**4/9 - 172*h**3/9 - 56*h**2 - 1204*h. Factor p(v).
-2*(v + 2)**2*(v + 42)/3
Suppose 106 = 337*m - 33 - 535. Let g(u) be the first derivative of -1/20*u**4 + 0*u + 0*u**3 - 4/25*u**5 + 0*u**m - 3. Solve g(c) = 0.
-1/4, 0
Let y(t) = t**3 + 13*t**2 - 18*t - 28. Let m be y(-16). Let n be (18/52 - 0)/((-381)/m). Factor 8/13*j**2 - n*j + 0.
2*j*(4*j - 3)/13
Let h(q) be the first derivative of 14/33*q**3 - 13/11*q**2 + 25 - 4/11*q. Find v, given that h(v) = 0.
-1/7, 2
Let c be (-2 - -24) + -679 + 661. Factor -6/7 + 1/7*d**5 + 24/7*d**3 - 8/7*d**c - 34/7*d**2 + 23/7*d.
(d - 3)*(d - 2)*(d - 1)**3/7
Let j(l) = -15*l**2 - 120*l - 350. Let d(i) = 7*i**2 + 59*i + 170. Let f(g) = -5*d(g) - 2*j(g). Factor f(k).
-5*(k + 5)*(k + 6)
Let -217*c - 4 + 3*c**3 - 311*c + 378*c**2 + 179 + 209 - 237*c = 0. Calculate c.
-128, 1
Factor 472/7*a**2 + 2/7*a**3 - 472/7 - 2/7*a.
2*(a - 1)*(a + 1)*(a + 236)/7
Let d(u) be the first derivative of -u**6/45 - 58*u**5/25 - 67*u**4/6 - 98*u**3/9 + 112*u**2/5 + 664*u/15 + 3631. Solve d(p) = 0.
-83, -2, -1, 1
Let k = 40865/10908 - -10/2727. Let j(d) be the first derivative of 0*d + 9/5*d**5 + 36 - 3*d**3 - k*d**4 + 6*d**2 + 1/2*d**6. Let j(r) = 0. What is r?
-4, -1, 0, 1
Let y(t) be the second derivative of 100/7*t**2 + 220/21*t**3 - 191*t + 0 + 47/14*t**4 + 11/35*t**5 + 1/105*t**6. Factor y(w).
2*(w + 1)**2*(w + 10)**2/7
Solve 29/3*p**3 - 10/3 + 25*p**2 - 3*p**4 + 9*p = 0 for p.
-1, 2/9, 5
Let g = -671070 - -59053451/88. Let c = -63/8 - g. Factor c*s**4 - 64/11*s + 32/11 + 48/11*s**2 - 16/11*s**3.
2*(s - 2)**4/11
Factor 0*u**3 - 1314 + 62 + 1584*u - 200 - 135*u**2 + 3*u**3.
3*(u - 22)**2*(u - 1)
Suppose j = u + 17, 13 = -2*u + 4*j - 31. Let i be (-3)/u + 28/16. Let 7*t**2 + 10*t + 0 - 4 - 2*t**i + 9 = 0. What is t?
-1
Let q(a) = 4*a**2 + 33*a + 58. Let b be q(-6). Let k(x) be the first derivative of 16/3*x - 3 + 8/3*x**2 - 1/3*x**b - 4/9*x**3. Find m, given that k(m) = 0.
-2, -1, 2
Let i(g) = 5*g**3 + 50*g**2 - 20*g - 210. Let j(o) = -15*o**3 - 150*o**2 + 60*o + 629. Let d(y) = 29*i(y) + 10*j(y). Factor d(t).
-5*(t - 2)*(t + 2)*(t + 10)
Suppose 3*y + 0*y = -5*b + 1, -4*y = -5*b - 13. Let 6*g**5 + 32*g**4 - 33*g + 25*g**4 - 526*g**3 - 7*g - 5*g**4 + 652*g**3 + 72*g**y = 0. What is g?
-5, -2, 0, 1/3
Let q = -23/100 + 961/700. Let -9/7 + q*y**2 - 6/7*y + 1/7*y**4 + 6/7*y**3 = 0. What is y?
-3, -1, 1
Let b = 823/5 + -1641/10. Let g(k) be the second derivative of -3/20*k**5 + 0 + b*k**3 + 0*k**4 - 31*k + 0*k**2. Factor g(x).
-3*x*(x - 1)*(x + 1)
Solve -1440*j**2 - 90*j**4 + 1324*j - 545*j**3 - 5*j**5 - 4831*j + 1807*j - 720 = 0 for j.
-9, -4, -2, -1
Solve 10*w - 26846 - 25*w**5 + 26846 - 8*w**2 - 17*w**2 - 95*w**4 - 105*w**3 = 0 for w.
