(v) = w*g(v) + o(v). Factor m(a).
2*(a - 1)*(a + 3)
Let h be 4/20 - (8 - 9). Let d be 1 + 95/25 + -4. Factor -d*i - h + 2/5*i**2.
2*(i - 3)*(i + 1)/5
Let g(b) = -4*b**3 + 116*b**2 - 1568*b - 2. Let k(p) = -p**3 + 2*p**2 - 1. Let r(j) = g(j) - 2*k(j). Determine l, given that r(l) = 0.
0, 28
Let w(g) be the second derivative of g**5/180 - 7*g**4/27 + 98*g**3/27 - 2*g. Factor w(s).
s*(s - 14)**2/9
Let w(p) be the third derivative of 2*p**6/45 + p**5/6 + p**4/6 - p**3/9 - 17*p**2 + 4*p. Factor w(h).
2*(h + 1)**2*(8*h - 1)/3
Let z(p) be the first derivative of p**3/3 - 14*p**2 + 27*p - 339. Factor z(y).
(y - 27)*(y - 1)
Let i(u) be the first derivative of -1/14*u**4 - 11 + 16/7*u - 4/21*u**3 + 4/7*u**2. Factor i(a).
-2*(a - 2)*(a + 2)**2/7
Let c(j) be the first derivative of -j**2/2 - 3. Let t(x) = 3*x**2 + 4*x. Let s(u) = 4*c(u) + t(u). Solve s(i) = 0 for i.
0
Let t(k) be the second derivative of 44*k + 1/6*k**4 + 1/80*k**5 + 3/4*k**2 + 0 + 13/24*k**3. What is g in t(g) = 0?
-6, -1
Let o = -4/10701 + -3980752/53505. Let t = 75 + o. Solve -21/5*z**2 + 9*z - 27/5 + t*z**3 = 0 for z.
1, 3
Let r(f) be the first derivative of 0*f - 6 + 2/3*f**3 + 1/2*f**2 - 1/30*f**5 - 1/12*f**4. Let s(w) be the second derivative of r(w). Factor s(k).
-2*(k - 1)*(k + 2)
Let a(o) = 3*o**2 - 11*o + 5. Let x(t) be the first derivative of -5*t**3 + 27*t**2 - 24*t - 29. Let l(z) = 24*a(z) + 5*x(z). Solve l(v) = 0 for v.
0, 2
Let t(i) be the second derivative of i**6/1980 + i**5/330 + i**4/132 - 2*i**3/3 + 10*i. Let z(c) be the second derivative of t(c). Find l, given that z(l) = 0.
-1
Let a(u) = -11*u**2 - 58*u - 257. Let h(f) = 32*f**2 + 176*f + 769. Let n(g) = -17*a(g) - 6*h(g). Factor n(b).
-5*(b + 7)**2
Let x = 576/133 - -10/19. Let z = x - 564/119. Factor 0*d**2 + z*d**4 - 2/17 - 4/17*d + 4/17*d**3.
2*(d - 1)*(d + 1)**3/17
Let m = 3191/2397 - -5/2397. Determine h so that 0 + 32/3*h + m*h**4 - 20/3*h**3 + 8/3*h**2 = 0.
-1, 0, 2, 4
Determine l so that -41*l**3 - 4*l**4 - 24*l**2 - 32*l**3 + 6*l**4 + 6*l**4 - 4 + 71*l**3 + 22*l = 0.
-2, 1/4, 1
Suppose 5*g - 14 = -2*g. Let z = 5 - 3. Solve 3*c - c**z - 5*c**g + 8*c**3 - 5*c**3 = 0 for c.
0, 1
Suppose -1 + 1/4*b**2 + 3/4*b = 0. What is b?
-4, 1
Let p = -15 - -23. Suppose j = -p + 10. Factor 32*b - 30*b + j - 2*b**3 + 0 - 2*b**2.
-2*(b - 1)*(b + 1)**2
Factor -1/8*m**5 + 0*m - 5/8*m**3 + 1/4*m**2 + 1/2*m**4 + 0.
-m**2*(m - 2)*(m - 1)**2/8
Let w = 610 - 3048/5. Factor 0 + 4/5*r**2 + w*r**3 - 6/5*r.
2*r*(r - 1)*(r + 3)/5
Let q(n) be the third derivative of n**7/21 + 23*n**6/60 + n**5 + n**4/3 - 8*n**3/3 + n**2 - 270. Suppose q(r) = 0. What is r?
-2, -1, 2/5
Let v be (-2)/(-17) + 60/(-510). Solve -4/3*j**2 - 2/3*j**4 - 2*j**3 + v + 0*j = 0 for j.
-2, -1, 0
Let g(d) = -5*d**2 + 5*d - 1. Let c(h) = -7*h**2 + 6*h - 1. Let q(a) = -4*c(a) + 5*g(a). Let l be q(1). Factor -1/6*p**l + 0 + 1/6*p + 0*p**2.
