Let g(a) be the first derivative of f(a). Factor g(v).
2*(v - 3)*(v + 2)**2
Let t be ((-6)/10)/((-24)/80). Suppose -3*y**3 + 95*y**t + 3*y**4 - 51*y**2 - 47*y**2 + 3*y**5 = 0. Calculate y.
-1, 0, 1
Factor 579 - 272 + 1301 + 756*m - 700*m**2 + 696*m**2 + 1480.
-4*(m - 193)*(m + 4)
Suppose 5*o = -x + 32, 1675*x + 2*o = 1671*x + 20. Let y(s) be the second derivative of -1/72*s**4 + 0*s**x + 9*s + 1/18*s**3 + 0. Let y(m) = 0. Calculate m.
0, 2
Let -170*k - 129*k**2 - k**3 + 136*k + 93*k**2 - 595*k + 148*k**2 - 742 = 0. Calculate k.
-1, 7, 106
Let o(n) = n**3 + 128*n**2 - 276*n - 18823. Let g be o(-129). Find h such that -368/3*h + 64 - 176/3*h**2 + 12*h**4 + g*h**3 = 0.
-12, -1, 2/3
Suppose 0*r + 32 = 3*r + c, r - 5*c + 16 = 0. Factor a**2 + 7*a**3 - 10*a**2 - 16*a - 5 + 4*a + r.
(a - 2)*(a + 1)*(7*a - 2)
Let u be 2/(-6) - (-44)/(-12). Let y(q) = q**3 + 7*q**2 + 5*q - 4. Let n be y(u). Suppose 30 - 5*f**2 - 14*f**2 + n*f**2 - 35*f = 0. Calculate f.
1, 6
Let k(l) be the second derivative of -32/3*l**3 - 2/21*l**7 - 14/15*l**6 - 8*l**2 - 19/5*l**5 + 14*l - 25/3*l**4 + 4. Factor k(x).
-4*(x + 1)**3*(x + 2)**2
Let q be -3 - (1 - (-24)/(-4)). Let 2*m**q + 42 - 78 + 2*m**2 + 44 + 12*m = 0. Calculate m.
-2, -1
Let m(c) be the third derivative of -c**5/420 + 731*c**4/42 - 1068722*c**3/21 - 2*c**2 - 23*c + 11. Factor m(a).
-(a - 1462)**2/7
Let m(a) = a**3 + 1. Let f be 1/((-1)/(-3 + 0)). Let s(q) = 2*q**3 + 75*q**2 + 375*q + 622. Let g(h) = f*m(h) + s(h). Factor g(k).
5*(k + 5)**3
Let t(o) = o**2 - 10*o + 10. Let k be t(9). Suppose -4*f + 49 - k = 0. Solve 6 + 2*p**2 - 2*p**2 - 4*p + 2*p**2 + f*p = 0 for p.
-3, -1
Let d(n) be the first derivative of -n**6/20 - 9*n**5/40 + n**4/8 + 3*n**3/4 - 91*n - 70. Let u(k) be the first derivative of d(k). Find t such that u(t) = 0.
-3, -1, 0, 1
Let j be ((-2)/(-12))/((-2)/12) - -5. Let v(c) = 5*c**2 - 304*c + 4500. Let f(x) = 20*x**2 - 1215*x + 18000. Let d(t) = j*f(t) - 15*v(t). Factor d(r).
5*(r - 30)**2
Suppose 162*w - 163*w - 2 = -f, 5*w = -f + 2. Let q(n) be the second derivative of 27*n + 0*n**f + 0 + 3*n**4 + 3/20*n**5 + 18*n**3. Factor q(j).
3*j*(j + 6)**2
Let m(d) be the first derivative of d**7/630 + d**6/120 - d**4/18 + d**2 - 19*d + 33. Let k(v) be the second derivative of m(v). Factor k(s).
s*(s - 1)*(s + 2)**2/3
Let t(d) = -d**3 - 176*d**2 - 7118*d + 65. Let n be t(-63). Factor 3/5*v - 4/5*v**n + 1/5*v**3 + 0.
v*(v - 3)*(v - 1)/5
Let o(j) be the third derivative of -j**5/180 + 5*j**4/24 + 3*j**3 - 409*j**2. Let o(m) = 0. What is m?
-3, 18
Let a = 402 + -400. Find y such that -57*y - 71*y + 9 + 143*y + 7 - y**a = 0.
-1, 16
Let q(h) be the second derivative of -2*h**7/21 - 22*h**6/15 - 24*h**5/5 + 4*h**4/3 + 64*h**3/3 + 596*h + 1. Solve q(f) = 0.
-8, -2, 0, 1
Let a = -106389 + 531959/5. Let 46/5*h**2 - 10*h - a*h**3 + 18/5 = 0. What is h?
