 Factor -j*t**2 + t - m.
-(t - 3)*(t - 2)/5
Let n be 12/(-63)*(306/36 + -10). Solve 0 - n*u**2 - 10/7*u = 0.
-5, 0
Let r(g) = -7*g**2 + 17*g**2 - 3*g**2 + 1342 + 104*g. Let h(k) = 8*k**2 + 104*k + 1340. Let p(s) = -5*h(s) + 6*r(s). Let p(x) = 0. Calculate x.
-26
Let x be 18/((-36)/8 + 4). Let d = x + 38. Factor -4*o + 6 + 2*o - 2*o**d + 6*o.
-2*(o - 3)*(o + 1)
Let c be (-2)/(-4) - (12 + (-440)/16). Factor -l**3 - 10*l**3 + 11*l**2 - 4*l**3 + c*l**2 - 2*l**2.
-5*l**2*(3*l - 5)
Suppose 2*a + 787*j = 788*j + 61, -93 = -3*a + 3*j. Let u(o) be the second derivative of 0 + 3/2*o**3 + 1/4*o**4 - a*o + 3*o**2. Factor u(t).
3*(t + 1)*(t + 2)
Let r(x) be the second derivative of x**6/60 - 7*x**5/40 - x**4/3 - 226*x - 3. Factor r(n).
n**2*(n - 8)*(n + 1)/2
Suppose -147 = -13*n + 685. Let t be n/28 - (-4)/(-14). Factor -17 - 8 + 12*d + 17 - 4*d**t.
-4*(d - 2)*(d - 1)
Suppose 2*r - 12 = 5*r, 12 = -4*q + 3*r. Let v be (4 - (-192)/(-36))*q/2. Factor 3*a**3 - 1/2*a**v + 0 - 11/2*a**2 + 3*a.
-a*(a - 3)*(a - 2)*(a - 1)/2
Let h(w) be the second derivative of w**4/18 - 106*w**3/9 + 103*w**2 - 5*w - 988. Factor h(r).
2*(r - 103)*(r - 3)/3
Let i be (10/3)/5 - -13*(-26)/845. Let q(w) be the second derivative of 8/3*w**3 - i*w**6 + 4/3*w**4 + 0*w**2 + 2/21*w**7 - 3/5*w**5 + 0 + 38*w. Factor q(c).
4*c*(c - 2)**2*(c + 1)**2
Let w be (-165)/75 + (-2)/(-10). Let f(o) = -o**4 - o**2 - o. Let s(u) = -4*u**3 - 2*u**2 - 2*u. Let m(i) = w*s(i) + 4*f(i). Factor m(j).
-4*j**3*(j - 2)
Let z(h) be the first derivative of -h**6/10 + 3*h**5/5 - 5*h**4/4 + h**3 + 105*h - 25. Let a(g) be the first derivative of z(g). Factor a(x).
-3*x*(x - 2)*(x - 1)**2
Let o(f) = 42*f**3 + f**2 - 13*f + 8. Let x be o(3). Suppose 1109*h - x*h = -9. Let -1/2*z - 1/4*z**2 + 0 + 1/4*z**h = 0. What is z?
-1, 0, 2
Let r(v) = -6*v**2 + 4*v - 3. Let z be r(1). Let i(l) = -3*l - 12. Let n be i(z). Factor -1 + 11*j**4 + 7*j - 48*j**2 + 3*j**5 - 8*j**5 + 38*j**2 - 2*j**n.
-(j - 1)**3*(j + 1)*(5*j - 1)
Let s(v) be the first derivative of v**3 + 153*v**2/2 - 486*v + 6809. Determine m, given that s(m) = 0.
-54, 3
Let x(j) be the first derivative of -676*j**3/15 + 2808*j**2/5 - 11664*j/5 + 1823. Factor x(m).
-4*(13*m - 54)**2/5
Suppose 0 = -3*y - 4*d + 6, 7*d = 4*d. Factor 23*z**3 - 38*z**3 + 17*z**3 - 6*z**y + 6*z - 4 + 2.
2*(z - 1)**3
Factor 1182*b**3 - 1186*b**3 + 20*b**2 - 480 + 208*b + 4*b**2.
-4*(b - 10)*(b - 2)*(b + 6)
Suppose y - a - 23 = -15, 4*a + 4 = 0. Let x be (-8)/32*(-48)/y. Find n, given that -10/7*n + x - 4/7*n**2 + 2/7*n**3 = 0.
-2, 1, 3
Let x(h) be the first derivative of -1/2*h**4 - 11*h**2 - 2/5*h**5 + 6*h**3 + 8*h - 58. Find j, given that x(j) = 0.
-4, 1
Let b(t) be the third derivative of t**7/1680 + 11*t**6/960 - 73*t**5/480 + 109*t**4/192 - t**3 - 521*t**2. Factor b(u).
