1
Let y = 7353/2 + -3676. Factor -3/8*m**4 - 1/2*m**3 + 0 + 0*m + y*m**2.
-m**2*(m + 2)*(3*m - 2)/8
Let l(t) = -t**2 - 7*t + 370. Let w be l(-23). Factor 9/4*f**w + 27 + 1/8*f**3 + 27/2*f.
(f + 6)**3/8
Let j(d) be the third derivative of 0 + 0*d + 0*d**4 + 0*d**3 + 3/160*d**6 - 1/40*d**5 - 1/280*d**7 + 19*d**2. Factor j(a).
-3*a**2*(a - 2)*(a - 1)/4
Suppose -11*v - 8824 - v**2 + 2*v**2 + 2*v + 8802 = 0. What is v?
-2, 11
Let v be 3*(-4)/((-16)/4). Let 0*f**2 + 4*f - 3*f**2 + 11*f**3 - 10*f**v - f**2 = 0. Calculate f.
0, 2
Let i = -648 - -12963/20. Let k = 2/5 - i. Determine t, given that 0*t**2 - k*t**4 - 1/2*t + 1/4 + 1/2*t**3 = 0.
-1, 1
Let k = 27624 + -27624. Factor 4/5*a**2 + k + 2/5*a.
2*a*(2*a + 1)/5
Let v(z) = 3*z**2 - 284*z + 6621. Let c(x) = -30*x**2 + 2841*x - 66207. Let i(b) = -2*c(b) - 21*v(b). Let i(q) = 0. Calculate q.
47
Let d(a) = 71*a - 420. Let n be d(6). Let b be 1 - (-3 - 1*-2). Factor n - 15/2*w + 3/2*w**b.
3*(w - 4)*(w - 1)/2
Let c be (4 - (4 + -7)) + 2. Suppose 3 = 10*p - c*p. Find v, given that 5*v**2 - 11*v**2 - v**p - 2*v**3 - 3*v = 0.
-1, 0
Let w(p) = 2*p**5 - p**4 - 3*p**3 + 3*p. Let q(b) = -b**5 + b**2 - b. Let v(c) = q(c) + w(c). Factor v(x).
x*(x - 2)*(x - 1)*(x + 1)**2
Factor -82*a + a**4 + a**5 + 22*a - 5*a**2 + 27*a + 31*a - 3*a**3.
a*(a - 2)*(a + 1)**3
Factor -19 + 18*j**2 - 17*j**2 + 63*j + 2*j**3 - 37*j**2 + j**3 - 11.
3*(j - 10)*(j - 1)**2
Let z = 5 - 2. Suppose -11*w - 3 = -25. Suppose 3 - 4*t + 3*t**w - 5*t**z + 2*t + 1 + 14*t = 0. Calculate t.
-1, -2/5, 2
Let p(d) = 21*d**3 + 384*d**2 - 1761*d + 1764. Let q(n) = 3*n**3 + 55*n**2 - 252*n + 252. Let m(h) = -4*p(h) + 27*q(h). Suppose m(f) = 0. Calculate f.
-21, 2
Let y(t) = 0 - 44*t - 2*t + 0 - 6*t**2. Let j(o) = -o**2 - 9*o. Suppose 17 = -3*x - 5*r, 0 = -x - 0*r - 3*r + 1. Let k(l) = x*j(l) + 3*y(l). Factor k(q).
-4*q*(q + 3)
Find k such that -172/7 + 4/7*k**2 + 24*k = 0.
-43, 1
Find o such that -5*o - 35/4*o**2 - 5/4*o**3 + 15 = 0.
-6, -2, 1
Let s(l) = -4*l**3 - 44*l**2 + 134*l - 6. Let t(q) = -q**3 - 2*q**2 + q - 1. Let h(j) = s(j) - 6*t(j). Determine u so that h(u) = 0.
0, 8
Factor 21/8*c + 9/8*c**2 - 15/4.
3*(c - 1)*(3*c + 10)/8
Let p be ((-2)/(-3))/(4*(-5)/(-2160)). Let h be (p/63)/(2/7). Determine g, given that 0 - 1/5*g**3 - 4/5*g**2 + 4/5*g**h + 1/5*g = 0.
-1, 0, 1/4, 1
Find q such that -25*q - 13*q**3 + 13*q**4 - 10 - 3*q**4 + 13*q**3 + 25*q**3 = 0.
-2, -1, -1/2, 1
Let l(d) be the first derivative of -9*d + 13 - 5*d**2 - 1/3*d**3. What is b in l(b) = 0?
-9, -1
Let q(v) be the first derivative of -5*v**4/4 + 40*v**3/3 + 29. Suppose q(m) = 0. What is m?
0, 8
Let r(p) be the third derivative of 0 + 0*p - 5/48*p**4 + 1/6*p**3 + 1/30*p**5 + 3*p**2 - 1/240*p**6. Factor r(n).
