0
Factor -40/7*f + 2/7*f**2 + 24.
2*(f - 14)*(f - 6)/7
Let k = 4482913/4 + -1120723. Factor 0*d + 0 - k*d**2 + 31/4*d**3 + 1/4*d**5 - 11/4*d**4.
d**2*(d - 7)*(d - 3)*(d - 1)/4
Let s be (-7)/(-9)*-31*(-212)/11501. Suppose -5*h = -4*h - 2. Let 1/9*x**3 - s*x**h - 2/9 + 5/9*x = 0. Calculate x.
1, 2
Let h(f) be the third derivative of -f**8/84 + 4*f**7/5 - 299*f**6/30 - 978*f**5/5 - 1008*f**4 - 2304*f**3 - 1172*f**2. Determine o so that h(o) = 0.
-3, -2, -1, 24
Factor -2381*r + 4770 + 542*r**2 + 451*r**3 + 362*r**3 - 815*r**3 - 817*r.
-2*(r - 265)*(r - 3)**2
Let w(u) be the first derivative of -2*u**5/55 - 40*u**4/11 + 328*u**3/33 - 7081. Suppose w(r) = 0. Calculate r.
-82, 0, 2
Find l, given that 254/7*l - 2/7*l**2 + 256/7 = 0.
-1, 128
Let p(y) = -2*y**4 - 2*y**3 + 2*y. Let r(b) be the first derivative of 4*b**5/5 + 3*b**4/4 - 5*b**2/2 + 18. Let m(d) = -5*p(d) - 2*r(d). Factor m(l).
2*l**3*(l + 2)
Let w(s) = -3*s**2 - 16*s + 36. Let o(z) be the second derivative of -z**4/6 - 5*z**3/2 + 18*z**2 - 50*z. Let a(v) = 4*o(v) - 3*w(v). Factor a(h).
(h - 6)**2
Suppose -364*u + 383*u - 323 = 0. Let k(a) be the first derivative of 1/24*a**6 + 3/20*a**5 + 0*a**2 + 0*a**4 - 1/3*a**3 + 0*a + u. What is r in k(r) = 0?
-2, 0, 1
Factor -6/23*g + 20/23 - 2/23*g**2.
-2*(g - 2)*(g + 5)/23
Determine l so that -9252/7*l**3 + 5616/7*l**2 + 0 + 3264/7*l**4 - 256/7*l**5 - 972/7*l = 0.
0, 3/8, 3, 9
Let f be (28/(-30))/(4018/5740) - 12/(-9). Find v such that 0*v**2 + 1/3*v**4 - 1/6*v**3 + f - 1/6*v**5 + 0*v = 0.
0, 1
Suppose -103*h + 517 + 218 - 323 = 0. Solve -321/2*f**2 - 18 + 357/2*f**h + 387/2*f**3 - 147/2*f**5 - 120*f = 0.
-1, -2/7, 1, 3
Let n(d) be the first derivative of 44*d**2 + 9 + 1/12*d**6 + 8*d**4 - 40*d - 76/3*d**3 - 13/10*d**5. Factor n(x).
(x - 5)*(x - 2)**4/2
Suppose -66/5*d**4 + 4/5*d**5 - 82/5*d**2 - 1596/5*d + 784/5 + 308/5*d**3 = 0. What is d?
-2, 1/2, 4, 7
Let j(x) be the first derivative of 2*x**6/21 - 2*x**5/7 + 3*x**4/14 + 2*x**3/21 - x**2/7 + 2194. Factor j(m).
2*m*(m - 1)**3*(2*m + 1)/7
Let t(f) = 21*f**2 - 56*f + 83. Let x(a) = 14*a + 79 - 39 - 61 - 3*a**2 - 2*a**2. Let i(y) = 6*t(y) + 26*x(y). Suppose i(n) = 0. What is n?
3, 4
Let a(g) = -g**3 - 7*g**2 + 2*g - 2. Let p(b) = -10*b**3 + 10*b**2 - 156*b - 12. Let j(m) = -6*a(m) + p(m). Determine t, given that j(t) = 0.
0, 6, 7
Let j(u) be the third derivative of 7*u**5/60 - 5*u**4/24 + u**3 - 14*u**2. Let v be j(2). Factor -v*n**2 - 196 + 13*n**2 + 7*n**2 - 56*n.
-4*(n + 7)**2
Let r(f) = 19*f**3 - 34*f**2 - 85*f + 104. Let i(x) = -42*x**3 + 69*x**2 + 171*x - 207. Let z = 306 + -302. Let s(k) = z*i(k) + 9*r(k). Factor s(y).
3*(y - 12)*(y - 1)*(y + 3)
Suppose -2 = 2*u, -818 = -3*c - 3*u + 862. Factor -c*i**2 - 17*i**5 - 126*i**3 + 6*i**4 + 38*i**5 + 357*i**2 - 18 - 111*i.
