Let l be 0/(6/(-30)*0 - 3). Factor 0 + l*o + 1/2*o**3 + 1/2*o**4 + 0*o**2.
o**3*(o + 1)/2
Let s(d) = d**3 - 10*d**2 - 12*d + 13. Let j be s(11). Factor 0*b**2 - 3 + 3*b**2 + 0*b**j.
3*(b - 1)*(b + 1)
Let m(w) = 4*w. Let g be m(2). Suppose 2*r = 2*u + 2, -2*u = -6 + g. Determine q, given that r - 3/5*q**2 + 6/5*q = 0.
0, 2
Let j(h) be the first derivative of h**6/360 - h**5/24 + h**4/6 + 4*h**3 + 38. Let x(a) be the third derivative of j(a). Suppose x(r) = 0. What is r?
1, 4
Let j(o) be the first derivative of -o**3 - 3*o**2/2 - 52. Suppose j(y) = 0. What is y?
-1, 0
Suppose 4*c = 2*g - 660, -6*g + 4*g - c = -635. Factor 0*t**2 + 316*t - g*t + 2*t**2 + 2.
2*(t - 1)**2
Suppose 2*o + 3638 = 3644. Factor 4/7*m**2 - 8/7*m - 16/7 + 2/7*m**o.
2*(m - 2)*(m + 2)**2/7
Let m(j) be the second derivative of 5*j**4/12 - 35*j**3/6 + 30*j**2 + j - 4. Let m(u) = 0. What is u?
3, 4
Let g = -17 + 32. Suppose 5*z = 2*w + 15, -2*z + 7*z + 2*w = g. Suppose 7*u - u**3 + z*u**2 - u**2 - 4*u = 0. Calculate u.
-1, 0, 3
Factor -6*d**3 - 15*d**3 - 9*d**2 - 414*d + 418*d + 8*d**3.
-d*(d + 1)*(13*d - 4)
Let r(o) be the first derivative of -4*o**5/45 + 10*o**4/9 - 44*o**3/9 + 8*o**2 + 135. Find l such that r(l) = 0.
0, 3, 4
Let r be -25 - -18 - -43*3/18. Let o(m) be the second derivative of 0*m**2 - r*m**4 - 9*m + 0*m**3 + 0. Suppose o(x) = 0. What is x?
0
Let g(f) be the third derivative of f**6/1080 - f**3/3 + 9*f**2. Let c(w) be the first derivative of g(w). Find q, given that c(q) = 0.
0
Let i = -18658 + 93294/5. Factor -2/5*q**2 + 6/5 + i*q.
-2*(q - 3)*(q + 1)/5
Let v(d) be the third derivative of d**7/420 + d**6/80 - d**5/30 + 5*d**2. What is t in v(t) = 0?
-4, 0, 1
Let h(w) = -2*w + 29. Let j be h(13). Determine r so that -j*r**2 + 7*r - 5*r - 2*r**3 + 4*r**3 - r**2 = 0.
0, 1
Let h(a) be the third derivative of -3*a**5/20 - 55*a**4/12 - 4*a**3 + 2*a**2 - 42. Factor h(f).
-(f + 12)*(9*f + 2)
Let k(x) be the first derivative of -4*x**3/3 - 8*x**2 + 48*x + 99. Suppose k(f) = 0. Calculate f.
-6, 2
Let y(b) be the third derivative of -b**7/8820 + b**6/2520 + b**4/4 + 10*b**2. Let q(f) be the second derivative of y(f). Let q(i) = 0. What is i?
0, 1
Let a(l) = -8*l**2 - l + 7. Let m(z) = -z**2 + 1. Let d(t) = -4*a(t) + 28*m(t). Let r(c) = 7*c**2 + 7*c. Let u(x) = -5*d(x) + 3*r(x). Factor u(f).
f*(f + 1)
Let q(j) be the first derivative of -j**5/5 - 3*j**4/2 - 4*j**3/3 + 3*j**2 + 5*j + 99. Let q(t) = 0. What is t?
-5, -1, 1
Let w = 20 + -16. Suppose 5*l + 3*l**5 - w*l**3 + l**3 - 5*l = 0. Calculate l.
-1, 0, 1
Let y(k) be the third derivative of k**5/210 - 5*k**4/84 - 2*k**3/7 + 89*k**2. Let y(v) = 0. What is v?
-1, 6
Let q = 3227 - 3227. Factor q + 1/7*v**2 - 1/7*v.
v*(v - 1)/7
Suppose -23*z = 3*i - 20*z - 24, 0 = i + 5*z - 28. What is r in 2 - 25/2*r**2 - 6*r - 9/2*r**i = 0?
-2, -1, 2/9
Factor 1/4*w**2 + 11/4*w + 5/2.
