*3/5
Let c = 2188874/755185 - 1088/2069. Let x = 2/73 + c. Factor x*d**3 - 12/5*d + 3/5 - 3/5*d**2.
3*(d - 1)*(d + 1)*(4*d - 1)/5
Let m(l) be the first derivative of -l**6/30 + 4*l**5/25 - l**4/4 + 2*l**3/15 + 103. Factor m(o).
-o**2*(o - 2)*(o - 1)**2/5
Let c(v) be the second derivative of v**7/504 - v**6/72 - v**5/8 + 4*v**4/3 - 20*v. Let i(p) be the third derivative of c(p). Solve i(k) = 0 for k.
-1, 3
What is q in -392/19 + 56/19*q - 2/19*q**2 = 0?
14
Let s(g) = 2*g**2 - 2. Let a(x) = 16*x**2 + 458*x + 210. Let d(l) = -2*a(l) + 20*s(l). Factor d(z).
4*(z - 115)*(2*z + 1)
Suppose -1/9*i**2 - 19/9*i + 92/9 = 0. Calculate i.
-23, 4
Let 18/5*b - 114/5*b**2 + 24/5*b**4 + 2 - 98/5*b**3 = 0. What is b?
-1, -1/4, 1/3, 5
Factor 0*u - 1/2*u**2 + 1/2.
-(u - 1)*(u + 1)/2
Let m(j) be the second derivative of 3*j**5/10 - 13*j**4/3 - 3*j**3 + 10*j + 1. Suppose m(l) = 0. Calculate l.
-1/3, 0, 9
Suppose -3 + 11 = 4*v. Factor 8*n**2 + 3 + 0*n**2 + 12*n + 6*n**2 - v*n**2.
3*(2*n + 1)**2
Suppose w + 10 = 4*y, -13*y + 8*y + 3*w = -9. Let l(z) be the second derivative of 1/3*z**y - 7/30*z**4 + 8*z + 0 + 2/5*z**2. Factor l(b).
-2*(b - 1)*(7*b + 2)/5
Let z(t) be the third derivative of 0*t + 0 - 1/9*t**3 + 1/72*t**4 - 32*t**2 + 1/180*t**5. Factor z(r).
(r - 1)*(r + 2)/3
Let p(r) = 21*r**4 - 71*r**3 + 109*r**2 - 89*r + 8. Let f(o) = 4*o**4 - 14*o**3 + 22*o**2 - 18*o + 2. Let v(h) = -11*f(h) + 2*p(h). Find k, given that v(k) = 0.
1, 3
Let -2 - 176*x**2 + 2 + 181*x**2 - 45*x = 0. Calculate x.
0, 9
Let m(f) be the third derivative of f**8/1680 + f**7/525 - f**6/300 - 2*f**5/75 - 7*f**4/120 - f**3/15 + 46*f**2 - f. Factor m(j).
(j - 2)*(j + 1)**4/5
Let h(g) be the first derivative of 1/90*g**4 - 2*g + 3 - 1/45*g**3 + 0*g**2. Let f(w) be the first derivative of h(w). Let f(i) = 0. What is i?
0, 1
Let d(w) be the third derivative of w**7/21420 - 7*w**6/6120 + w**5/170 + 19*w**4/24 - 10*w**2. Let p(u) be the second derivative of d(u). Factor p(m).
2*(m - 6)*(m - 1)/17
Suppose 4*b - 2*j - 20 = 2*j, 3 = -j. Factor 3*t**b + 31*t - 83*t + 12 + 37*t.
3*(t - 4)*(t - 1)
Suppose -y = d + 3, -4*y - 12 = 3*d - 7*d. Factor -1/4*f**2 + d + 1/4*f.
-f*(f - 1)/4
Let y be (-5)/(-28)*((-469)/(-35) - 13). Let a(o) be the first derivative of 5 - 8/7*o + 2/21*o**3 - 4/7*o**2 + y*o**4. Solve a(w) = 0.
-2, -1, 2
Factor -4861*s**2 + 304*s - 99*s**3 - 2*s**4 + 11552 - 205*s**3 - 6689*s**2.
-2*(s - 1)*(s + 1)*(s + 76)**2
Let k = 2/3155 - -6292/28395. Solve -2/9*f - k*f**3 - 4/9*f**2 + 0 = 0 for f.
-1, 0
Suppose 3*j + 8 = z, -4*j = -2*z - 2*z. Let c be (12/16 - (-21)/(-12))/z. Suppose 0 - 5/8*y**4 + 5/8*y**2 + c*y + 1/8*y**3 - 3/8*y**5 = 0. What is y?
-1, -2/3, 0, 1
Let o(i) be the second derivative of i**6/180 + 11*i**5/240 + i**4/8 + 8*i**3/3 + 29*i. Let y(n) be the second derivative of o(n). Solve y(g) = 0.