3*(i - 3)*(i + 1)**3*(7*i + 2)
Let y(q) be the first derivative of -q**6/36 + 16*q**5/15 - 7*q**4/6 - 49*q**3/9 + 157*q**2/12 - 31*q/3 + 2588. Solve y(n) = 0.
-2, 1, 31
Let y be 9*(-102)/45*20/6. Let g = -65 - y. Solve 2*x + 0 + 2/3*x**g + 8/3*x**2 = 0 for x.
-3, -1, 0
Let a be 1/(5/2 + -2). Suppose a*d - 9 = 21. Suppose -6*h**2 + d*h - h**2 + 2*h**2 - 10 = 0. Calculate h.
1, 2
Let j(g) be the second derivative of -g**3 + 0 + 3/35*g**5 - 92*g - 9/7*g**2 + 1/35*g**6 - 1/147*g**7 - 5/21*g**4. Factor j(l).
-2*(l - 3)**2*(l + 1)**3/7
Let m(u) be the second derivative of -1/25*u**5 - 286*u + 0 + 56/15*u**3 + 2/75*u**6 - 32/5*u**2 - 4/5*u**4. Let m(q) = 0. Calculate q.
-4, 1, 2
Let i(l) be the first derivative of l**4/16 + 11*l**3/6 + 117*l**2/8 + 12455. Determine s so that i(s) = 0.
-13, -9, 0
Let l(r) be the first derivative of 2*r**5/25 + 33*r**4/5 + 942*r**3/5 + 10692*r**2/5 + 52488*r/5 - 3258. Factor l(z).
2*(z + 6)**2*(z + 27)**2/5
Let o(y) be the first derivative of -4*y**5/15 - 19*y**4/3 - 392*y**3/9 - 352*y**2/3 - 128*y + 845. Determine s, given that o(s) = 0.
-12, -4, -2, -1
Let f(i) = i**4 - 12*i**3 - 41*i**2 - 26*i - 2. Let o(r) = -3*r**4 + 23*r**3 + 81*r**2 + 50*r + 5. Let l(b) = -10*f(b) - 4*o(b). Factor l(t).
2*t*(t + 1)*(t + 3)*(t + 10)
Let w(q) = q - 20. Let c be w(23). Suppose c*t = 5*z + 31, -5*t + 21*z = 18*z - 25. Let 0 - 2/7*g - 1/7*g**t = 0. What is g?
-2, 0
Suppose 0 = 13*z - 15*z - 30. Let x = -10 - z. Factor -39*h**3 - 12*h + 20*h**2 - x*h**5 + 20*h**4 + 7*h + 9*h**3.
-5*h*(h - 1)**4
Let p(r) = -3*r**3 - r**2 - 1. Let v(z) = 70*z**3 - 2425*z**2 - 4620*z + 925. Let q(n) = 5*p(n) + v(n). Factor q(b).
5*(b - 46)*(b + 2)*(11*b - 2)
Let h(s) be the second derivative of 1/4*s**4 - 33/2*s**2 + 5*s**3 + 0 - 125*s. Factor h(n).
3*(n - 1)*(n + 11)
Let f(v) = 2*v**3 - 24*v**2 - 134*v + 98. Let q be f(16). Solve 4*x**3 + 76/3*x**q - 272/3*x + 48 = 0 for x.
-9, 2/3, 2
Suppose 2*h - 319*j - 40 = -314*j, 2*h + 4*j = -14. Solve 4*y**2 - 2/7*y**h - 8/7*y**4 + 40/7*y + 16/7 - 2/7*y**3 = 0.
-2, -1, 2
Let c(s) be the second derivative of -1/32*s**4 + 0 + 39*s - 1/240*s**5 - 1/12*s**3 + 35/2*s**2. Let w(q) be the first derivative of c(q). Factor w(o).
-(o + 1)*(o + 2)/4
Factor 2442969*k**3 + 560389362*k**2 - 34*k**5 + 118*k**5 - 81*k**5 - 136127079*k**2 + 4689*k**4.
3*k**2*(k + 521)**3
Let 35*j**3 - 1235*j + 1245*j**2 + 5*j**4 - 3110*j**2 + 1290*j**2 - 630 = 0. Calculate j.
-14, -1, 9
Let j(k) = 4*k**2 + 3*k + 5. Suppose -6*b - 24 = 2*b. Let w(c) = 9*c**2 + 4*c + 9. Let t(a) = b*w(a) + 7*j(a). Factor t(o).
(o + 1)*(o + 8)
Let u(o) be the second derivative of 29/32*o**4 + 9/16*o**2 + 0 - 55/48*o**3 + 1/60*o**6 - 9/32*o**5 - 91*o. Solve u(w) = 0.
