, given that -17/4*x**3 + 0 + 3/4*x**5 + 3/2*x - 13/4*x**2 + 5/4*x**o = 0.
-3, -1, 0, 1/3, 2
Let b = -105 - -123. Suppose -b*f = -20*f + 16. Solve -n - 18*n**3 + 13*n**3 + 6 - 2*n - 6*n**2 + f*n**3 = 0.
-1, 1, 2
Let p(u) be the second derivative of -u**4/3 + 16*u**3/3 - 30*u**2 - 74*u - 8. Factor p(n).
-4*(n - 5)*(n - 3)
Let i(n) = -4*n**4 + 38*n**3 + 34*n**2 - 904*n + 1998. Let y(t) = t**3 + 7*t**2 - 2*t - 1. Let j(f) = i(f) - 2*y(f). Factor j(g).
-4*(g - 5)**2*(g - 4)*(g + 5)
Let m(z) be the second derivative of z**7/11340 + z**6/540 + z**5/108 + z**4/2 + 6*z**2 - 253*z. Let c(h) be the third derivative of m(h). Factor c(i).
2*(i + 1)*(i + 5)/9
Determine f, given that -93 + f**4 - 16*f**3 - 186*f + 40*f + 92*f**2 + 110*f**3 + 19*f + 33*f = 0.
-93, -1, 1
Suppose 3*j + 31*j = -104*j + 414. Factor -3/5*r + 9/5*r**2 + 3*r**4 + 0 + 27/5*r**j.
3*r*(r + 1)**2*(5*r - 1)/5
Let g(f) be the third derivative of -5*f**8/48 - 215*f**7/42 - 935*f**6/12 - 695*f**5/3 + 4025*f**4/3 - 3920*f**3/3 + f**2 + 2719. Solve g(a) = 0 for a.
-14, -4, 2/7, 1
Let u(x) be the first derivative of x**5/10 + 33*x**4/8 + 191*x**3/6 - 225*x**2/4 - 1294. Factor u(j).
j*(j - 1)*(j + 9)*(j + 25)/2
Let f(r) = 49*r**2 - 1 - 1 + 5 + 51*r - 56*r. Let h be f(2). Determine y, given that -y**2 + 4*y**3 - 3*y**2 + h*y - 12 - 209*y = 0.
-1, 3
Let a = 46 + -89. Let j = a + 45. Factor -14*h**3 - 369*h + 369*h + 4*h**j.
-2*h**2*(7*h - 2)
Let l(m) = -m + 6. Let i be l(4). Let w be ((3 - -6) + i)/1. Let 0 + 21 - 15*z - w + z**2 + 4*z**2 = 0. Calculate z.
1, 2
Factor 160*n - 475*n + 322*n**2 - 1926 + 552031*n**3 - 552032*n**3.
-(n - 321)*(n - 3)*(n + 2)
Let 164151/4*f**2 + 250128*f + 3017169/8 - 144*f**3 + 1/8*f**4 = 0. Calculate f.
-3, 579
Let s be (2/4*-34)/(-1). Let m = 19 - s. Solve -128 - 96*z - 22*z**m - 7*z**2 + 4*z**2 - 2*z**3 + z**2 = 0.
-4
Let f be 2*-6*((-3276)/(-1456) - (-10)/(-4)). Factor -28/5 - 32/5*d**2 + 58/5*d + 2/5*d**f.
2*(d - 14)*(d - 1)**2/5
Let k(x) be the third derivative of -2*x**7/105 + 7*x**6/30 - 7*x**5/15 - 5*x**4/2 + 979*x**2. Solve k(y) = 0 for y.
-1, 0, 3, 5
Let 6*b**4 - 19*b**3 + 95*b - 16*b**4 - 103*b**3 + 27*b**3 + 740 + 60*b**2 - 790 = 0. What is b?
-10, -1, 1/2, 1
Let j(n) = -28*n**2 + 2*n - 153. Let h(i) = -3*i**2 + 3*i - 1. Let u(g) = -18*h(g) + 2*j(g). Factor u(a).
-2*(a + 9)*(a + 16)
Let a(b) = 5*b**2 - 1707*b - 3586. Let y(z) = 4*z**2 - 1707*z - 3544. Let c(n) = -3*a(n) + 4*y(n). Solve c(o) = 0.
-2, 1709
Let -2/5*h**2 - 20852882/5 - 12916/5*h = 0. What is h?
-3229
Let p(k) be the third derivative of 1 - 2*k**2 - 133/90*k**5 - 47/180*k**6 - 2*k**3 + 0*k - 97/36*k**4 + 1/45*k**7. Solve p(f) = 0 for f.
-1, -2/7, 9
Factor -3/4*x**2 + 0 - 6153/4*x.