(u - 3)*(u - 1)**2*(u + 16)/8
Let s be 56 - 42 - (15 + -1). Let q(a) be the third derivative of -10*a**2 + 0 + 1/28*a**4 + 1/210*a**5 + s*a + 2/21*a**3. Find h such that q(h) = 0.
-2, -1
Let j(o) = -12*o + 9. Let i be j(-3). Let v be (2 + 7)*3/i. Solve -24/5 - 21/5*t + v*t**2 = 0 for t.
-1, 8
Let b(f) be the second derivative of -f**4/12 - 237*f**3 - 505521*f**2/2 - 149*f - 9. Factor b(s).
-(s + 711)**2
Suppose 2*o + 81 - 251 = -2*v, -173 = -2*v - 5*o. Factor 12*w - 3/7*w**2 - v.
-3*(w - 14)**2/7
Let a = -2/112909 - -451654/1016181. Determine l so that a*l**2 + 5/9*l + 2/9 + 1/9*l**3 = 0.
-2, -1
Let c = -1049001/76 + 13803. Let z = c + 15/38. Let -3/8*p**2 - z*p - 3/8 = 0. What is p?
-1
Suppose 20*g + y + 15 = 21*g, 3*g + 5*y - 5 = 0. Suppose -8 = g*f - 8. Suppose -6/7*l**4 + f - 1/7*l**5 + 0*l - 12/7*l**3 - 8/7*l**2 = 0. Calculate l.
-2, 0
Let f(k) be the second derivative of k**6/12 + 46*k**5/5 + 217*k**4/24 - 73*k**3/6 + 4303*k. Factor f(l).
l*(l + 1)*(l + 73)*(5*l - 2)/2
Let n(x) = x**3 - 4*x**2 - 6*x - 4. Let z be n(6). Suppose -4*l + 19 = -z*p + 37*p, 18 = 5*p + 3*l. Solve 2/5 - 8/5*q**p + 0*q**2 + 6/5*q = 0.
-1/2, 1
Let f be 1892/20 - (25 - 3). Let s(a) be the second derivative of 35*a + 891/10*a**3 + 0 - f*a**2 + 21/100*a**5 - 39/5*a**4. Factor s(g).
3*(g - 11)**2*(7*g - 2)/5
Suppose 2*a = -3*a + 180. Suppose 6*w = -6*w + a. Suppose 8*m - 24*m**2 - 26*m**2 + 34*m**2 + 2*m**w + 6*m**4 = 0. Calculate m.
-2, 0, 2/3, 1
Solve -552/5*y**3 + 16/5*y**4 - 2159/5*y**2 - 152/5 + 1182/5*y = 0.
-4, 1/4, 38
Let d(s) = s**3 + s - 1. Let r(i) = -4*i**3 + 8*i**2 - 20*i + 8. Let g = 253 + -254. Let l(c) = g*r(c) - 8*d(c). Factor l(o).
-4*o*(o - 1)*(o + 3)
Let b be 6/(-8) + (((-15284)/3600)/1 - -5). Let f(p) be the third derivative of 1/450*p**5 + 19*p**2 + 0*p**3 + 0 + b*p**6 + 0*p**4 + 0*p. Solve f(a) = 0.
-1/4, 0
Suppose -3*w + 20 = -w. Let h be (-6)/w*45/(-54). Let -1/6*v**2 - 1/6*v**4 + h*v + 1/3 - 1/2*v**3 = 0. What is v?
-2, -1, 1
Factor 14/9*c**3 - 332/9*c**2 - 32/3*c + 0.
2*c*(c - 24)*(7*c + 2)/9
Let v(p) = p**3 - 18*p**2 + 43*p + 56. Let s be v(15). Suppose -5*n = -s*n + 42. Factor -8/11*q**n + 70/11*q + 18/11.
-2*(q - 9)*(4*q + 1)/11
Let y(f) be the first derivative of 8 + 64/27*f**3 + 0*f + 1/3*f**4 + 14/3*f**2. Factor y(b).
4*b*(b + 3)*(3*b + 7)/9
Factor 10*d**2 + 2*d**3 - 176*d + 569*d - 194*d - 195*d - 16.
2*(d - 1)*(d + 2)*(d + 4)
Let b(q) = -q**2 - 2*q + 1. Suppose -29*f + 8 = -21*f. Let a(z) = 9*z**2 - 21. Let v(g) = f*a(g) + 6*b(g). Factor v(t).
3*(t - 5)*(t + 1)
Suppose 3*m - 2*d = 2 - 0, 3*d = 3*m. Let i = 1115/2 - 544. Factor 3 + 6*w**m + i*w.
3*(w + 2)*(4*w + 1)/2
Let s be 37/7 - ((-8)/(-7))/4. Factor s*h - 4*h + 10*h**2 - h - 5*h**3.
