1, 1
Suppose 4*f - h + 3*h - 4 = 0, 2*f + 2*h = 0. Let b be (4 - 249/63)*(-56)/(-16). Determine q so that -b*q**f + 2/3*q + 0 = 0.
0, 4
Let p(n) be the third derivative of -n**5/60 + 101*n**4/12 - 10201*n**3/6 + 286*n**2. Factor p(k).
-(k - 101)**2
Let b(m) = -7*m**5 - 14*m**4 + 77*m**3 - 96*m**2 - 12. Let k(n) = 34*n**5 + 68*n**4 - 386*n**3 + 480*n**2 + 56. Let h(p) = 14*b(p) + 3*k(p). Factor h(z).
4*z**2*(z - 2)**2*(z + 6)
Suppose 2*m = -3*z + 25, -3*z + 22 = 5*m - 0. Let v be (3/z)/(14/84). Factor 0 - 3/4*x**v + 3/2*x.
-3*x*(x - 2)/4
Suppose 14/5*k**2 + 0 + 0*k - 2/5*k**5 + 18/5*k**4 - 6*k**3 = 0. Calculate k.
0, 1, 7
Let a = -229/3 + 1835/24. Let b(f) be the second derivative of 0 + a*f**4 - 5*f - 1/2*f**2 + 1/12*f**3. Factor b(j).
(j + 1)*(3*j - 2)/2
Factor -106*h - 30*h**2 + 26*h**2 + 134*h.
-4*h*(h - 7)
Let i = -4/183 - -47/1220. Let o(l) be the third derivative of 2*l**2 - 1/30*l**5 + 0*l**4 - i*l**6 + 0*l**3 + 0*l + 0. Let o(b) = 0. Calculate b.
-1, 0
Let l = -1408 + 1412. Let t(z) be the first derivative of 0*z**2 + 1 + 0*z + 0*z**5 + 1/6*z**l - 1/9*z**6 + 0*z**3. Find b, given that t(b) = 0.
-1, 0, 1
Let t(a) = a**4 + 3*a**2 - 2. Let d(c) = 44*c**3 - 60*c**2 + 8. Let z(v) = -d(v) - 4*t(v). What is k in z(k) = 0?
-12, 0, 1
Let m = 10/17 + -283/510. Let f(i) be the second derivative of 5*i - m*i**5 - 2/3*i**2 + 1/9*i**3 + 1/9*i**4 + 0. Determine v so that f(v) = 0.
-1, 1, 2
Let h(q) be the third derivative of q**7/2100 - q**5/300 - 5*q**3/3 - 4*q**2. Let i(v) be the first derivative of h(v). Factor i(m).
2*m*(m - 1)*(m + 1)/5
Let c = 2/14501 - -43499/29002. Factor 0 + 3/2*g**2 - 3*g - c*g**4 + 3*g**3.
-3*g*(g - 2)*(g - 1)*(g + 1)/2
Suppose 5*h - 15 = -3*t, -2*h + 6 = -0*t + 2*t. Let y be ((-3)/(-6))/((-2)/(-12)). Factor j**h + 3*j**2 + 2*j**4 + j**5 - y*j**2.
j**3*(j + 1)**2
Let h be ((-176)/(-24))/((-6)/171). Let a = 419/2 + h. Find d such that 1/4*d**2 - 3/4 + a*d = 0.
-3, 1
Let m(x) = -5*x**2 + 6*x - 3. Let q(j) = -125 + 60 + 66 + j**2. Let o(p) = -2*m(p) - 6*q(p). Solve o(d) = 0.
0, 3
Let t be (-8)/1*5/10. Let s be 21/35 + t/(-10). Find i, given that 5*i + i + 3 + 2 - s + 2*i**2 = 0.
-2, -1
Let z(t) = -t - 12. Let q be z(-27). Let c be 22/10 + 4 + (-63)/q. Determine m, given that 5/2*m**3 - 3*m**2 - c*m - 1/2*m**4 + 4 = 0.
-1, 2
Let v be 201/60 + (-1)/(-3)*(-168)/(-224). Suppose -8/5 - 4/5*c**2 + v*c = 0. What is c?
1/2, 4
Suppose -35 = -2*l - 5*x, 0*x - 4*x = 4*l - 88. Factor -14*y + 28 + l - y - 58 + 140*y**2.
5*(4*y - 1)*(7*y + 1)
Find t, given that 0*t**3 + 2/7*t**4 - 16/7 - 22/7*t**2 + 36/7*t = 0.
-4, 1, 2
Let q = 3213 + -3211. Suppose 0 + 0*d**3 + 4/3*d - 2*d**q + 2/3*d**4 = 0. What is d?
-2, 0, 1
Let j(y) = 7*y**3 - 2*y**2 + 47*y + 14. Let f(n) = 8*n**3 - 5*n**2 + 48*n + 12. Let v(x) = 6*f(x) - 7*j(x). Factor v(k).