1/4, 1, 9
Let i(r) be the first derivative of r**3/2 + 2598*r**2 + 4499736*r + 1392. Solve i(l) = 0.
-1732
Let k(f) be the second derivative of -f**7/126 + 6*f**6/5 - 243*f**5/5 - 2945*f. Find n such that k(n) = 0.
0, 54
Let y = -895 - -900. Suppose y = 3*i + 4*h, 7 = -3*i + 5*h + 21. Factor 3/5*f**i - 3/5*f**5 + 0*f + 0*f**4 + 0*f**2 + 0.
-3*f**3*(f - 1)*(f + 1)/5
Let d(v) = -2*v**2 + 5*v - 1. Let b be d(1). Factor -6*t + 25*t**3 - 283*t**b + 248*t**2 - 4*t + 5*t**5 - 20*t + 35*t**4.
5*t*(t - 1)*(t + 1)**2*(t + 6)
Let c(m) = 1. Let f be ((-22)/(-44))/((1/(-2))/1). Let x(r) = 5*r**2 - 30*r + 26. Let d(s) = f*x(s) + c(s). Determine z so that d(z) = 0.
1, 5
Let w(i) = 46*i**3 - 24*i**2 - 46*i + 40. Let l(j) = 0*j + 12 + 10*j + 9*j**3 - 4 - 19*j - 5*j**2. Let y(u) = 16*l(u) - 3*w(u). Factor y(m).
2*(m - 1)*(m + 1)*(3*m - 4)
What is j in 4/3*j**3 + 124/3*j - 44/3*j**2 - 28 = 0?
1, 3, 7
Let d(a) = 2*a**4 - 142*a**3 + 792*a**2 - 1022*a - 2108. Let y(u) = -4*u**2 - u - 2. Let m(w) = -2*d(w) + 60*y(w). Factor m(n).
-4*(n - 64)*(n - 4)**2*(n + 1)
Let g be ((-3)/(-42))/(((-848)/128)/(-53)). Let r be 1 + ((-24)/28)/(-3). Factor g*l**3 - 12/7*l**2 + r*l - 2/7.
(l - 2)*(2*l - 1)**2/7
Suppose -55*p - 202 - 320*p - 928 - 4*p**2 - 658 - 233*p = 0. What is p?
-149, -3
Let o(b) = b**3 + 2*b**2 - b. Let w(g) = 9*g**3 + 513*g**2 + 12996*g + 12500. Let r(k) = 4*o(k) - w(k). Factor r(t).
-5*(t + 1)*(t + 50)**2
Suppose -143*n + 1580 - 137 = 152*n + 186*n. Solve 2/7*y**2 - 2/7*y**n + 0 + 4/7*y = 0 for y.
-1, 0, 2
Let l(w) = w**2 - w. Let c(o) = 4*o**2 - 7*o + 10. Let x(b) = -c(b) + 5*l(b). Let q be x(-5). Determine m, given that -m - 5 + q*m**2 + 5 - 4*m = 0.
0, 1
Let w = -35 - -11. Let z be (57/27*3)/((-2)/w). Let 4*h - 160*h**2 + h**3 + 79*h**2 + z*h**2 = 0. Calculate h.
0, 1, 4
Let u(y) be the third derivative of -y**8/840 + 2*y**7/175 + 3*y**6/25 + 4*y**5/15 + 126*y**2 - y. Solve u(q) = 0.
-2, 0, 10
Let m(p) be the first derivative of -48*p**5/5 + 140*p**4 - 532*p**3 + 780*p**2 - 448*p - 6527. Find i, given that m(i) = 0.
1/2, 7/6, 2, 8
Suppose -4*b + 2*y = -2*y, -5*b - 2*y = 3*y. Suppose b - 12/11*w + 2/11*w**2 = 0. What is w?
0, 6
Determine b, given that -196/5*b - 96/5 + 0*b**3 - 102/5*b**2 + 2/5*b**4 = 0.
-6, -1, 8
Let n = 261 - 173. Suppose -35*o + n = -13*o. Let 2/3*a**o + 8 + 16/3*a**3 + 46/3*a**2 + 56/3*a = 0. What is a?
-3, -2, -1
Suppose -4*i - 12 = 0, -5*i - 18 = -2*k + 3. Let k + 1 + 91*d**3 + 24*d**2 - 103*d**3 - 20*d + 2*d**4 + 2 = 0. What is d?
1, 3
Suppose -33*c = 6 - 72. Factor -158 - 4*q**4 + 228*q**3 + 114*q + 50 - 188*q**3 + 102*q - 144*q**c.
-4*(q - 3)**3*(q - 1)
Let g = 7506 - 7506. Let x(y) be the third derivative of 0 - 26*y**2 + g*y + 0*y**3 - 1/8*y**4 - 1/60*y**5. Factor x(q).
-q*