 -1, 3
Let i(z) = -4*z**3 + 3*z**2. Let w(a) = -26*a**3 + 88*a**2 - 576*a - 648. Let s(k) = -6*i(k) + w(k). Determine r so that s(r) = 0.
-1, 18
Suppose -15*m + 28 = -17. Factor 4*x**5 + 9*x**4 - 118*x**3 + 11*x**4 + 94*x**m.
4*x**3*(x - 1)*(x + 6)
Let f = -232/4389 - -252286/4389. Let -f*v**3 + 3930/7*v + 900/7 + 2614/7*v**2 + 2*v**4 = 0. What is v?
-1, -2/7, 15
Let r = -491 + 493. Find m, given that 261*m + 1482*m**r - 27*m**4 - 1928*m**2 - 1828*m**2 - 1866*m + 519*m**3 + 600 - 615*m = 0.
-1, 2/9, 10
Let h(d) be the first derivative of d**4 - 88*d**3/3 + 1357. Factor h(n).
4*n**2*(n - 22)
Let q(n) be the first derivative of -25*n + 5/3*n**3 + 10*n**2 - 26. Determine m so that q(m) = 0.
-5, 1
Determine o so that -33*o**2 + 234*o**2 + 10336*o**3 - 10339*o**3 = 0.
0, 67
Suppose -14 = -4*o - 2*s, -3*s + 19 = 4*o - 6*s. Suppose -13*y = -3*y - 20. Factor 9*f**2 - 16*f + 21*f**y + 4*f**o - 16*f**3 + 4 - 6*f**2.
4*(f - 1)**4
Let z(t) = -5*t**3 + 29*t**2 - 65*t + 225. Let g be z(5). Factor g*f + 0*f**3 + 0*f**2 - 2/5*f**5 - 8/5*f**4 + 0.
-2*f**4*(f + 4)/5
Factor 1311 - 17*r**4 + 135*r**2 - 1743*r + 2217 + 0*r**4 + 27*r**3 + 12*r**4 + 2*r**4.
-3*(r - 7)**2*(r - 3)*(r + 8)
Let j(r) be the second derivative of -r**5/4 - 365*r**4/4 - 720*r**3 - 2150*r**2 + 5*r - 63. Suppose j(i) = 0. What is i?
-215, -2
Let p(b) be the third derivative of b**5/90 - 110*b**4/9 - 49*b**3 + 2*b**2 - 154*b. Determine j, given that p(j) = 0.
-1, 441
Let t = -52519/26 + 2020. Let n(c) be the second derivative of -t*c**4 + 0 - 3/130*c**5 - 1/195*c**6 + 12*c - 1/39*c**3 + 0*c**2. Factor n(g).
-2*g*(g + 1)**3/13
Let g(j) = j**2 - 4*j + 4. Let v be g(5). What is n in v*n + 12 + 244*n**3 - 245*n**3 + 4*n = 0?
-3, -1, 4
Let x = 71/18 + -7/2. Suppose -3 = 4*w - 11, -2*a + 12 = 3*w. Factor 4/9*v**a - x*v**2 - 8/9*v + 0.
4*v*(v - 2)*(v + 1)/9
Let w(a) be the third derivative of -1/390*a**5 + 33*a**2 + 5/156*a**4 - 4/39*a**3 + 0 + a. Find i such that w(i) = 0.
1, 4
Let s be (-5*(-10)/150)/(1/5). Let i(h) be the second derivative of 0 - 1/16*h**5 + s*h**3 + 25/48*h**4 - 15/2*h**2 - 17*h. Factor i(w).
-5*(w - 6)*(w - 1)*(w + 2)/4
Let n(d) be the second derivative of -d**6/360 - 3*d**5/40 - d**4/3 + d**3/3 + 6*d**2 + 13*d + 1. Let m(o) be the second derivative of n(o). Factor m(x).
-(x + 1)*(x + 8)
Let b(j) = j**2 + 18*j + 98. Let u(w) = 2*w**2 + w. Let x(q) = -9*q**2 - 91*q - 489. Let i(s) = 2*u(s) + x(s). Let f(n) = 11*b(n) + 2*i(n). Factor f(m).
(m + 10)**2
Factor 3443*p + 4002 + 2428*p - 19988 - 5477 - 240*p**2 + 3*p**3 - 24023.
3*(p - 42)*(p - 19)**2
Let m = -534 + 552. Suppose -m = -6*p - 3*p. Find x, given that 1/2*x - 1/4*x**4 + 0*x**3 + 3/4*x**p + 0 = 0.
-1, 0, 2
Suppose 8*g - 10*g - 20 = -2*o, -2*o - 5 = 3*g. Let t be (18/(-24))/((o/(-4))/5). Determine w, given that 8/5*w**t - 10*w**2 + 84/5*w - 18/5 = 0.