-(k + 1)*(k + 2)*(k + 13)
Let i(b) be the second derivative of b**7/33 - 2*b**6/15 - 16*b**5/55 + 13*b**4/33 + 25*b**3/33 - 4*b**2/11 + 335*b. Let i(y) = 0. What is y?
-1, 1/7, 1, 4
Let s(f) = -8*f**3 + 190*f**2 + 8*f - 190. Let w(b) = b**3 - 27*b**2 - b + 27. Let l(d) = 6*s(d) + 44*w(d). Factor l(o).
-4*(o - 1)*(o + 1)*(o + 12)
Let x be 6/27 + 16/9. What is u in 707*u - 3*u**x + 0*u**2 + 2 - 712*u = 0?
-2, 1/3
Let t be 8 - (3 + 7 - 6). Factor 0*s**2 + 0*s + 2/3*s**t + 2/3*s**3 + 0.
2*s**3*(s + 1)/3
Let a be ((-9)/(-12))/((-3)/(-16)). Let o(b) be the third derivative of 0*b**3 + 1/40*b**a + 1/100*b**5 - 5*b**2 + 0 + 0*b. Factor o(x).
3*x*(x + 1)/5
Let y be (-24)/(-20)*(-20)/(-6) + 0. Factor 12*o - 3*o - y*o**2 + 23*o - 64.
-4*(o - 4)**2
Let u(z) be the second derivative of -2/35*z**5 + 0 - 3/7*z**4 - 19*z - 12/7*z**2 - 26/21*z**3. What is d in u(d) = 0?
-2, -3/2, -1
Suppose 3434*t - 3430*t + 9 = -b, 4*t = -4*b. Solve 140/3*d**4 + 0 - 8/3*d + 2*d**b - 98/3*d**5 - 40/3*d**2 = 0 for d.
-2/7, 0, 1
Let h = -22/53 - -317/636. Let y(m) be the second derivative of 5*m - h*m**4 + 2/3*m**3 - 2*m**2 + 0. Factor y(c).
-(c - 2)**2
Let l(j) = 2*j**3 + 16*j**2 + 14*j. Let t(f) = -f**3 - 8*f**2 - 7*f. Let c(z) = -4*l(z) - 10*t(z). Solve c(o) = 0.
-7, -1, 0
Let q(l) be the third derivative of -l**7/525 - l**6/300 + 2*l**5/75 + l**4/15 + 67*l**2. Solve q(z) = 0.
-2, -1, 0, 2
Let h(u) = 3*u**2 - 208*u + 1357. Let g(x) = -3*x + 22. Let d be g(9). Let a(m) = -20*m**2 + 1352*m - 8820. Let s(y) = d*a(y) - 32*h(y). Factor s(c).
4*(c - 13)**2
Let u = -7/1006 + 7559/2012. Factor -u - 3*g + 3/4*g**2.
3*(g - 5)*(g + 1)/4
Let v(m) be the first derivative of -m**4/4 - m**3 + 9*m**2/2 + 27*m - 59. Let v(a) = 0. What is a?
-3, 3
Suppose -m - 3 = -h - 0, 0 = -m + 2*h - 6. Let l(g) be the first derivative of -2 - 1/6*g**3 + 1/10*g**5 + 1/4*g**4 - 1/2*g**2 + m*g. Factor l(s).
s*(s - 1)*(s + 1)*(s + 2)/2
Let s(b) be the second derivative of -1/6*b**3 - 2*b - 1/36*b**4 + 0 + 0*b**2. Factor s(l).
-l*(l + 3)/3
Let p(a) be the first derivative of 2*a**3/15 + 12*a**2/5 - 26*a/5 + 8. Factor p(l).
2*(l - 1)*(l + 13)/5
Factor -3/8*q**3 + 3/2*q - 3/8*q**2 + 3/2.
-3*(q - 2)*(q + 1)*(q + 2)/8
Suppose -6 = -3*b - a, 8*b - a = 3*b + 18. Solve -2/15*z**b + 0*z + 2/15*z**2 + 0 - 2/15*z**4 + 2/15*z**5 = 0 for z.
-1, 0, 1
Let p(o) = o**4 + 20*o**3 + 29*o**2 - 131*o - 3. Let z(c) = 2*c**4 + 38*c**3 + 59*c**2 - 261*c - 5. Let k(l) = -5*p(l) + 3*z(l). Factor k(w).
w*(w - 2)*(w + 8)**2
Let j = -439 + 439. Let p(a) be the first derivative of j*a**2 + 2 + 2/15*a**3 - 2/25*a**5 + 0*a + 0*a**4. Factor p(f).
-2*f**2*(f - 1)*(f + 1)/5
Let s(c) be the third derivative of c**7/315 + 4*c**6/45 + 77*c**5/90 + 49*c**4/18 - 82*c**2. Solve s(z) = 0.