-2, -1, 0, 1/5
Let m(c) be the third derivative of 0 + 0*c + 1/240*c**6 + 92*c**2 + 1/16*c**4 - 1/30*c**5 + 0*c**3. Find u, given that m(u) = 0.
0, 1, 3
Let r(b) be the first derivative of 58*b**3/27 - 346*b**2/9 - 16*b/3 + 449. Factor r(y).
2*(y - 12)*(29*y + 2)/9
Let i(p) be the second derivative of 4*p**6/25 - 29*p**5/25 + 23*p**4/15 + 4*p**3 + 405*p. Solve i(c) = 0.
-2/3, 0, 5/2, 3
Let y(z) = -24*z - 158. Let b be y(-11). Factor -b*i + 295*i**2 - 209 - 296*i**2 - 2600.
-(i + 53)**2
Suppose 0 + 12*x**2 + 0*x + 3/4*x**5 - 3/4*x**4 - 12*x**3 = 0. What is x?
-4, 0, 1, 4
Let z be 48/(-9)*(3 - 6). Find n, given that -26*n - 12 - z*n + 3*n**2 + 33*n = 0.
-1, 4
Solve -j**2 + 2*j**4 - 114*j + 2*j**5 - 36*j**3 - 135*j**2 + 5*j**4 - 3*j**4 - 44*j - 60 = 0.
-3, -2, -1, 5
Let c(x) be the third derivative of 1/10*x**3 - 1/300*x**5 + 1/60*x**4 + 0 - 199*x**2 + 0*x. Suppose c(v) = 0. What is v?
-1, 3
Let l(v) = v**3 + 3*v**2 - 9*v - 6. Let k be l(-4). Determine y so that -5*y + y**3 - 6*y**2 + 3 - 2*y**2 + k*y**2 - 5*y**2 = 0.
-3, 1
Let m(b) = b**3 + 80*b**2 - 161*b**2 + 82*b**2. Let z(q) = -4*q**3 - 4*q**2. Let f(p) = 5*m(p) + z(p). Factor f(i).
i**2*(i + 1)
Let o be (-6 + (-164)/(-28))*-175. Let q be ((-18)/105)/(3*(-5)/o). Factor q - 2/7*k**3 - 6/7*k + 6/7*k**2.
-2*(k - 1)**3/7
Let g(s) be the second derivative of -s**5/80 - 21*s**4/16 - 31*s**3/12 + 2639*s. Factor g(j).
-j*(j + 1)*(j + 62)/4
Let i(z) be the second derivative of -z**6/30 + 1219*z**5/20 - 82621*z**4/2 + 33708962*z**3/3 - 33461708*z**2 + 1855*z. Factor i(x).
-(x - 406)**3*(x - 1)
Let y be 24/((-118)/288 + (-14)/(-63)). Let j be (3/14)/((-12)/y). Suppose 4/7 + j*p**2 + 2*p + 6/7*p**3 = 0. Calculate p.
-1, -2/3
Let u(b) be the third derivative of 0*b**3 + 0 - 1/360*b**5 + 0*b + 1/72*b**4 + 4*b**2 - 1/720*b**6. Factor u(k).
-k*(k - 1)*(k + 2)/6
Let x(q) be the first derivative of q**6/1080 - q**5/36 - 4*q**3/3 + 21*q - 120. Let o(c) be the third derivative of x(c). Factor o(b).
b*(b - 10)/3
Let q(g) be the second derivative of -g**5/20 + 173*g**4/6 - 33*g. Solve q(c) = 0 for c.
0, 346
Let w(o) = o**3 - 43*o**2 - 96*o + 274. Let b be w(45). Let x(z) be the second derivative of 8*z**2 + 4/3*z**3 + 0 - 1/3*z**b - 1/10*z**5 + 2*z. Factor x(a).
-2*(a - 2)*(a + 2)**2
Factor -116/3*m - 4/3*m**3 - 17*m**2 - 20.
-(m + 2)*(m + 10)*(4*m + 3)/3
Let h(o) be the first derivative of -2*o**5/65 - 7*o**4/26 - 6*o**3/13 + 7*o**2/13 + 20*o/13 + 1429. Find l, given that h(l) = 0.
-5, -2, -1, 1
Factor 7*l**3 + 2*l**2 - 11*l**3 - 2*l**3 + 8 + 5*l**3 + 85*l + 146.
-(l - 11)*(l + 2)*(l + 7)
Let n(y) be the second derivative of -y + 1/24*y**4 + 2 + 1/3*y**3 - 3*y**2. Solve n(a) = 0 for a.
-6, 2
What is x in -31 + 113 + 46 - 83*x**2 + 3*x**3 - 426*x + 192 = 0?
-5, 2/3, 32
Let t(v) = -v**4 - 5*v**3 - 5*v**2 - 7*v + 3. Let k(b) = -b**2 - 2. Let p(l) = -l**2 - l - 3. Let h(j) = -2*k(j) + p(j). Let d(u) = -3*h(u) + t(u). Factor d(m).
