v) = 3*v**2 - 5*v + 2. Let w(u) = -u**3 - 9*u**2 + 22*u - 2. Let r be w(-11). Let z(h) = -3*h**2 + 6*h - 3. Let d(q) = r*z(q) - 3*i(q). Factor d(m).
-3*m*(m - 1)
Let b(o) = 9*o**4 + 11*o**3 - 11*o**2 + 11*o - 11. Let q(l) = -8*l**4 - 20*l**4 + 30*l**4 + 2*l + 2*l**3 - 2 - 2*l**2. Let j(h) = 2*b(h) - 11*q(h). Factor j(r).
-4*r**4
Let a(j) be the first derivative of j**6/21 + 74*j**5/35 + 272*j**4/7 + 7936*j**3/21 + 2048*j**2 + 40960*j/7 - 120. Let a(s) = 0. What is s?
-8, -5
Suppose -m = -4, 3*m - 2 = -4*q + 18. Let t(d) = -5*d**2 - 62*d - 182. Let n(l) = 85*l**2 + 1055*l + 3095. Let v(b) = q*n(b) + 35*t(b). Factor v(r).
-5*(r + 6)**2
Suppose 5*y = -4*v + 20, 20 = v + 2*y + 3*y. Let l(m) be the third derivative of 0 + 1/210*m**5 + m**2 + 1/84*m**4 + 0*m + v*m**3. Factor l(g).
2*g*(g + 1)/7
Let u(d) be the second derivative of 29*d**6/75 + 27*d**5/50 - d**4/15 - 2*d + 10. Suppose u(j) = 0. Calculate j.
-1, 0, 2/29
Find s, given that 1250/7*s**2 + 200/7*s + 8/7 = 0.
-2/25
Suppose -81*z - 23 = -80*z + 5*b, 5*z + 2*b = 0. Factor 27/8*r**z + 3/8*r**3 + 9*r + 6.
3*(r + 1)*(r + 4)**2/8
Let h be 0 - 2 - (1/12)/((-144)/40176). Factor -31/2*y - 3 - 25/8*y**3 - h*y**2.
-(y + 6)*(5*y + 2)**2/8
Factor -6/7 - 2/7*i**2 + 8/7*i.
-2*(i - 3)*(i - 1)/7
Factor -128/15*b + 224/15*b**2 - 22/5*b**3 - 28/15*b**4 - 2/15*b**5 + 0.
-2*b*(b - 1)**2*(b + 8)**2/15
Let b(w) be the first derivative of 1/9*w**3 + 1/6*w**4 + 0*w**2 + 1/15*w**5 + 0*w + 32. Factor b(h).
h**2*(h + 1)**2/3
Let w(z) be the third derivative of 0 + 1/2*z**4 - z**2 + 3/20*z**5 - 2*z**3 - 1/20*z**6 - 1/70*z**7 + 0*z. Factor w(h).
-3*(h - 1)**2*(h + 2)**2
Let b(j) be the third derivative of -j**6/280 - 17*j**5/140 - j**4 - 26*j**3/7 + 76*j**2. Find s such that b(s) = 0.
-13, -2
Suppose -5453 = -5*i + v - 2202, 0 = -4*v + 16. Determine a so that -150*a + 12 - 2241/2*a**3 + i*a**2 + 1215/2*a**4 = 0.
2/9, 2/5, 1
Let c(m) be the first derivative of m**6/6 - 3*m**5/5 - 5*m**4/2 - 2*m**3/3 + 9*m**2/2 + 5*m + 340. Determine x, given that c(x) = 0.
-1, 1, 5
Let j(p) = -12*p**2 + 6*p - 3. Let k(s) = s**3 + 13*s**2 - 5*s + 3. Let c(q) = 4*j(q) + 3*k(q). Factor c(y).
3*(y - 1)**3
Let f(m) be the third derivative of -m**8/161280 + m**7/8064 + m**5/60 - 3*m**2. Let i(p) be the third derivative of f(p). Factor i(n).
-n*(n - 5)/8
Let c(r) = -5*r**4 + r**3 - 5*r**2 + 3*r. Let q(j) = 14*j**4 - 4*j**3 + 14*j**2 - 8*j. Let z(b) = -8*c(b) - 3*q(b). Find d such that z(d) = 0.
0, 1
Suppose -2*z - 3*j = -1, -5*j + 11 = 4*z - 8*j. Suppose 8/5*n + 0 + 8/5*n**z + 2/5*n**3 = 0. Calculate n.
-2, 0
Let o(a) = -a**3 - a**2 + 2. Let b(p) = -8*p**3 + 24*p**2 - 60*p + 44. Let t(x) = -b(x) + 4*o(x). Determine q, given that t(q) = 0.