1/4, 3
Factor -32*n**2 - 52 + 10/3*n**3 + 242/3*n.
2*(n - 6)*(n - 1)*(5*n - 13)/3
Factor 5*l**5 + 17306*l**4 + 4*l**2 - 17341*l**4 + 0*l**2 - 4*l**2.
5*l**4*(l - 7)
Let d(j) be the first derivative of 2*j**3/21 + 124*j**2 + 53816*j + 837. Determine p so that d(p) = 0.
-434
Let l(f) be the third derivative of 147*f**2 + 1/112*f**8 + 0 - 3/35*f**7 + 11/40*f**6 + 0*f - 3/2*f**4 + 4*f**3 - 1/10*f**5. Factor l(v).
3*(v - 2)**3*(v - 1)*(v + 1)
Suppose 6*c - 36*c + 120 = 0. Factor 16/3*v**3 - 2/3*v**c - 4*v**2 - 50/3 - 80/3*v.
-2*(v - 5)**2*(v + 1)**2/3
Let c be (-2)/((-13)/((-65)/(-2))). Find p such that 7*p**3 + 289 - 7*p**3 - 33*p**2 + c*p**3 - 255*p - 6*p**3 + 0*p**3 = 0.
-17, 1
Let q = -234570 + 234570. Let -17/5*n + 1/10*n**2 + q = 0. What is n?
0, 34
Factor -911/4*g - 455/2 - 1/4*g**2.
-(g + 1)*(g + 910)/4
Suppose -648 + l**4 + 14*l**3 + 22*l - 36*l - 16*l**2 + 663 = 0. What is l?
-15, -1, 1
Let k(d) = 1. Let v(p) = 4*p**2 + 4*p - 2. Let a be ((-1)/5 + -1)/(9/(-390)). Let u = a - 50. Let t(o) = u*k(o) + v(o). Factor t(j).
4*j*(j + 1)
Factor -413*z - 117*z**2 - 414 - 125*z**2 - 104*z**2 + 347*z**2.
(z - 414)*(z + 1)
Let t(g) be the first derivative of -g**5/150 + g**4/12 - 4*g**3/15 + 29*g**2/2 - 17. Let j(o) be the second derivative of t(o). Factor j(m).
-2*(m - 4)*(m - 1)/5
Determine j so that -56/3*j**3 + 4/3*j**2 + 2/3*j**5 - 28/3 + 8*j**4 + 18*j = 0.
-14, -1, 1
Let g be (25 + -28)/((-6)/(-16)*2). Let k(v) = v**3 + 3*v**2 + 7*v + 1. Let n(f) = -4*f**3 - 10*f**2 - 22*f - 2. Let o(t) = g*n(t) - 14*k(t). Factor o(l).
2*(l - 3)*(l + 1)**2
Let q(g) be the third derivative of -1/120*g**6 + 1/20*g**5 + 0*g + 0 - 1/12*g**4 + 130*g**2 + 0*g**3. What is p in q(p) = 0?
0, 1, 2
Let g(s) = 2*s**3 - 51*s**2 + 63*s - 948. Let m be g(25). Factor -7/4 + 1/4*k**m - 3/2*k.
(k - 7)*(k + 1)/4
Factor -48*y + 63*y**3 + 16*y**2 - 108*y - 173*y**3 - 504 + 114*y**3.
4*(y - 6)*(y + 3)*(y + 7)
Let p(x) = -x**2 - 10*x - 23. Let z be p(-5). Solve -r + 1 + r**2 + 1 - 4*r**2 + z*r**2 = 0 for r.
-2, 1
Let t(g) be the first derivative of g**6/2 + 12*g**5/5 - 6*g**4 - 42*g**3 - 27*g**2/2 + 162*g + 3261. Determine q, given that t(q) = 0.
-3, -2, 1, 3
Suppose 0 = -5*l + 166 + 94. Determine b, given that -2*b - 20*b**2 + l*b**2 - 37*b**2 = 0.
-2/5, 0
Let y(i) = -373*i**2 + 72*i + 146. Let q be y(-2). Let f = q + 2983/2. Factor -5/4 + f*m - 1/4*m**2.
-(m - 5)*(m - 1)/4
Let n(c) = c - 8. Let g(m) = 5*m**3 - 895*m**2 + 39601*m + 40492. Let k(j) = -g(j) + n(j). Find a such that k(a) = 0.
-1, 90
Let l(r) be the second derivative of r**6/30 - 9*r**5/20 + 5*r**4/3 - 2*r**3 - 5079*r. Solve l(i) = 0 for i.