-m*(m + 1)*(m + 2)**2
Find a such that -6/7*a**2 + 270/7*a - 2784/7 = 0.
16, 29
Let y(f) be the third derivative of -f**5/15 - 140*f**4/3 + 2997*f**2 + f + 1. Determine d so that y(d) = 0.
-280, 0
Let u(g) be the first derivative of -6/5*g**3 - 48 + 24/5*g - 4/5*g**2 + 2/25*g**5 + 0*g**4. Factor u(m).
2*(m - 3)*(m - 1)*(m + 2)**2/5
Let n be (-2)/8 - 115/(-460). Let s(w) be the third derivative of 5*w**2 + 2/315*w**5 + 1/252*w**6 + 0 + 0*w**3 - 1/252*w**4 + n*w. Solve s(k) = 0.
-1, 0, 1/5
Let c(t) = -t**2 + 4*t + 88. Let w be c(11). Suppose 5*n + 3*q - 2*q - w = 0, -n - 4*q + 6 = 0. Factor 18/5 + 3/5*o - 3/5*o**n.
-3*(o - 3)*(o + 2)/5
Factor 715*l + 0*l**3 + 256*l**2 + 444 - 45*l**2 + 5*l**3 + 0*l**3 - 7*l**2.
(l + 3)*(l + 37)*(5*l + 4)
Let g be -25 + 1 + 14516/573. Factor -g*w - 4*w**2 + 4 + 4/3*w**3.
4*(w - 3)*(w - 1)*(w + 1)/3
Suppose -21*a + 180 = -6*a. Let k(v) be the second derivative of 0 + 1/3*v**5 - a*v + 0*v**4 - 2/9*v**6 + 2/3*v**2 - 5/9*v**3 + 1/21*v**7. Factor k(b).
2*(b - 1)**4*(3*b + 2)/3
Determine q so that -2/9*q**5 + 8/3*q**3 + 4/9*q**2 + 0*q**4 - 6*q - 4 = 0.
-3, -1, 2, 3
Let a be (5 - 94/18) + (-40)/(-18). Factor 14*h + 2*h + 9 + 3 + 7*h**2 + 3*h**3 - a*h**3 + 0.
(h + 2)**2*(h + 3)
Suppose -307 = -9*u + 854. Factor 48*b + 40*b**4 - 68*b**5 - b**4 + 11*b - 275*b + u*b**3 + 71*b**5 + 45*b**2.
3*b*(b - 1)*(b + 3)**2*(b + 8)
Let g be -70 + 72 + -3*1. Let o(b) = -33*b - 29. Let t be o(g). Solve -t + 1/2*v**2 + v = 0 for v.
-4, 2
Let q be 92/(-3)*189/(-42). Factor -q + 38*i**2 - 65*i**2 + 8 + 32*i**2 + 55*i.
5*(i - 2)*(i + 13)
Let u(w) = w**3 + 147*w**2 - 1085*w + 51. Let l be u(7). Suppose 4/3 + 0*z**l - 2/3*z**3 + 2*z = 0. What is z?
-1, 2
Let q(h) be the second derivative of -3/5*h**5 + 0*h**2 - 2 - 1/21*h**7 - 2/3*h**4 + 9*h - 4/15*h**6 - 1/3*h**3. Factor q(j).
-2*j*(j + 1)**4
Let g(v) = -7*v**4 - 4*v**5 - 5 - 4*v**3 - 25 + 3*v**5 + 26. Let i(u) = 6*u**4 + 3*u**3 + 3. Let d(o) = -3*g(o) - 4*i(o). Solve d(r) = 0.
0, 1
Let z(q) be the second derivative of -8/3*q**3 - 1/30*q**5 - 16/3*q**2 - 118*q + 0 - 1/2*q**4. Factor z(i).
-2*(i + 1)*(i + 4)**2/3
Suppose 350 = 5*g - 6*f + f, 5*g - 362 = 2*f. Let d(x) = 4*x - 290. Let h be d(g). Let -8 - 2/9*t**5 + 16/3*t + 2*t**4 - h*t**3 + 46/9*t**2 = 0. What is t?
-1, 2, 3
Factor 336/5*o - 66/5*o**2 + 0 + 3/5*o**3.
3*o*(o - 14)*(o - 8)/5
Suppose -39*p = -41*p + 6. Suppose 15*l**2 + 48*l**3 + 8*l - 102*l**p + 53*l**3 - 22*l = 0. What is l?
0, 1, 14
Let o(u) = -2*u**2 + 8*u + 21. Let a be o(5). Find n such that -10*n**4 - a*n**3 + 2*n**3 + 5*n**5 - 6*n**3 + 0*n**3 = 0.
-1, 0, 3
Let n be ((-192)/62