1, 3
Let o = -15 - -19. Suppose 0 = -2*p - 0*p + o. What is d in 6*d**5 + 20 - 20 + 2*d**p - 6*d**3 - 2*d**4 = 0?
-1, 0, 1/3, 1
Let s be (-1 - (-15)/3)/(32/24). Factor -3 + 3/4*p**4 - 6*p - 3/4*p**5 + 15/4*p**s - 3/4*p**2.
-3*(p - 2)**2*(p + 1)**3/4
Let r(f) be the first derivative of -7*f**5/60 - 13*f**4/12 + 4*f**3/3 - 13*f**2 + 17. Let v(s) be the second derivative of r(s). What is j in v(j) = 0?
-4, 2/7
Let b(r) = 3*r**2 + 2*r + 1. Let v(p) = -13*p**2 - 8*p - 4. Let g(x) = 2*x**2 - 2*x + 4. Let n be g(3). Let w = n - 7. Let o(c) = w*b(c) + 2*v(c). Factor o(u).
(u + 1)**2
Let v(t) = -9*t**3 + 29*t**2 + 23*t - 5. Let b(d) = 11*d**3 - 29*d**2 - 22*d + 6. Let h(g) = 5*b(g) + 6*v(g). Let h(k) = 0. What is k?
-28, -1, 0
Suppose 19*m = -31 + 107. Let t(b) be the third derivative of 0 + 0*b + 1/6*b**m - 1/30*b**5 + b**2 - 1/3*b**3. Determine l so that t(l) = 0.
1
Suppose 2*p = 43 - 27. Let a be (-2)/p*-5 + 1/4. Factor 3/2*w - 3/2*w**2 + 0 + a*w**4 - 3/2*w**3.
3*w*(w - 1)**2*(w + 1)/2
Let r = 2/6687 + 26738/33435. Determine y so that 8/5*y + 0 + r*y**2 = 0.
-2, 0
Let p(z) be the first derivative of -z**4/22 + 106*z**3/11 + 135. Factor p(d).
-2*d**2*(d - 159)/11
Find d such that 3/8*d**2 + 27/8*d - 27/8 - 3/8*d**3 = 0.
-3, 1, 3
Let k(h) be the second derivative of -h**7/630 + h**5/30 + 2*h**4/3 + 13*h. Let u(c) be the third derivative of k(c). Factor u(q).
-4*(q - 1)*(q + 1)
Let a(v) = 192*v + 576. Let i be a(-3). Factor -1/2*g + i + g**2 - 1/2*g**3.
-g*(g - 1)**2/2
Suppose 110 - 113 = -3*t. Let w(q) be the first derivative of t + 2*q - 3/2*q**2 - 1/3*q**3 + 3/4*q**4 - 1/5*q**5. Determine c so that w(c) = 0.
-1, 1, 2
Let x(h) = h**3 + 7*h**2 + 1. Let c(j) = 8*j**3 + 71*j**2 + 60*j + 5. Let g(i) = -c(i) + 5*x(i). Factor g(p).
-3*p*(p + 2)*(p + 10)
Let 1/6*o**2 + 13/3*o - 28/3 = 0. Calculate o.
-28, 2
Suppose -q = -5, -27*q + 23 = 4*g - 24*q. Let b be (3/12)/((-6)/(-16)). Factor 6 + b*v**g + 4*v.
2*(v + 3)**2/3
Let l(x) be the third derivative of 0 - 1/78*x**5 - 1/52*x**4 + 3/13*x**3 + 9*x**2 + 0*x - 1/780*x**6. Factor l(m).
-2*(m - 1)*(m + 3)**2/13
Let t(r) = 30*r**2 - 2175*r + 2250. Let d(c) = 3*c**2 - 218*c + 225. Let m(n) = 21*d(n) - 2*t(n). Factor m(b).
3*(b - 75)*(b - 1)
Let d(t) be the first derivative of -t**7/210 + t**6/420 + t**5/60 - t**4/84 + 15*t**2 - 37. Let f(h) be the second derivative of d(h). Factor f(b).
-b*(b - 1)*(b + 1)*(7*b - 2)/7
Let l(d) be the first derivative of 16/13*d**2 + 16 + 1/26*d**4 + 0*d - 16/39*d**3. Factor l(x).
2*x*(x - 4)**2/13
Let d = 112838/15 - 7522. Factor -4/5*a**2 - 2/15*a**4 + 8/15*a**3 + d*a - 2/15.
-2*(a - 1)**4/15
Let n(f) = 4*f**2 + 10*f + 16. Let z(p) = 5*p**2 + 10*p + 18. Let o(j) = -3*n(j) + 2*z(j). Suppose o(q) = 0. Calculate q.