1, 9/7
Solve 463300*m**2 + 105515*m + 8199*m**3 - 26*m**5 - 1107*m**4 + 65013*m - m**5 - 99588352 + 177859*m**2 = 0 for m.
-73/3, 16
Let w(o) = -48*o - 176. Let v be w(-4). Let j be 32/v*10/35. Solve 0*c - 16/7*c**2 + j*c**3 + 0 = 0 for c.
0, 4
Let f(z) = -102*z**3 + 1569*z**2 + 1090*z + 185. Let h(u) = 509*u**3 - 7846*u**2 - 5447*u - 924. Let m(b) = 42*f(b) + 9*h(b). Solve m(j) = 0 for j.
-1/3, 182/11
Let v(n) be the second derivative of n**7/49 + 17*n**6/105 + 13*n**5/70 - 61*n**4/42 - 32*n**3/7 - 36*n**2/7 - 585*n. Solve v(d) = 0 for d.
-3, -1, -2/3, 2
Factor -8 - 13985*q**2 + 27959*q**2 - 13983*q**2 - 22*q.
-(q + 2)*(9*q + 4)
Let a(n) be the second derivative of -3/8*n**4 + 138*n + 0 - 1/4*n**3 + 3/40*n**5 + 1/20*n**6 + 3/2*n**2. Factor a(w).
3*(w - 1)**2*(w + 1)*(w + 2)/2
Let d(m) be the second derivative of m**6/195 - 9*m**5/65 - 56*m**4/39 - 2*m**3 + 207*m**2/13 + 151*m - 4. Suppose d(v) = 0. What is v?
-3, 1, 23
Determine s so that 36/5*s**2 + 1/5*s**5 + 0*s - 24/5*s**3 + 0 + 1/5*s**4 = 0.
-6, 0, 2, 3
Let z(n) = 8*n**2 - 7*n + 1. Let r(v) = -73*v**2 + 469*v - 1218. Let k(d) = -4*r(d) - 36*z(d). Factor k(h).
4*(h - 403)*(h - 3)
Let p(x) = -14*x**4 + 110*x**3 - 24*x**2 - 64*x + 40. Let y(g) = g**4 - 8*g**3 + g**2 + 2. Let l(h) = p(h) + 12*y(h). Determine z, given that l(z) = 0.
-2, 1, 4
Determine k, given that -38*k**2 + 896/3 - 800/3*k + 2/3*k**4 + 16/3*k**3 = 0.
-8, 1, 7
Let w(v) be the third derivative of 2*v**7/105 - 11*v**6/5 + 68*v**5 + 1156*v**4/3 + 266*v**2 + v. Determine q, given that w(q) = 0.
-2, 0, 34
Let u(y) = -5*y**5 - 14*y**3 - 5*y + 12. Let f(o) = 9*o**5 + 26*o**3 + 9*o - 22. Let i(v) = 6*f(v) + 11*u(v). Factor i(h).
-h*(h - 1)**2*(h + 1)**2
Determine x so that -6/5*x**3 - 6*x**2 + 396/5*x + 0 = 0.
-11, 0, 6
Let o be 4/(-3) - (-9)/27. Let c be (-24)/48 + (1 - o). Determine t so that -c*t**2 + 3 - 3/2*t = 0.
-2, 1
Determine r so that -1/2*r**4 + 0 + 15*r**3 + 0*r - 1/2*r**5 + 36*r**2 = 0.
-4, -3, 0, 6
Solve 9*u**2 - 9/8*u**4 - 15/4*u**3 - 15/8 - 9/4*u = 0.
-5, -1/3, 1
Let x(j) be the first derivative of -27/2*j**2 + 0*j - 1/18*j**5 + 0*j**4 - 8 + 0*j**3 + 1/180*j**6. Let n(z) be the second derivative of x(z). Factor n(l).
2*l**2*(l - 5)/3
Let p(m) be the second derivative of m**8/1680 - 17*m**7/630 + 31*m**6/180 - m**5/2 - 3*m**4/4 + 157*m. Let k(i) be the third derivative of p(i). Factor k(y).
4*(y - 15)*(y - 1)**2
Let l(n) be the third derivative of -n**6/720 - 53*n**5/360 - 17*n**4/24 - 515*n**2 - 2. Factor l(a).
-a*(a + 2)*(a + 51)/6
Suppose -4*y + 20 = 0, -2*r - 6 - 22 = -4*y. Let b be (-6)/r - ((-10)/(-4))/(-5). Factor -42*a**3 - 3*a - 5*a + a**5 - 5*a**5 - 20*a**4 + 6*a**3 - 28*a**b.