-2, -3/4
Let n(c) be the second derivative of -1/30*c**5 + 3*c + 1/3*c**3 - 1/2*c**2 + 0 + 0*c**4. Let y(a) be the first derivative of n(a). Let y(d) = 0. What is d?
-1, 1
Let x = -262 + 259. Let b(n) = -3*n**3 - 8*n**2 - 6. Let s be b(x). Factor 0*c**2 + 0 + 6/19*c**s + 0*c + 2/19*c**4.
2*c**3*(c + 3)/19
Let c = -7705/11 - -705. Factor 128/11 + c*g**3 - 40/11*g**2 - 160/11*g + 20/11*g**4 + 2/11*g**5.
2*(g - 1)**2*(g + 4)**3/11
Let l(t) be the first derivative of 11*t**3/27 - t**2/2 - 2*t/9 - 313. Factor l(w).
(w - 1)*(11*w + 2)/9
Let m be -7*(-14)/(-147) - (208/(-21))/8. Factor m*l**2 + 8/7*l + 0.
4*l*(l + 2)/7
Suppose -9*b = -6*b - 3. Let c(x) = -x**2. Let v(i) = -i**2 + 7*i - 2. Let r be 6/5*20/6. Let z(g) = b*v(g) + r*c(g). Factor z(w).
-(w - 1)*(5*w - 2)
What is a in -70*a + 5*a**2 + 34 + 33*a**2 - 2548*a**3 + 2546*a**3 = 0?
1, 17
Suppose -3*j + q + 3 = 0, 0 = -5*j + 3*q - 33 + 34. What is g in 2/3 - 6*g**3 + 10*g**j - 14/3*g = 0?
1/3, 1
Let l(y) be the second derivative of -2/9*y**3 + 0 + 1/45*y**6 - 22*y + 0*y**2 - 1/6*y**4 + 0*y**5. Factor l(v).
2*v*(v - 2)*(v + 1)**2/3
Factor -7*z**3 - 23 - 4*z**2 + 16*z**2 + 45*z - 33*z**2 + 6*z**3.
-(z - 1)**2*(z + 23)
Let h(o) = -3*o**2 - o - 1. Let g(i) = -30*i**2 + 45*i + 12. Let s(d) = g(d) + 15*h(d). Factor s(f).
-3*(5*f - 1)**2
Factor 2/9*v**2 - 28/9*v + 80/9.
2*(v - 10)*(v - 4)/9
Suppose 5*l + 23 = -2*f + f, 5*f - l = 15. Let t = 51 - 48. Solve 2/7*x**4 + 2/7*x + 4/7 - 2/7*x**t - 6/7*x**f = 0.
-1, 1, 2
Let d(y) be the third derivative of -y**5/36 + 5*y**4/18 - 5*y**3/6 + 5*y**2 - 34. Factor d(i).
-5*(i - 3)*(i - 1)/3
Let n = -2541 + 7625/3. Factor n + 1/6*f**3 - 2/3*f - 1/6*f**2.
(f - 2)*(f - 1)*(f + 2)/6
Suppose l + 0 - 1 = 0. Let i = 11 - l. Suppose -i*b + 13*b - 5*b + 2*b**3 = 0. Calculate b.
-1, 0, 1
Let q(o) be the third derivative of o**6/120 + o**5/8 - 3*o**4/4 + 25*o**3/3 - 31*o**2. Let k(v) be the first derivative of q(v). Factor k(w).
3*(w - 1)*(w + 6)
Let f(q) = 2*q**3 + 75*q**2 - 77*q - 3. Let k(c) = 2*c**3 + 74*c**2 - 76*c - 4. Let d(l) = -4*f(l) + 3*k(l). Solve d(r) = 0 for r.
-40, 0, 1
Suppose -i - 4*i - 63*i**2 - i - 6*i**3 - i**4 + 52*i**2 = 0. Calculate i.
-3, -2, -1, 0
Factor -26*u + 51*u**3 - 15*u**2 + 54*u**3 - 158*u**3 + 52*u**3.
-u*(u + 2)*(u + 13)
Let m(f) = -f + 9. Let o be m(5). Let x = o + 0. Factor -4*h**4 + 0*h**2 + 2*h**4 - x*h**3 - 2*h**2.
-2*h**2*(h + 1)**2
Find w such that 0*w + 106*w**2 - 32*w - 101*w**2 - 40 - 3*w = 0.
-1, 8
Let t(i) be the second derivative of 24*i - 5*i**2 + 0 + 25/12*i**4 + 5/2*i**3. Let t(a) = 0. Calculate a.
-1, 2/5
Suppose 5*l + 6*i - i = 15, 3*l + 5*i = 9. Factor 3/4*w**l + 0 - 9/4*w**2 + 3/2*w.
