- 11*p**3 + 3*p**q + 44*p**3 + 138*p**2.
3*(p + 1)**2*(p + 5)**2
Let y(m) be the third derivative of -m**6/540 + 11*m**5/270 + m**4/9 + 29*m**2 - 5. Factor y(l).
-2*l*(l - 12)*(l + 1)/9
Factor 137 - 53 - 1507*a + 1595*a + 144 + 4*a**2.
4*(a + 3)*(a + 19)
Let w(a) = -5*a**3 + 5*a**3 + 9*a**3 - a**2 - 1 - 8*a**3. Let o(t) = -t**3 + 31*t**2 + 15*t - 39. Let z be 3/2*(-12)/3. Let i(b) = z*w(b) - o(b). Factor i(f).
-5*(f - 1)*(f + 3)**2
Suppose -1520 + 1490 = -10*o. Let v(d) be the first derivative of d**4 + 4/3*d**o + 1/5*d**5 + 6 + 0*d**2 + 0*d. Factor v(m).
m**2*(m + 2)**2
Let m(u) = -u**3 - 37*u**2 + 25*u + 142. Let a(f) = -2*f**2 - f + 2. Let c(x) = 6*a(x) - m(x). Let j be c(-26). Factor 4/3*d**2 - 4/3*d + j.
4*d*(d - 1)/3
Let j(n) be the third derivative of 0*n**3 + 104*n**2 + 1/2*n**6 + 0 + 0*n - 2/35*n**7 - 17/15*n**5 + n**4 - 1/84*n**8. Factor j(r).
-4*r*(r - 1)**3*(r + 6)
Let x(g) be the third derivative of g**5/90 - 73*g**4/18 - 296*g**3/9 + 3*g**2 - 29*g. Suppose x(c) = 0. Calculate c.
-2, 148
Let j(c) be the second derivative of c**6/840 + 3*c**5/140 + c**4/7 - c**3/3 + 13*c**2 + 86*c. Let x(a) be the second derivative of j(a). Factor x(t).
3*(t + 2)*(t + 4)/7
Let k(v) be the third derivative of v**8/168 + v**7/5 + 71*v**6/60 + 17*v**5/10 - 1993*v**2. Solve k(h) = 0 for h.
-17, -3, -1, 0
Let h(k) = -35*k**2 + 410*k + 123. Let y(w) = -1. Let i(n) = -7*n + 43. Let g be i(6). Let l(a) = g*h(a) + 3*y(a). Factor l(d).
-5*(d - 12)*(7*d + 2)
Let q(p) be the second derivative of -p**5/130 - 127*p**4/39 - 253*p**3/39 + 9*p + 46. Find k, given that q(k) = 0.
-253, -1, 0
Let q(v) be the third derivative of 1/70*v**7 + 3*v**3 + 0*v + 7/40*v**6 + 17/8*v**4 + 0 + 17/20*v**5 + 73*v**2. Suppose q(u) = 0. Calculate u.
-3, -2, -1
Let k = 9195 - 9188. Let w(f) be the third derivative of 1/108*f**6 + 0 - 1/945*f**k + 1/27*f**4 + 0*f**3 - 4/135*f**5 + 0*f - 18*f**2. Factor w(n).
-2*n*(n - 2)**2*(n - 1)/9
Let k = 111 + -77. Factor 117*r - k*r + 4*r**2 + 1936 + 117*r - 24*r.
4*(r + 22)**2
Let x(c) be the first derivative of -c**4/12 + 89*c**3/9 + c**2/6 - 89*c/3 + 3451. Factor x(d).
-(d - 89)*(d - 1)*(d + 1)/3
Let w(g) = g**3 - 33*g**2 - 30*g - 23. Let t be w(34). Let -3*m**3 + 24 + 17*m - t*m - 6 + 130*m**2 - 160*m**2 - 114 = 0. What is m?
-4, -2
Let v(h) = -3*h**2 - 24*h - 146. Let z(u) = -7*u**2 - 48*u - 293. Let w be (0/(-3) - -2) + 34/(-2). Let f(n) = w*v(n) + 6*z(n). Factor f(r).
3*(r + 12)**2
Let l(x) be the second derivative of -x**4/66 - 37*x**3/3 + 408*x**2/11 + 25*x - 1. Factor l(n).
-2*(n - 1)*(n + 408)/11
Let r(b) be the third derivative of b**6/80 + 7*b**5/8 - 73*b**4/16 + 37*b**3/4 - 31*b**2. Factor r(c).
3*(c - 1)**2*(c + 37)/2
Suppose 3690*k**2 - 2904 + 15/2*k**4 - 663/2*k**3 - 462*k = 0. What is k?