-4*a*(a + 1)**3*(a + 2)
Suppose 4*j - 5 = -1, s - 2*j - 2 = 0. Factor -22*w**4 + 12*w**3 - 16*w - 14*w**2 + 2*w**5 + 2*w**5 + 6*w**s + 30*w**2.
4*w*(w - 2)**2*(w - 1)*(w + 1)
Let o = 33 + -1. Suppose 41*r**4 - 116*r**4 + 37*r**4 + 60*r**2 + 42*r**4 + 32*r - o*r**3 - 64 = 0. What is r?
-1, 1, 4
Let v(c) be the second derivative of 0 - 50/3*c**3 + 5/12*c**4 + 250*c**2 - 75*c. Find d such that v(d) = 0.
10
Let l(k) = -10*k**3 + 4*k**2 - 2*k - 22. Let m(p) = -280*p - 24 + 277*p - 12*p**3 + 1 + 3*p**2. Let w(h) = 7*l(h) - 6*m(h). Solve w(b) = 0.
-4, -2, 1
Let m(o) = -3*o**3 - 312*o**2 + 606*o - 309. Let u(g) = g**3 + 156*g**2 - 303*g + 154. Let v(n) = -4*m(n) - 9*u(n). Solve v(b) = 0 for b.
1, 50
Let t(s) be the second derivative of s**5/40 - 5*s**4/72 - 13*s**3/6 + 647*s. What is r in t(r) = 0?
-13/3, 0, 6
Suppose 3*o + c - 13 = -2*o, -3*o + c + 3 = 0. Determine t so that -8421 + 0*t**2 + 20*t + 8443 - 2*t**o = 0.
-1, 11
Let l(t) be the first derivative of 2*t**4/5 + 454*t**3/15 + 167*t**2/5 - 112*t/5 - 5857. Factor l(w).
2*(w + 1)*(w + 56)*(4*w - 1)/5
Let z be ((-2)/5)/(37008/(-1179630)). Suppose 6 + z*q + 3/2*q**2 = 0. Calculate q.
-8, -1/2
Let l(r) = -2*r**2 + 17*r + 19. Let g be l(-1). Suppose x + 4*x - 3*h + 6 = 0, 2*h - 4 = g. What is o in 6/7*o**3 + x*o - 4/7*o**2 + 0 - 2/7*o**4 = 0?
0, 1, 2
Let d(r) be the second derivative of -8*r + 0*r**2 + 0 - 7/54*r**3 - 1/108*r**4. Let d(l) = 0. What is l?
-7, 0
Let t be 1 + -1 + (-104 - 30 - -136). Find p such that 1/2*p**t - 24*p - 49/2 = 0.
-1, 49
Let m(o) = 74*o**3 + 430*o**2 - 2079*o. Let t(b) = 13*b**3 + 72*b**2 - 346*b. Let u(r) = 6*m(r) - 34*t(r). Factor u(v).
2*v*(v - 5)*(v + 71)
Let b(c) be the second derivative of c**7/168 - 209*c**6/120 + 1027*c**5/5 - 36166*c**4/3 + 984256*c**3/3 - 913952*c**2 - 17*c + 6. Let b(w) = 0. Calculate w.
1, 52
Let m = 118794 + -118792. Factor 3/2*c - 3/8*c**m + 0.
-3*c*(c - 4)/8
Let d be ((-19)/19)/((-2)/(-4)). Let g be (1 + 0)*((-13)/d - 6). Factor g - 5/4*r + r**2 - 1/4*r**3.
-(r - 2)*(r - 1)**2/4
Let h(s) be the second derivative of 8/21*s**4 + 0*s**2 - 1/35*s**5 + 0*s**3 - s - 2. Factor h(k).
-4*k**2*(k - 8)/7
Let v(r) be the first derivative of 5*r**4/4 + 10*r**3 - 725*r**2/2 - 750*r + 1485. Factor v(n).
5*(n - 10)*(n + 1)*(n + 15)
Solve 0*i + 2/7*i**4 - 40/7*i**3 + 72/7*i**2 + 0 = 0 for i.
0, 2, 18
Let v(b) be the third derivative of b**7/42 - 11*b**6/24 - 13*b**5/12 + 55*b**4/24 + 10*b**3 + 1287*b**2. Let v(f) = 0. What is f?
-1, 1, 12
Let c(u) be the third derivative of u**7/21 + 51*u**6/40 + 45*u**5/4 + 679*u**4/24 + 49*u**3/2 + 3741*u**2. Factor c(f).
(f + 1)*(f + 7)**2*(10*f + 3)
Let q be (1/(-10))/(((-3366)/220)/51). Factor 2/9 + 5/9*h + q*h**2.
(h + 1)*(3*h + 2)/9