-7, -2, 0
Find p, given that -2*p**3 - 105*p + 57 - 39*p**2 + 6*p**3 - 7*p**3 + 90 = 0.
-7, 1
Suppose -15 = -216*f + 211*f. Let j be -1 + 3/(-12) + 37/20. Factor -3/5*g + j*g**2 + 3/5*g**f - 3/5.
3*(g - 1)*(g + 1)**2/5
Let j(l) be the first derivative of l**5/40 + l**4/8 + l**3/4 + l**2/4 + l/8 - 138. Factor j(u).
(u + 1)**4/8
Let v be (-6)/9*18/(-16). Factor -v*u**2 + 3/4*u**3 - 3/4*u + 3/4*u**4 + 0.
3*u*(u - 1)*(u + 1)**2/4
Factor -4*c**4 + 1340*c + 647*c - 164*c**3 + 198*c - 421*c - 1596*c**2.
-4*c*(c - 1)*(c + 21)**2
Suppose -60*o = -99*o + 195. Let h(x) be the second derivative of 0 + 0*x**3 - 1/24*x**4 + 1/40*x**o - 6*x + 1/60*x**6 - 1/84*x**7 + 0*x**2. Factor h(r).
-r**2*(r - 1)**2*(r + 1)/2
Let k = 19 + -3. Let g(h) = -7*h**3 - 15*h**2. Let j(v) = 47*v**2 + 19*v**2 + 4*v**2 + 36*v**3 + 6*v**2. Let b(z) = k*g(z) + 3*j(z). Solve b(r) = 0 for r.
-3, 0
Let i(t) be the third derivative of t**6/480 + t**5/120 - 2*t**2 - 13*t. Solve i(x) = 0 for x.
-2, 0
Let o be ((-5)/3)/(3 + 115/(-6)). Let i = o - -726/485. Factor 2/5*h**2 + 8/5*h + i.
2*(h + 2)**2/5
Let v(k) be the third derivative of k**6/150 + 4*k**5/75 - 11*k**4/30 + 4*k**3/5 - 173*k**2. Find s, given that v(s) = 0.
-6, 1
Let v(j) be the first derivative of -51*j**5/10 + 147*j**4/8 - 14*j**3 - 3*j**2 - 296. Determine w, given that v(w) = 0.
-2/17, 0, 1, 2
Let i(o) be the second derivative of -22*o**6/75 + 9*o**5/25 + 8*o**4/5 + 8*o**3/15 - 86*o. Solve i(k) = 0 for k.
-1, -2/11, 0, 2
Solve 2/3*g**3 - 6 + 10*g - 14/3*g**2 = 0.
1, 3
Let r be (-11)/33 - (-14)/6. Factor 2*j**3 - 2 + 13*j**2 + 20 + 30*j + j**r.
2*(j + 1)*(j + 3)**2
Solve 17*u**3 - 5*u**2 + 15*u + 41*u**2 - 12*u**3 - 16*u**2 = 0 for u.
-3, -1, 0
Let l = -49 + 51. Factor 41*a - 20*a**3 - 48 - 9*a + 16*a**3 + 4*a**l.
-4*(a - 2)**2*(a + 3)
Factor 5/3 + 1/3*m**2 - 2*m.
(m - 5)*(m - 1)/3
Let n be (-12 - -12) + 0 + 10/2. Suppose 5*b - 25 = n*f, -5*b = f + 1 - 8. Let 2/5*i**b + 2/5 + 4/5*i = 0. Calculate i.
-1
Let y = 9011/5 + -1802. Suppose 2*b + 7 + 10 = 3*z, 0 = 5*z + 2*b - 7. Factor 1/5*d**z + 1/5*d**4 - 1/5*d + 0 - y*d**2.
d*(d - 1)*(d + 1)**2/5
Let v(l) = 5*l - 16. Let j be v(4). Let a be (((-4)/(-1))/j - 2)*0. Factor a*y - 2/3 + 2/3*y**2.
2*(y - 1)*(y + 1)/3
Let z(u) be the third derivative of u**6/60 - u**5/6 - u**4/12 + 5*u**3/3 + u**2 - 48*u. Factor z(c).
2*(c - 5)*(c - 1)*(c + 1)
Let v(f) be the first derivative of f**6/30 + 4*f**5/25 + 3*f**4/10 + 4*f**3/15 + f**2/10 - 136. Find b such that v(b) = 0.
-1, 0
Suppose -5*d - 51 = -4*p + 118, 0 = 3*d - 9. Solve 51*b**3 + b - 21*b - p*b**3 = 0 for b.
-2, 0, 2
Let j(i) be the first derivative of -i**5/5 + 7*i**4/20 - 2*i**3/15 - 12. Find n such that j(n) = 0.
0, 2/5,