-(n - 2)*(n - 1)**2/2
Factor -283*k - 2*k**2 - 3267 - 4*k**2 + 3*k**2 + 85*k.
-3*(k + 33)**2
Let f = -2125/9 - -11159/45. Let d = f + -56/5. Factor 1/3*g**2 + d + g.
(g + 1)*(g + 2)/3
Let u = 2141/60 + -107/3. Let q(b) be the third derivative of 1/210*b**7 + 0*b**6 + 0 + 0*b - u*b**5 + 0*b**3 + 4*b**2 + 0*b**4. Factor q(n).
n**2*(n - 1)*(n + 1)
Let n(w) = -w**3 - 9*w**2 - 6*w + 1. Let h be n(-9). Let x be 2/5 + (-22)/h. Factor 0 + r**2 + x*r + 1/2*r**4 + 3/2*r**3.
r**2*(r + 1)*(r + 2)/2
Factor -808/5*c - 20802/5*c**2 - 4040*c**3 - 1000*c**4 - 8/5.
-2*(c + 2)**2*(50*c + 1)**2/5
Let w(d) = 27*d**2 + 12*d + 2. Let p(k) = -k**2 - k - 1. Suppose -1 - 23 = -2*r. Suppose r = 4*j + 2*j. Let o(s) = j*p(s) + w(s). Factor o(q).
5*q*(5*q + 2)
Let y(d) = 2*d - 10. Let k be y(5). Suppose 4*l**2 + 5*l**4 - l**3 - 7*l**4 - l**3 + k*l**3 = 0. What is l?
-2, 0, 1
Suppose n + 63 = 37. Let i = 28 + n. Factor -8/5*k**i + 0 + 0*k - 2/5*k**4 - 8/5*k**3.
-2*k**2*(k + 2)**2/5
Let t(l) = 7*l**2 - 6*l - 7. Let b(r) = -r**2 + 2*r + 1. Let v(z) = 3*b(z) + t(z). Determine x, given that v(x) = 0.
-1, 1
Factor -2963088/5*j + 42224004/5 - 912/5*j**3 + 4/5*j**4 + 77976/5*j**2.
4*(j - 57)**4/5
Let d(v) be the first derivative of -16*v - 4/3*v**3 + 7 + 8*v**2. Solve d(w) = 0.
2
Let m(q) be the third derivative of q**5/360 - 7*q**4/72 + 2*q**3/3 + 50*q**2. Factor m(c).
(c - 12)*(c - 2)/6
Let l(f) be the second derivative of -22*f + 0 - 1/24*f**4 + 3/2*f**3 - 81/4*f**2. Find j such that l(j) = 0.
9
Suppose 0 = -4*h + 8*h + 5*r - 5, -h + 1 = r. Factor 4/3*d + h + 2/3*d**4 - 2*d**2 + 0*d**3.
2*d*(d - 1)**2*(d + 2)/3
Suppose -2*p + 8 = -f, -p = -5*f + 2*f + 1. Suppose h = 2*v, f*h - 8 = -0. What is j in 18*j**3 + 12*j + 3 + v*j + 30*j**2 - 1 = 0?
-1, -1/3
Let m(k) = 9*k**4 + 42*k**3 + 128*k**2 + 103*k + 43. Let y(n) = -5*n**4 - 21*n**3 - 65*n**2 - 51*n - 22. Let v(s) = -4*m(s) - 7*y(s). Solve v(h) = 0.
-18, -1
Factor 5 - 1/2*b**2 - 3/2*b.
-(b - 2)*(b + 5)/2
Let k(b) = 4*b**4 + 63*b**3 + 59*b**2 + 7*b + 7. Let q(p) = -3*p**4 - 42*p**3 - 39*p**2 - 5*p - 5. Let n(f) = -5*k(f) - 7*q(f). Suppose n(l) = 0. What is l?
-1, 0, 22
Let l(z) be the first derivative of 2*z**5/65 - 7*z**4/26 + 12*z**3/13 - 20*z**2/13 + 16*z/13 + 49. Factor l(w).
2*(w - 2)**3*(w - 1)/13
Factor -26 + 160 + 30*z + z**2 - 35 + 126.
(z + 15)**2
Let u(b) = b**3 - 3*b**2 + b + 3. Let a = -32 + 32. Let g be u(a). Factor 0*d - 1/3*d**2 + 0*d**g + 1/3*d**4 + 0.
d**2*(d - 1)*(d + 1)/3
Let m(g) = -6*g**3 + 60*g**2 + 13*g - 74. Let d(r) = 4*r**3 - 40*r**2 - 9*r + 50. Let p(h) = -7*d(h) - 5*m(h). Factor p(s).
2*(s - 10)*(s - 1)*(s + 1)
Let -6/5*v**2 + 6 + 1/5*v - 1/5*v**3 = 0. What is v?
-5, -3, 2
Let m(c) be the third derivative of c**6/80 - c**5/10 + c**4/4 - 83*c**2. Factor m(h).