3*w*(w - 2)*(w - 1)/4
Let i = -1118 + 1118. Let c = -13/2 - -7. Suppose -a**2 + i - 1/2*a - c*a**3 = 0. Calculate a.
-1, 0
Suppose l + l - 3*b + 14 = 0, 35 = -5*l - 2*b. Let k be 2/l - (-120)/28. Factor -1/3 + 1/6*h**2 - 1/2*h**3 + 1/2*h + 1/6*h**k.
(h - 2)*(h - 1)**2*(h + 1)/6
Let h(d) be the second derivative of -1/40*d**5 - 1/120*d**6 + 1/168*d**7 + 0*d**2 + 0*d**4 + 0*d**3 + 0 + 10*d. Factor h(k).
k**3*(k - 2)*(k + 1)/4
Let v(j) = j**2 - 2*j - 1. Let f(r) = 7*r**2 - 50*r - 5. Let x(q) = -f(q) + 5*v(q). Factor x(c).
-2*c*(c - 20)
Suppose 3*k - 3*p = -3, -3*k - 4 - 5 = -5*p. Let x(q) be the first derivative of -k*q**3 - 1/2*q**4 + 0*q - 2*q**2 - 2. What is i in x(i) = 0?
-2, -1, 0
Let i(n) be the third derivative of -11*n**2 - 8/165*n**6 - 64/55*n**5 - 4096/33*n**3 + 0*n - 512/33*n**4 + 0 - 1/1155*n**7. Factor i(p).
-2*(p + 8)**4/11
Suppose -299*d = -295*d + 8, -4*d - 20 = -4*t. Solve -25/3*j**t - 5/3*j**4 + 0 + 0*j + 0*j**2 = 0 for j.
-5, 0
Factor 0*w**2 + 0*w**3 - 4/7*w**5 + 0 - 4/7*w**4 + 0*w.
-4*w**4*(w + 1)/7
Let f(w) be the first derivative of -w**7/14 + 3*w**5/10 - w**3/2 - 32*w + 10. Let b(z) be the first derivative of f(z). Let b(l) = 0. Calculate l.
-1, 0, 1
Let j(y) be the first derivative of -y**3/6 + 3*y**2 - 10*y + 17. Determine g so that j(g) = 0.
2, 10
Suppose 1517/3*b**2 - 1681/3*b**3 + 160/3*b + 4/3 = 0. What is b?
-2/41, 1
Let d be 3 - 1 - (6 - 8). Let p = d - 2. Factor 17*w**3 - 6*w**p - 2*w**4 + 3*w - 11*w**3 - w.
-2*w*(w - 1)**3
Let 1/3*s**3 + 28/3*s**2 + 196/3*s + 0 = 0. Calculate s.
-14, 0
Let i(l) = -l + 11. Let y be i(8). Factor 17*m**3 + 6*m**2 - 9*m**y + 12*m**4 + 19*m**3.
3*m**2*(m + 2)*(4*m + 1)
Suppose 0 = 3*h - 2*o - 21, -3*h + 4 = -4*o - 17. Let y be 3*(-3)/3 + h. Factor y*r**2 - 4*r + 4*r - 7*r + 3*r.
4*r*(r - 1)
Suppose -l - 3 = 2*n, -8*n + 3*n + 5*l + 15 = 0. Let q(d) be the first derivative of 4/15*d**3 + n*d - 7 + 2/5*d**2. Factor q(m).
4*m*(m + 1)/5
Let g be (518/140)/((-2)/(-124)) + 3. Let c = -232 + g. Determine m so that c - 1/5*m**2 + 1/5*m = 0.
-1, 2
Let g(x) = 3*x**5 - x**3 - x**2 - x - 2. Let d(p) = 22*p**5 + 37*p**4 + 315*p**3 - 405*p**2 - 330*p + 347. Let u(r) = -2*d(r) + 14*g(r). Solve u(q) = 0.
-19, -1, 1
Let i(u) be the third derivative of 7*u**2 - 1/60*u**6 + 0 + 0*u**3 + 0*u**5 + 0*u + 1/12*u**4. Factor i(d).
-2*d*(d - 1)*(d + 1)
Let i(w) = -w**2 - w + 1. Let v(x) = -8*x**2 - 39*x - 249. Let l(p) = 28*i(p) - 4*v(p). Factor l(d).
4*(d + 16)**2
Let r(t) be the second derivative of 1/5*t**5 - 14*t - 2/21*t**7 + 0*t**3 + 0*t**2 - 1/3*t**4 + 0 + 2/15*t**6. Find n such that r(n) = 0.
-1, 0, 1
Let w(c) be the first derivative of -2*c**3/15 + 2*c**2/5 + 6*c/5 + 32. Factor w(f).
-2*(f - 3)*(f + 1)/5
Factor -26*s + 12*s**3 + 15*s - 33*s + 12