-3*x*(x + 2051)/4
Let c be (2/24)/(-1 + (-26)/(-8)). Let i(r) be the first derivative of c*r**3 - 1/9*r + 0*r**2 + 16. Solve i(o) = 0 for o.
-1, 1
Let r(z) be the first derivative of 66*z**2 - 54*z + 37 + 5/2*z**3. Factor r(g).
3*(g + 18)*(5*g - 2)/2
Suppose 180*l**4 + 408*l**2 + 147*l**3 - 140*l**4 + l**5 - 300*l**2 = 0. Calculate l.
-36, -3, -1, 0
Let m(v) be the first derivative of -3*v**5/20 - 177*v**4/8 - 3109*v**3/4 + 16461*v**2/2 - 25947*v + 983. Find x such that m(x) = 0.
-62, 3
Let t = -775 - -817. Suppose 17*n - t = 26. Determine g so that -2/3*g**n + 16/9 + 28/9*g - 28/9*g**3 - 10/9*g**2 = 0.
-4, -1, -2/3, 1
Determine i, given that -25/2*i**5 + 45/2*i**4 - 1513/2*i - 165*i**2 - 867/2 + 193*i**3 = 0.
-3, -1, 17/5
Factor 4*x**2 + 2*x**3 - x**3 - 19*x - 4 + 14 + 0 + 4.
(x - 2)*(x - 1)*(x + 7)
Suppose 27*v = 31*v - 18*v. Let d(p) be the first derivative of 5 - 2/5*p**2 + 1/5*p**4 + v*p**3 + 0*p. Let d(u) = 0. What is u?
-1, 0, 1
Factor 4/7 - 40/7*o**2 + 2*o + 22/7*o**3.
2*(o - 1)**2*(11*o + 2)/7
Let u(f) be the third derivative of -f**6/720 + 799*f**5/360 - 9950*f**4/9 - 40000*f**3/9 + 101*f**2 + 4*f. Factor u(n).
-(n - 400)**2*(n + 1)/6
Let z(u) = -64*u**2 - 992*u + 1987. Let r(d) = -41*d**2 - 661*d + 1325. Let o(k) = -11*r(k) + 7*z(k). Factor o(a).
3*(a - 2)*(a + 111)
Let c(q) be the first derivative of -q**4/26 - 2*q**3/13 + q**2/13 + 6*q/13 + 3908. Let c(d) = 0. Calculate d.
-3, -1, 1
Suppose -5*b + 18 = -2*t, b + 4*t + 8 = -6. Let o(m) = -m**3 - 3*m**2 + 2*m + 6. Let d be o(-4). What is q in -4*q**3 - d*q**b - 19*q + 3*q**3 + 7*q - q**3 = 0?
-6, -1, 0
Let q(a) be the second derivative of 0 + 0*a**2 - 145*a + 1/48*a**4 + 1/6*a**3. Determine s, given that q(s) = 0.
-4, 0
Let k be -2 + 24 + (-7 - -8) + -5. Determine o, given that -2*o + 42 - 2*o + 3*o**3 - 11*o - o - k*o**2 - 11*o = 0.
-2, 1, 7
Let q = 389397/67 - 5812. Let r = 1813/603 - q. Find p such that r*p + 4/9*p**2 + 40/9 = 0.
-5, -2
Let j(c) = -c**2 - c + 7. Let f be j(-3). Suppose 3*o - 13 = -f. Factor -147*t**o - 14*t + 149*t**4 + 18*t**2 - 10*t**3 - 1 + 5.
2*(t - 2)*(t - 1)**3
Let l(k) = -k**3 + 5*k**2 + 3*k - 10. Let b be l(5). Factor b*u**2 + 22 + u - u - 102.
5*(u - 4)*(u + 4)
Let f(p) be the first derivative of p**7/21 + p**6/15 - 3*p**5/10 - 5*p**4/6 - 2*p**3/3 + 70*p - 201. Let k(x) be the first derivative of f(x). Factor k(c).
2*c*(c - 2)*(c + 1)**3
Let t(k) be the third derivative of k**2 - 2/3*k**4 - 4/15*k**5 + 1/672*k**8 - 3*k - 11/420*k**7 + 0 + 4*k**3 + 3/20*k**6. Determine d, given that t(d) = 0.
-1, 2, 6
Let a(p) be the first derivative of p**3/4 + 30*p**2 + 228*p + 1796. Let a(o) = 0. What is o?
-76, -4
Let q = -123842 - -123844. Suppose 0*m - 3/7*m**5 - 27/7*m**3 - 18/7*m**4 - 12/7*m**q + 0 = 0. What is m?