(w + 1)*(w + 10)/4
Let l(k) = -k**3 + k**2 - k - 1. Let t(w) = -w**3 - 2*w. Let i = -11 - -9. Let q(z) = i*t(z) + 3*l(z). Solve q(y) = 0.
-1, 1, 3
Factor 1/11*p + 0 - 1/11*p**2.
-p*(p - 1)/11
Let w = 18 + -29. Let a = 16 + w. Suppose 3*g**2 + 5 + 43 + a*g**2 - 5*g**2 - 24*g = 0. What is g?
4
Suppose 0 = -n - 3*n - 8. Let k be ((-16)/(-6))/(n/3*-1). Factor 0*a**k - 1/3*a**5 - 1/3*a + 0 + 2/3*a**3 + 0*a**2.
-a*(a - 1)**2*(a + 1)**2/3
Let t be 4/(-2) + (-3 - 4). Let d = -7 - t. Factor 6*g - g**d - 9 - 3*g + 7.
-(g - 2)*(g - 1)
Solve -2*h**2 - h**2 + 4*h**3 - 8*h**4 + 5*h**5 + 6*h**3 - 5*h**4 + h**3 = 0.
0, 3/5, 1
Let k(s) = 35*s**4 - 835*s**3 + 42930*s**2 - 743520*s - 787380. Let v(t) = t**4 - t**3 + 2*t - 2. Let n(u) = k(u) - 30*v(u). Factor n(w).
5*(w - 54)**3*(w + 1)
Let b(k) be the first derivative of -1/5*k**5 + 4/15*k**3 + 0*k + 8 - 3/10*k**4 + 4/5*k**2 - 1/30*k**6. Factor b(p).
-p*(p - 1)*(p + 2)**3/5
Let a(c) be the third derivative of c**8/112 + 9*c**7/70 + 3*c**6/8 + 7*c**5/20 + 81*c**2. Determine l, given that a(l) = 0.
-7, -1, 0
Let p(u) be the third derivative of 0*u**3 - 7/20*u**5 - 1/20*u**6 + 0*u - 3/8*u**4 - 7*u**2 + 0. Solve p(f) = 0 for f.
-3, -1/2, 0
Let r(i) be the third derivative of 1/30*i**6 - 12*i**2 + 1/3*i**4 + 0 - 1/5*i**5 + 0*i**3 + 0*i. Suppose r(v) = 0. Calculate v.
0, 1, 2
Let x(j) be the third derivative of -12*j**2 - 1/540*j**6 - 4/27*j**3 - 1/54*j**5 + 0 - 2/27*j**4 + 0*j. Determine k so that x(k) = 0.
-2, -1
Factor -152/5*h**2 + 2/5*h**5 - 24/5 + 108/5*h**3 - 32/5*h**4 + 98/5*h.
2*(h - 12)*(h - 1)**4/5
Solve -18*v**4 + 15*v**5 - 29*v**5 + 21*v**3 + 11*v**5 = 0 for v.
-7, 0, 1
Let t(i) be the first derivative of -3*i**3/7 - 12*i**2/7 + 9*i/7 + 485. Factor t(u).
-3*(u + 3)*(3*u - 1)/7
Let j(m) be the first derivative of -4*m**4/7 - 4*m**3/21 + m**2 + 6*m/7 + 145. Find w, given that j(w) = 0.
-3/4, -1/2, 1
Let c = 109 + -109. Let z(t) be the third derivative of -t**2 + 0*t + c + 1/450*t**5 - 1/180*t**4 + 0*t**3. Factor z(b).
2*b*(b - 1)/15
Let w(y) be the second derivative of 15/2*y**4 - 32/3*y**3 + 81/10*y**5 - 36*y + 0 + 4*y**2. Factor w(s).
2*(s + 1)*(9*s - 2)**2
Let p be 100 - 104 - (-5 - -1). Let i(u) be the third derivative of 1/20*u**5 + 1/6*u**3 + 3*u**2 + 1/120*u**6 + 1/8*u**4 + 0 + p*u. Let i(g) = 0. Calculate g.
-1
Let x(w) be the second derivative of 2*w**7/21 - 4*w**5/5 - 2*w**4/3 + 2*w**3 + 4*w**2 + 15*w. Factor x(g).
4*(g - 2)*(g - 1)*(g + 1)**3
Let u(p) be the third derivative of p**6/40 + 27*p**5/5 - p**4/8 - 54*p**3 + 5*p**2 + 3*p. Suppose u(m) = 0. Calculate m.
-108, -1, 1
Let h be (176/(-110))/((-2)/5). Let y(b) = -8*b**2 - 12*b - 20. Let x(p) = -7*p**2 - 13*p - 19. Let g(l) = h*x(l) - 3*y(l). Factor g(r).