-5*h**2*(h - 2)
Let b = -175417/3 + 58473. Let -4/3*q + 2*q**4 - 2*q**2 + 2/3*q**3 + b*q**5 + 0 = 0. What is q?
-2, -1, 0, 1
Suppose 1/5*i**2 + 0 + 182/5*i = 0. What is i?
-182, 0
Suppose 642*c - 1428 - 1144 + 646 = 0. Suppose 121/6*b**5 + 6*b + 0 + 829/6*b**c + 341/3*b**4 - 62*b**2 = 0. What is b?
-3, 0, 2/11
Factor -607*d**3 - 535*d**2 - 260*d**2 - 604*d**3 + 1810*d**3 - 598*d**3.
d**2*(d - 795)
Let w(j) be the second derivative of -j**6/15 - 17*j**5/10 - 22*j**4/3 - 28*j**3/3 - 763*j. Factor w(u).
-2*u*(u + 1)*(u + 2)*(u + 14)
Let r(v) = 4*v**3 + 10*v**2 - 8*v. Suppose -9 = -0*m - 3*m. Let w(d) = d**2 - d + 1 - m + d**3 + 2. Let k(t) = -r(t) + 6*w(t). What is a in k(a) = 0?
0, 1
Let m(f) be the second derivative of -f**6/30 + 23*f**5/4 - 3361*f**4/12 + 1007*f**3/2 + 3249*f**2 - 1598*f. Determine s, given that m(s) = 0.
-1, 2, 57
Let k(s) be the third derivative of -1/15*s**5 + 6 - 3*s**2 - 56/3*s**3 + 0*s - 29/6*s**4. Factor k(c).
-4*(c + 1)*(c + 28)
Let g be (8298/(-4610))/(3/15*-3). Factor -27/2*i**2 + 3/4*i**g - 42 + 45*i.
3*(i - 14)*(i - 2)**2/4
Let i = 2247/106 - 1044/53. Let q(k) be the first derivative of -6*k + 2*k**3 - 31 + 3/4*k**4 - i*k**2. Factor q(f).
3*(f - 1)*(f + 1)*(f + 2)
Let f be (22 - 7) + (-2 - -2). Suppose -f = -g - 2*g, -4*a + 205 = g. Factor 11 + 5*k - 35*k**3 + 15*k**2 + 5*k**4 - 11 + a*k**3.
5*k*(k + 1)**3
Suppose t + 12 = 5*a - 2*t, -4 = -2*a + t. Suppose 16*k - 80 = -a. Factor 24*l**2 + k + 11 - 1606*l + 4*l**3 + 1642*l.
4*(l + 1)**2*(l + 4)
Let k = -1512 - -2592. Let i = k - 1075. Solve 36/5 - 56/5*s**2 + 4*s**4 + 12/5*s - 8/5*s**3 - 4/5*s**i = 0.
-1, 1, 3
Let d be 2/6 - (-25)/15. Let z = -2097 - -2112. Suppose -d*m**5 - 12*m**4 - 9*m**3 - 28*m**2 + 12*m**2 - z*m**3 = 0. Calculate m.
-2, 0
Let i be 24388/147 + 4/6 + -6. Let x = 161 - i. Factor 0*g - 6/7*g**2 - x*g**5 + 0 + 9/7*g**3 + 0*g**4.
-3*g**2*(g - 1)**2*(g + 2)/7
Let l(s) be the first derivative of 3/4*s**4 - 3*s**3 + 34 - 9*s**2 + 24*s. Factor l(c).
3*(c - 4)*(c - 1)*(c + 2)
Let f(n) be the third derivative of -n**5/50 - 13*n**4/20 + 14*n**3/5 - 10*n**2 - 53*n. Let f(s) = 0. Calculate s.
-14, 1
Suppose -2*z + 7 = 2*g - 3*z, -g = -5*z - 17. Let 5*w**3 - 23*w**3 + 9*w**3 + 11*w + 10*w**3 + 12*w**g = 0. Calculate w.
-11, -1, 0
Factor -73*g**3 + 167 - 1179*g + 79*g**3 - 54*g**3 + 2376*g**2 - 20.
-3*(g - 49)*(4*g - 1)**2
Let s be 4*(-3)/(2070/35). Let p = s - -236/483. Let 0 - 2/7*c**2 - p*c = 0. What is c?
-1, 0
Let z(g) = 10*g - 84. Let n be z(9). Let p be (-7)/22 - (-12)/144*n. Factor 8/11*i**3 + 2/11 - p*i**2 - 8/11*i.
2*(i - 1)*(i + 1)*(4*i - 1)/11
Let l(q) be the first derivative of 5/4*q**4 - 20/3*q**3 - 9 - 35/2*q**2 + 50*q. Determine a, given that l(a) = 0.
-2, 1, 5
Let i be (2 - 115