-4, -1, 0
Suppose 14*f = -14*f - 59*f + 18*f. Let c = 45 - 134/3. Factor 1/3*r**5 + 1/3*r**2 - c*r**4 + 0 + f*r - 1/3*r**3.
r**2*(r - 1)**2*(r + 1)/3
Let y = 74 - 145/2. Suppose -3*p + 5*h = -1, 0 = 5*p + h - 2*h - 9. Factor 1 - y*k + 1/2*k**p.
(k - 2)*(k - 1)/2
Let c(w) be the second derivative of w**4/3 + 76*w**3/3 + 74*w**2 - 4001*w. Suppose c(t) = 0. Calculate t.
-37, -1
Let i(d) = -3658*d + 69505. Let g be i(19). Solve -2/3*u**2 + 1/3*u**g + 0*u + 0 = 0.
0, 2
Let r(n) be the first derivative of -3*n**4/4 + 153*n**3 - 453*n**2 - 1523. Factor r(m).
-3*m*(m - 151)*(m - 2)
Let k(f) be the second derivative of f**4/66 - 40*f**3/33 + 76*f**2/11 - 1131*f. Factor k(u).
2*(u - 38)*(u - 2)/11
Let n = 27 + 17. Suppose -3*w + 5*y = -n, 3*w - 2*w + 2 = 5*y. Let -2*m**4 - 17*m**2 - w*m**2 + 2*m**5 + 42*m**2 - 2*m**3 = 0. Calculate m.
-1, 0, 1
Let f = 2 - -2. Suppose 9 = -f*z + 5*w, -4*z + 12*w - 17*w + 41 = 0. Determine a, given that 5/3*a**3 - a**z + 2/3 + 1/3*a**2 - 5/3*a = 0.
-1, 2/3, 1
Let h = 4819 + -4813. Let o(x) be the second derivative of -23/5*x**5 - 40/3*x**3 + 0 + 16*x**2 - 14*x**4 + 5*x - 8/15*x**h. Find f such that o(f) = 0.
-2, 1/4
Let g(i) be the first derivative of 79 + 0*i + 1/45*i**5 - 1/27*i**3 + 1/9*i**4 - 2/9*i**2. Determine w so that g(w) = 0.
-4, -1, 0, 1
Find k, given that -330/13*k + 4/13 + 326/13*k**2 = 0.
2/163, 1
Let v(l) = -14*l**3 + 196*l**2 + 5344*l - 40352. Let f(q) = -2*q**3 - 3*q**2 + q + 2. Let d(o) = 8*f(o) - v(o). Factor d(c).
-2*(c - 6)*(c + 58)**2
Let p(g) be the first derivative of 311 - 3*g - 23/4*g**2 - 8/3*g**3 - 3/8*g**4. Factor p(t).
-(t + 2)*(t + 3)*(3*t + 1)/2
Suppose 0 = -2*q + 2*h + 18, -5*h - 21 = -16*q + 14*q. Let a be 2/(2 - ((-45)/q)/(-5)). Find f, given that a - 2/7*f**2 + 4/7*f = 0.
-2, 4
Let v(i) = -i**5 + 75*i**4 + 60*i**3 - 240*i**2 - 284*i. Let n(d) = -d**5 + 15*d**2 + d. Let l(f) = 4*n(f) - v(f). Suppose l(k) = 0. Calculate k.
-24, -2, -1, 0, 2
Suppose -313*b + 122 = -252*b. Let k(i) be the second derivative of 1/48*i**4 - 20*i - 1/4*i**b + 0 + 1/24*i**3. Factor k(r).
(r - 1)*(r + 2)/4
Let s(q) = -18*q**2 + 276*q + 3. Let c(y) = 47*y**2 - 828*y - 8. Let g(b) = -3*c(b) - 8*s(b). Factor g(a).
3*a*(a + 92)
Let o be 7 + (-5)/((-35)/(-224)). Let s be 4/((-20)/o) - (-435)/(-95). Let -64/19*k + 130/19*k**3 - 58/19*k**2 - s = 0. What is k?
-2/5, -2/13, 1
Solve 2898 + 79*a - 11*a - 2786 + 0*a**2 - 2*a**3 + 2*a**2 = 0.
-4, -2, 7
Let k(b) = -5*b**3 - 7981*b**2 - 3184007*b + 3192009. Let y(p) = 30*p**3 + 47887*p**2 + 19104044*p - 19152053. Let c(j) = 23*k(j) + 4*y(j). Factor c(g).
5*(g - 1)*(g + 799)**2
Let w be 30/(-1 - (-53)/49). Let n = -317778 + 1283117/4. Factor w*a**2 + 5/4*a**4 + 1715*a + n + 35*a**3.
5*(a + 7)**4/4
Let y be (-33)/(-28) - 45/240*4. Let l be (-2)/21*(3 + -6 