-4*(r + 2)**2
Let y = -1/2340 + 3511/2340. Determine d, given that 1/2*d**5 - y*d + 3/2*d**4 - 1/2 + d**3 - d**2 = 0.
-1, 1
Let v(g) = g**3 - 19*g**2 + 19*g - 9. Let x be v(18). Suppose 2*u + 5 = 7*u. Suppose -2*l**2 - x + 6 - 4*l + u = 0. Calculate l.
-1
Let t be ((-2)/14*(-42)/12)/2. Let -1/4*r**2 + t*r**3 + 0 - 1/2*r = 0. What is r?
-1, 0, 2
Let w = -68 + 74. Factor 18*r + 7*r + 15 + w*r + 3*r**2 - 13*r.
3*(r + 1)*(r + 5)
Suppose 10*u = 8*u - 260. Let m = u - -392/3. Find x such that 2*x - 4/3 - m*x**2 = 0.
1, 2
Factor -h + 142*h**2 + 5*h - 141*h**2.
h*(h + 4)
Let j(k) be the third derivative of k**8/168 - 4*k**7/105 - k**6/30 + 2*k**5/5 + 3*k**4/4 - 129*k**2. What is q in j(q) = 0?
-1, 0, 3
Let v = 1891/15 - 126. Let x(h) be the third derivative of 0 + 1/60*h**6 - v*h**5 + 9*h**2 - 1/12*h**4 + 0*h + 2/3*h**3. Factor x(q).
2*(q - 2)*(q - 1)*(q + 1)
Suppose 3*a - 78 = -23*a. Find g, given that -3/8*g**a + 0 - 9/8*g**2 + 3/4*g**4 + 0*g = 0.
-1, 0, 3/2
Factor 375/4*h - 15/2*h**3 + 0 + 3*h**4 - 25*h**2 - 1/4*h**5.
-h*(h - 5)**3*(h + 3)/4
Suppose 3*s + 5*y = 29, 4*y - 10 - 18 = -4*s. Suppose -3*x - 13 = c, -4*c + 23 = -0*c - s*x. Determine a so that -1/2*a + 2*a**c - 3/2*a**3 + 0 = 0.
0, 1/3, 1
Let g(j) be the second derivative of 3*j**5/140 + j**4/7 + j**3/14 - 9*j**2/7 + 2*j + 133. Solve g(d) = 0 for d.
-3, -2, 1
Let s = -1309/18 + 437/6. Let x(w) be the first derivative of 0*w + 1/27*w**3 + s*w**2 - 9. Factor x(f).
f*(f + 2)/9
Suppose 16/7*x - 18/7 + 2/7*x**2 = 0. Calculate x.
-9, 1
Suppose 12 = 38*r - 34*r. Let y(c) be the second derivative of 1/10*c**6 + 2/5*c**5 - 2/9*c**4 + 4*c + 0 - 16/9*c**r + 8/3*c**2. Factor y(x).
(x + 2)**2*(3*x - 2)**2/3
Let -10*u**4 - 8*u + 50*u**3 + 48/5 - 292/5*u**2 = 0. Calculate u.
-2/5, 2/5, 2, 3
Let x(m) be the third derivative of 1/18*m**3 + 16*m**2 + 5/16*m**5 + 0*m + 0 + 5/24*m**4. Factor x(w).
(15*w + 2)**2/12
Let c be 1238/5992 + (-1)/(-4). Let w = c - 3/107. Factor w + 12/7*l**2 + 15/7*l.
3*(l + 1)*(4*l + 1)/7
Let o be -6*(-3)/36*8. Factor 24*m**3 - 16*m**2 + 4*m**4 + m**5 - 7*m**4 - 6*m**o.
m**2*(m - 4)**2*(m - 1)
Let m(t) = -t**2 - 6*t + 1. Let z(o) = -o**2 - o. Let h(j) = -m(j) - 2*z(j). Let l be h(-3). Factor 4/5 - 18/5*k + 14/5*k**l.
2*(k - 1)*(7*k - 2)/5
Suppose 4/3*q**2 + 68/9*q - 80/9 = 0. What is q?
-20/3, 1
Let j(a) be the third derivative of a**6/30 + 2*a**5/5 + 88*a**2. Solve j(r) = 0.
-6, 0
Let w(g) = 2*g**3 + 7*g**2 - g - 9. Let i be w(-3). Let j(o) be the first derivative of 2 + 0*o - 1/15*o**i - 1/10*o**2. Factor j(l).
-l*(l + 1)/5
Let g(r) be the first derivative of r**5/40 + 2*r**4 - 11*r**3/4 - 4*r**2 + 65*r/8 + 114. Factor g(w).
(w - 1)**2*(w 