-4/5, 1, 22
Let v be -18 + -48 + 61 - -5. Solve v - 20/13*p + 2/13*p**3 - 6/13*p**2 = 0 for p.
-2, 0, 5
Factor 17/6*t**2 + 1/6*t**3 + 0 + 8/3*t.
t*(t + 1)*(t + 16)/6
Let z(p) be the third derivative of 0*p - 8/45*p**5 - 3 + 5/4*p**4 + 18*p**3 - 15*p**2 + 1/180*p**6. Factor z(g).
2*(g - 9)**2*(g + 2)/3
Suppose 16*p - 123 + 18 = -57. Let v(n) be the first derivative of -1/5*n**2 - 4/15*n**3 + 4/25*n**5 + 1/15*n**6 + p + 0*n + 0*n**4. Factor v(w).
2*w*(w - 1)*(w + 1)**3/5
Let d = 516 + -3356/7. Find p, given that -2/7*p**3 - d + 4*p**2 - 64/7*p = 0.
-2, 8
Solve 1928 + 5776/3*a - 2/3*a**3 + 1438/3*a**2 = 0.
-2, 723
Let t = -4521 - -4521. Let p(w) be the second derivative of -2*w**3 + t - 1/5*w**5 - w**4 - 2*w**2 - 19*w. Find y such that p(y) = 0.
-1
Let h(l) be the second derivative of -l**4/6 + 23*l**3/3 - 76*l**2 - 643*l. Determine x so that h(x) = 0.
4, 19
Let d(n) be the third derivative of -n**8/168 + 31*n**7/35 + 47*n**6/30 + 1065*n**2. Let d(c) = 0. Calculate c.
-1, 0, 94
Let m(a) be the first derivative of a**6/120 + 31*a**5/240 + 187*a**3/3 + 118. Let b(s) be the third derivative of m(s). Let b(y) = 0. Calculate y.
-31/6, 0
Let t(a) be the first derivative of a**6/3 - 34*a**5/5 + 75*a**4/2 + 26*a**3/3 - 272*a**2 - 384*a + 1106. Solve t(d) = 0 for d.
-1, 3, 8
Let l(k) = k**3 + 13*k**2 + 93*k + 1848. Let v be l(-15). Factor -4*z**2 + 16*z + 0 + 1/4*z**v.
z*(z - 8)**2/4
Factor 7733*u**4 + 13*u**3 + 66*u - 6*u - 3866*u**4 - 52*u**2 - 3868*u**4.
-u*(u - 6)*(u - 5)*(u - 2)
Let b be (-11562)/329 + 35 + (-30)/(-63). What is r in 0 + 0*r + b*r**2 + 4/3*r**4 - 5/3*r**3 = 0?
0, 1/4, 1
Factor -822*u + 2*u**2 + 3*u**2 + 624*u - 407*u.
5*u*(u - 121)
Let m(b) be the third derivative of -124*b**2 + 0 - 5/24*b**4 + 0*b + 55/24*b**6 + 14/3*b**5 - 5/3*b**3. Factor m(h).
5*(h + 1)*(5*h + 1)*(11*h - 2)
Let s(a) be the first derivative of -a**6/3 - 342*a**5/5 - 10371*a**4/2 - 511450*a**3/3 - 2089896*a**2 - 10719144*a + 2708. Solve s(y) = 0 for y.
-53, -6
Let x(d) be the third derivative of 1/6*d**5 + 1/60*d**6 + 2/3*d**4 + 0 + 0*d - 52*d**2 + 4/3*d**3. Determine f so that x(f) = 0.
-2, -1
Suppose -35 - 133 = 7*q. Let y = -20 - q. Suppose l**5 + 7*l**4 + 18*l**4 + y*l**5 - 5*l**4 + 10*l**2 + 25*l**3 = 0. Calculate l.
-2, -1, 0
Let s(i) = -3*i - 3. Let b be s(-11). Let w = b + -27. Factor 3*y**w - y**5 + 2*y**2 + 71*y**4 - 71*y**4.
-y**2*(y - 2)*(y + 1)**2
Let u(v) = v**3 + 12*v**2 - 28*v + 2. Let w be u(-14). Factor -24 - 36 - 36*k + 0*k**w - 3*k**2.
-3*(k + 2)*(k + 10)
Let y(h) be the third derivative of -6*h**3 + 0 - 5/6*h**4 + 3/5*h**5 - 151*h**2 + 1/6*h**6 + 0*h. Factor y(r).
4*(r - 1)*(r + 1)*(5*r + 9)
Suppose -5*h - 4*f + 22 = 0, -2*f + 10 = 2*h - 0. Factor 23 - 15*b**h + 32*b + 8*b**3 - 39 - b**4 - 9*b**2.