3*h*(h - 2)**2/2
Suppose -5*u = 6*u - 2*u. Suppose -3*i + 6 + u = 0. Factor -2/5*y**2 - i*y**4 + 0 + 0*y - 8/5*y**3 - 4/5*y**5.
-2*y**2*(y + 1)**2*(2*y + 1)/5
Determine r so that 0*r + 0 - 20/3*r**2 + 2/9*r**3 = 0.
0, 30
Let s = 3443 + -3440. Factor -8/3*x + 4/3*x**2 + 76/3*x**4 + 28/3*x**5 + 20*x**s + 0.
4*x*(x + 1)**3*(7*x - 2)/3
Let h(t) be the first derivative of -2*t**5/45 + 31*t**4/18 - 220*t**3/9 + 1300*t**2/9 - 2000*t/9 - 78. Factor h(l).
-2*(l - 10)**3*(l - 1)/9
Let k be (-4)/(-2) + 20/(-11). Let o(y) = y**3 + 21*y**2 - 23*y - 22. Let q be o(-22). Factor 0 - 2/11*h**3 + q*h - k*h**4 + 4/11*h**2.
-2*h**2*(h - 1)*(h + 2)/11
Let k = -7 - -4. Let z be (-3)/(-1) + (k - -2). Factor 11*r - 8*r - z*r**2 - r**2.
-3*r*(r - 1)
Factor -1/3*l**2 - 8*l - 23/3.
-(l + 1)*(l + 23)/3
Let j(y) = y - 2. Let g(o) = -3*o**2 - 22*o - 40. Let c(m) = g(m) - 2*j(m). Suppose c(f) = 0. Calculate f.
-6, -2
Let w be (-1 + 4)*9/(-45)*-55. Factor -w*r**2 - 75 + 30*r + 17*r**3 - 14*r**3 + 75*r.
3*(r - 5)**2*(r - 1)
Let f be 2/((-5)/(-2) + -2). Let r(z) = -z + 3. Let w be r(0). Determine l, given that w*l**2 + f*l**3 + 3*l - 3*l**4 - l**3 - 6*l**3 = 0.
-1, 0, 1
Let h(j) be the second derivative of -j**7/1512 + j**6/216 - j**5/72 - 25*j**4/12 + 28*j. Let k(u) be the third derivative of h(u). Factor k(o).
-5*(o - 1)**2/3
Let h(g) = 13*g - 43. Let w(z) = 3*z - 11. Let i(q) = 2*h(q) - 9*w(q). Let m be i(9). Let -o - m*o - o**2 + 5*o = 0. What is o?
0
Let l be (1 + -1)/(2 + (6 - 13)). Let k(h) be the second derivative of 0*h**2 + l + 0*h**3 - 1/30*h**4 - 3*h. Factor k(t).
-2*t**2/5
Suppose 0 + 45 = x. Factor -5*c**4 - 10*c - 15*c**3 - 102*c**2 + x*c**2 + 5*c**5 + 82*c**2.
5*c*(c - 1)**3*(c + 2)
Let f(a) be the third derivative of -a**6/240 - 7*a**5/120 + 6*a**2 + 5*a. Factor f(r).
-r**2*(r + 7)/2
Let y(m) = 16*m**5 - 6*m**4 + 8*m**3 - 14. Let w(i) = -i**5 + i**4 + 46 + 47 - 92. Let l(k) = 28*w(k) + 2*y(k). Factor l(z).
4*z**3*(z + 2)**2
Let m = 1335 + -28025/21. Let b(i) be the third derivative of 0*i**3 - 2/3*i**6 - m*i**7 - 4/15*i**5 + 0*i**4 + 7*i**2 + 0 + 0*i. Suppose b(t) = 0. What is t?
-2/5, 0
Let b(t) be the first derivative of 11*t**4/24 - 29*t**3/3 + 56*t**2 + 64*t/3 + 193. Find m such that b(m) = 0.
-2/11, 8
Let f(l) be the first derivative of 1/3*l**3 - 4*l + 2*l**2 - 1/4*l**4 + 7. Let f(w) = 0. Calculate w.
-2, 1, 2
Let o be (-550)/(-2717) - (-14)/133. Factor o*j + 0 - 18/13*j**2.
-2*j*(9*j - 2)/13
Let f(g) = -3*g**5 - 3*g**4 - 11*g**3 - 15*g**2 - 9*g. Let k(o) = -o**5 + o**3 - o. Let l(u) = f(u) - 5*k(u). Suppose l(n) = 0. Calculate n.
-1, -1/2, 0, 4
Factor 0 - 2/7*x**2 + 264/7*x.
-2*x*(x - 132)/7
Let a = 8457 - 8453. Let -12 - 3/2*f**5 - 3/2*f**3 + 6*f**a - 21*f**2 + 30*f = 0. Calculate f.
-2, 1, 