0, 1, 2, 6
Let u(b) be the first derivative of 1/60*b**5 - 37 - 5/6*b**3 - 25/2*b**2 + 0*b + 1/6*b**4. Let n(s) be the second derivative of u(s). Factor n(h).
(h - 1)*(h + 5)
Let u(h) be the third derivative of 2*h**7/105 - 4*h**6/15 - 2649*h**2. Solve u(r) = 0.
0, 8
Let u(j) be the first derivative of -j**5 - 45*j**4/4 - 40*j**3/3 + 150*j**2 + 91. Factor u(p).
-5*p*(p - 2)*(p + 5)*(p + 6)
Let l(z) = z**4 + 2*z**3 - z. Suppose -4*r - 15 + 35 = -2*i, 5*r + 17 = -i. Let n(b) = -8*b**4 - 28*b**3 - 4*b**2 + 16*b. Let a(j) = i*l(j) - n(j). Factor a(f).
-4*f*(f - 1)**2*(f + 1)
Let t(z) be the first derivative of 7*z**6/960 + 17*z**5/120 + 23*z**4/48 - 2*z**3/3 - 121*z**2 + 262. Let h(i) be the second derivative of t(i). Factor h(b).
(b + 2)*(b + 8)*(7*b - 2)/8
Let h = 12622/5 - 2621. Let m = h - -499/5. What is j in m*j**4 + 56/5*j - 16/5 + 2*j**5 - 38/5*j**3 - 28/5*j**2 = 0?
-2, 2/5, 1
Suppose 4*n = 5*t + 364, -2*n - 2*t - 91 = -3*n. Let z = 131 - n. Factor -u**4 - 4 - 5 + 18*u**3 + z*u - 2*u**4 - 10*u - 36*u**2.
-3*(u - 3)*(u - 1)**3
Let a(b) be the second derivative of -b**6/300 + 19*b**5/50 - 88*b**4/5 + 6292*b**3/15 - 5324*b**2 + 2*b - 1188. Factor a(s).
-(s - 22)**3*(s - 10)/10
Let j = -274 + 279. Solve 4*q**2 - 4342*q - 14*q**2 + 4327*q + j*q**3 = 0 for q.
-1, 0, 3
Suppose -2*l**3 + 112/9 - 2/9*l**4 + 8*l - 20/9*l**2 = 0. What is l?
-7, -2, 2
Let n(c) be the first derivative of c**3/4 - 27*c**2 + 213*c/4 + 428. Suppose n(d) = 0. What is d?
1, 71
Let k(r) be the third derivative of 1/300*r**6 + 0 - 6*r**2 - 1/30*r**3 - 1/120*r**4 + 1/150*r**5 - 1/1680*r**8 + 5*r - 1/1050*r**7. Find x such that k(x) = 0.
-1, 1
Suppose 30 = 2*q + 22. Factor -45*v**4 + 3*v + 0*v**5 + 6*v**3 + q*v**2 + 49*v**4 + v**5 - 2*v.
v*(v + 1)**4
Let q(h) be the second derivative of -13/10*h**5 - h + 82 + 0*h**4 + 0*h**2 + 0*h**3 - 1/15*h**6. Suppose q(g) = 0. Calculate g.
-13, 0
Let q(j) be the second derivative of -j**4/6 - 1714*j**3/3 - 734449*j**2 - 2990*j. Factor q(o).
-2*(o + 857)**2
Let b(o) be the second derivative of -169*o + 0 - 23/36*o**4 + 2/3*o**2 - 22/9*o**3. What is j in b(j) = 0?
-2, 2/23
Suppose 3*t - 830 = 7*o - 2*o, 0 = -4*o + 2*t - 664. Let f be o/332*(-2 + 0 + 1). Factor -1/2*p**2 - f + p.
-(p - 1)**2/2
Let w(h) be the third derivative of 0*h**3 + 1/84*h**8 - 1/30*h**6 + 0*h**5 + 0 - 3*h**2 + 0*h**7 + 0*h**4 + 13*h. Factor w(j).
4*j**3*(j - 1)*(j + 1)
Suppose -56*b - 73*b = -71*b - 116. Factor -65/3*k + 230/3 - 25/3*k**b.
-5*(k - 2)*(5*k + 23)/3
Let z(v) = -13*v**2 - 49*v - 428. Suppose -9*g = 9*g - 108. Let p(q) = -7*q**2 - 24*q - 213. Let o(i) = g*z(i) - 11*p(i). Factor o(x).
-(x + 15)**2
Let q(m) = -16*m**2 - 2555*m - 2913. Let w(r) = -3*r**2 - 518*r - 583. Let z(d) = -2*q(d) + 11*w(d). Factor z(x).
-(x + 1)*(x + 587)
Let