*w**3 - m = 0.
2/5, 2/3, 1, 2
Let s(l) be the first derivative of l**6/3 - 202*l**5/75 + 193*l**4/30 - 94*l**3/45 - 32*l**2/5 + 24*l/5 - 41. Find q, given that s(q) = 0.
-2/3, 2/5, 1, 3
Let o be (-13)/1950*5/(-14). Let z(g) be the third derivative of o*g**6 + 0*g - 1/21*g**3 - 1/84*g**4 + 1/210*g**5 - 2*g**2 + 0. Find y, given that z(y) = 0.
-1, 1
Let g(i) be the first derivative of -3*i**5/5 + 2*i**3 - 3*i + 1. Let g(k) = 0. What is k?
-1, 1
Let u be 3/6*(-12)/23. Let y = 35/46 + u. What is w in 1/2*w**5 - y*w**2 + 3/2*w**3 + 0 + 0*w - 3/2*w**4 = 0?
0, 1
Let t(l) be the first derivative of -l**5/300 + l**4/40 - l**3/15 + 4*l**2 + 5. Let g(q) be the second derivative of t(q). Let g(u) = 0. What is u?
1, 2
Suppose -8*y + 18 = y. Let u(s) be the second derivative of 0*s**y - 3*s - 3/40*s**5 + 0*s**3 + 0*s**4 - 1/20*s**6 + 0. Let u(j) = 0. Calculate j.
-1, 0
Factor 0*b**5 - 5*b**2 - 14 - 3*b**4 - 3*b**5 + 23 - 15*b + 18*b**3 - b**2.
-3*(b - 1)**3*(b + 1)*(b + 3)
Suppos