-3, -2
Suppose 0 = 6*g - 3*g + 4*f - 19, -4*f + 29 = 5*g. Let a(k) be the second derivative of 2/5*k**2 + 0*k**4 - 1/5*k**3 + 0 + 1/50*k**g - 2*k. Factor a(m).
2*(m - 1)**2*(m + 2)/5
Factor 27*m**5 + 13*m**4 - 56*m**3 - 24*m**5 + 644*m**3 - 97*m**4.
3*m**3*(m - 14)**2
Let j(q) be the second derivative of q**6/10 + 54*q**5/5 + 1221*q**4/4 - 1369*q**3 + q + 41. Suppose j(z) = 0. What is z?
-37, 0, 2
Let s(a) = -3*a**3 - 69*a**2 + 280*a - 400. Let z(l) = 40*l**3 + 965*l**2 - 3920*l + 5600. Let c(n) = -55*s(n) - 4*z(n). Suppose c(r) = 0. Calculate r.
4, 5
Let m(p) = -5*p**4 - 6*p**3 - 3*p**2 - 2*p + 2. Let j(o) = -12*o**4 - 13*o**3 - 5*o**2 - 4*o + 5. Let y(q) = -4*j(q) + 10*m(q). Factor y(a).
-2*a*(a + 1)**2*(a + 2)
Let h(a) = -a - 3 + 0 + 0 - 4. Let p be h(-9). Factor 2*t**2 - 2*t**5 - 2*t**3 + 2*t**5 + p*t**5 - 2*t**4 + 0*t**3.
2*t**2*(t - 1)**2*(t + 1)
Let h = 1230 + -1227. Suppose h*y + 15/7*y**3 - 6/7 - 3/7*y**4 - 27/7*y**2 = 0. What is y?
1, 2
Let z = 3 + -3. Suppose 3*g + 14 = 2*p, -3*p - 7*g + 2*g - 17 = z. Determine a so that p - 1/4*a**2 + 0*a = 0.
-2, 2
Let k(o) be the second derivative of -o**5/60 - o**4/9 - 5*o**3/18 - o**2/3 + 3*o - 2. Suppose k(h) = 0. What is h?
-2, -1
Let i(q) be the third derivative of -3/8*q**4 + 0*q - 1/4*q**5 - 1/40*q**6 + 9/2*q**3 + 0 - 23*q**2. Suppose i(v) = 0. What is v?
-3, 1
Let k(i) = i**2 + 4*i - 13. Let u be k(-11). Let g be (36/14 - 0) + u/(-112). Factor -4/5*a**g - 2/15*a**4 + 8/15*a + 16/15 - 2/3*a**3.
-2*(a - 1)*(a + 2)**3/15
Let t = 22499/6 - 11245/3. Determine z so that -3 - t*z**2 + 9/2*z = 0.
1, 2
Let a(w) be the first derivative of 5*w**3/6 - 65*w**2/4 - 35*w - 78. Find m such that a(m) = 0.
-1, 14
Let -332*q**2 + 0*q**3 + 489*q - 2792*q + 134 - q**3 + 2267 + 235*q**2 = 0. Calculate q.
-49, 1
Let i(u) be the first derivative of 2*u**5/15 + u**4 + 2*u**3 - 68. Factor i(g).
2*g**2*(g + 3)**2/3
Let h(u) = u**3 - 6*u + 4. Let y be h(2). What is l in -3/5*l**2 + 3/5*l + y = 0?
0, 1
Let -2/13*k**3 - 72/13*k - 64/13 - 24/13*k**2 = 0. Calculate k.
-8, -2
Let u(z) = 4*z**2 + z - 37. Let c be u(3). Let h(j) be the first derivative of 0*j**3 + 0*j**c + 1/2*j**4 - 2/5*j**5 + 0*j + 1. Factor h(m).
-2*m**3*(m - 1)
Let w(a) be the second derivative of 3/10*a**5 + 0*a**2 + 0*a**4 - 1/14*a**7 - 1/2*a**3 + 0 + 0*a**6 + 2*a. Suppose w(u) = 0. Calculate u.
-1, 0, 1
Let q(n) = n**2 + 11*n + 28. Let p be q(-8). Let 3 - 21*y**3 - 6 - 4*y**p + 24*y + 39 - 3*y**3 - 32*y**2 = 0. Calculate y.
-3, -1, 1
Let v(a) be the first derivative of -a**5/12 + 25*a**4/24 - 9*a**2/2 + 18. Let n(d) be the second derivative of v(d). Factor n(r).
-5*r*(r - 5)
Let w = -119 - -123. Suppose 4*h = -w*h. Factor 1/2*q + 1/2*q**2 + h.
q*(q + 1)/2
Solve 24/13 - 2/13*x**2 - 22/13*x = 0 for x.
-12, 1
Let l(p) be the third derivative o