-(b - 2)**4
Let t(k) be the first derivative of -2*k**5/45 + 7*k**4/6 + 44*k**3/27 - 253. Factor t(a).
-2*a**2*(a - 22)*(a + 1)/9
Let d(b) be the third derivative of -b**5/75 + 217*b**4/30 - 428*b**3/5 - 2*b**2 + 655*b. Suppose d(i) = 0. Calculate i.
3, 214
Let r(x) = -2*x**2 - 2*x + 3. Let k(a) = -31*a**2 + 82*a - 690. Let w(c) = 2*k(c) - 30*r(c). Factor w(f).
-2*(f - 105)*(f - 7)
Let y(a) be the second derivative of a**7/210 + 13*a**6/180 + 2*a**5/5 + 3*a**4/4 + 41*a**3/3 + 5*a. Let i(x) be the second derivative of y(x). Factor i(j).
2*(j + 3)**2*(2*j + 1)
Let u be 3/(-2)*(-5 + (-42)/(-18)). Solve 3*p**4 + 2*p**u - 1144*p**2 + 20*p + 25*p**3 + 1184*p**2 = 0.
-2, -1, 0
Let f(d) be the second derivative of -d**5/190 - 17*d**4/38 - 240*d**3/19 - 1728*d**2/19 - 42*d - 1. Factor f(x).
-2*(x + 3)*(x + 24)**2/19
Suppose c + 1053 = -4*g - 0*c, 4*c - 504 = 2*g. Let r = g - -264. Factor 5/7*t + 2/7 + 1/7*t**3 + 4/7*t**r.
(t + 1)**2*(t + 2)/7
Suppose 2*w = -3*s + 8, -w + 4 = 160*s - 165*s. Solve s + 1/5*z**3 - 6/5*z - 1/5*z**2 = 0 for z.
-2, 0, 3
Suppose -5*n + 24 + 11 = 0. Suppose n*y = 3*y + 16. Factor -7*s + s - 4 - 4*s**y + 8*s**2 + 6*s.
-4*(s - 1)**2*(s + 1)**2
Let w = 7561 - 7557. Let m(h) be the second derivative of -1/3*h**w + 0 + 8/3*h**3 + 3*h - 8*h**2. Factor m(r).
-4*(r - 2)**2
Let a be 0 - 2 - (-160)/42. Suppose 157*r = -42*r + 419 + 178. Determine x so that -16/7*x + 32/21 + a*x**4 - 142/21*x**2 - 6/7*x**r - 2/7*x**5 = 0.
-1, 1/3, 4
Let v(o) = -14*o**2 + 6024*o - 4548124. Let m(d) = 25*d**2 - 12050*d + 9096249. Let k(i) = -4*m(i) - 7*v(i). Find f such that k(f) = 0.
1508
Let x(w) be the second derivative of w**5/80 + 13*w**4/16 + 105*w**3/8 - 1323*w**2/8 + 506*w. Factor x(c).
(c - 3)*(c + 21)**2/4
Suppose -5*w + 20 = 2*h, -18*h - 15 = -15*h. Let -4*b**2 + b - w + 2*b + b**2 - 5*b - 7*b = 0. Calculate b.
-2, -1
Let c(z) be the third derivative of -z**6/30 + 17*z**5/15 + 1223*z**2. Determine f so that c(f) = 0.
0, 17
Factor -1116*r**3 - 42499*r**2 + 35074*r**2 - 450456 + 87957*r**2 + 4*r**4 - 368804*r.
4*(r - 137)**2*(r - 6)*(r + 1)
Let a(i) be the third derivative of i**5/70 + 32*i**4 + 28672*i**3 + 1310*i**2. Factor a(s).
6*(s + 448)**2/7
Let t be (7 - (-26)/3)*3. Suppose a = -t*a + 96. Factor 5/3*r + 5/3*r**4 + 5*r**a + 0 + 5*r**3.
5*r*(r + 1)**3/3
Let r(s) = 310*s**2 - s - 2. Let j be r(2). Let x be (1 - j/(-21)) + 5/35. Factor 8 + 10 - 35*l**2 - x*l + 0*l**2 + 2.
-5*(l + 2)*(7*l - 2)
Let o(a) be the third derivative of a**6/200 + 11*a**5/100 + 7*a**4/40 - 147*a**3/10 - 2*a**2 + 625*a. Solve o(x) = 0.
-7, 3
Let t(g) be the third derivative of -g**7/8820 - g**6/840 - 23*g**4/24 + 71*g**2. Let f(k) be the second derivative of t(k). Find p such t