-p*(p - 1)*(p + 1)/6
Let 11*p**2 + 9*p**3 + p**4 - 10*p**3 + p - 12*p**2 = 0. Calculate p.
-1, 0, 1
Suppose 0*b + 3*b - 9 = 0. Suppose -s = 0, 5 = 4*t - 2*s - b. Determine r so that -3*r**2 + t*r**2 + 2*r**4 + 2*r**2 + 4*r**3 + r**2 = 0.
-1, 0
Solve 11/4*t**2 + 2*t**3 - 1/4*t**4 - 9/2*t + 0 = 0 for t.
-2, 0, 1, 9
Let z(w) = 2*w**2 + 16*w - 6. Let l be z(-9). What is i in l - 2*i**3 - 28*i - 1131*i**4 + 1132*i**4 - 6*i**3 + 23*i**2 = 0?
1, 2, 3
Suppose 107 - 17 = 5*m - r, -5*m - 2*r = -90. Let b = 20 - m. Factor 7*s**3 + 12*s**2 + 3 + 9*s**b - 17*s + 2*s**3.
(s + 3)*(3*s - 1)**2
Let v(w) be the second derivative of w**6/240 - w**4/16 - w**3/6 - 3*w**2/16 - 213*w. Determine d so that v(d) = 0.
-1, 3
Let c(s) be the second derivative of 0 + 1/150*s**5 + 0*s**2 + 1/30*s**4 - 10*s + 2/45*s**3. Find d such that c(d) = 0.
-2, -1, 0
Let t(p) be the second derivative of 7*p**5/5 - 4*p**4 + 2*p**3 + 4*p**2 + p + 178. Factor t(z).
4*(z - 1)**2*(7*z + 2)
Suppose 6*l**3 - 39/2*l**2 - 1/2*l**4 + 14*l + 0 = 0. What is l?
0, 1, 4, 7
Let x be -4 - (4 + -1 + 102/(-14)). Factor 2/7*q**3 - 2/7*q**2 - x*q + 2/7*q**4 + 0.
2*q*(q - 1)*(q + 1)**2/7
Let c(h) = -h**4 - h. Let w(y) = y**2 + 5*y - 2. Let l be w(-4). Let g(q) = 4*q**4 + 4*q**3 - 2*q**2 + 6*q. Let d(a) = l*c(a) - g(a). Factor d(i).
2*i**2*(i - 1)**2
Let u(z) = -2*z**5 + z**3 - 4*z**3 + 2*z**4 - 6*z**4. Let k be (2 - -2)*6/(-8). Let m(g) = -5*g**5 - 9*g**4 - 7*g**3. Let c(r) = k*m(r) + 7*u(r). Factor c(f).
f**4*(f - 1)
Let v(r) be the first derivative of r**5/90 - r**4/27 + 25*r - 24. Let p(t) be the first derivative of v(t). Factor p(z).
2*z**2*(z - 2)/9
Let i(k) be the second derivative of -8*k**6/5 + 9*k**5/5 + 15*k**4/16 + k**3/8 + 2*k - 5. Factor i(f).
-3*f*(f - 1)*(8*f + 1)**2/4
Suppose 4*l + 168 - 142 = 2*h, -3*h + 2*l = -19. Suppose -10/9*k**4 + 0*k - 16/9*k**h + 8/9*k**2 + 0 = 0. Calculate k.
-2, 0, 2/5
Suppose -5*t + 175 = a + 4*a, 145 = 3*t - 5*a. Suppose 6*n - 11*n = -t. What is c in -10*c**2 + 4*c**2 - 2 + n*c**2 = 0?
-1, 1
Let w(g) = g**3 - 3*g**2 + 4*g - 2. Let y be w(2). Factor 10*h**2 - 3*h**2 + 6 - 5*h**2 - 8*h**y - 3*h + 3*h**3.
3*(h - 2)*(h - 1)*(h + 1)
Suppose -p = x - 0*x + 5, 6*p + 4*x + 20 = 0. Factor 1/3*n**5 + 5/3*n**3 + p*n + 4/3*n**4 + 2/3*n**2 + 0.
n**2*(n + 1)**2*(n + 2)/3
Let q(f) be the second derivative of -7/3*f**3 + 0 - 25*f + 6*f**2 + 1/6*f**4. Solve q(x) = 0 for x.
1, 6
Let x(y) be the third derivative of y**5/300 - y**4/8 + 6*y**3/5 - 2*y**2 + 18. Factor x(v).
(v - 12)*(v - 3)/5
Let c(n) be the second derivative of n**5/540 + n**4/24 + 4*n**3/27 + 15*n**2 - 50*n. Let r(x) be the first derivative of c(x). Find p, given that r(p) = 0.
-8, -1
Let r = 179 + -157. Let -r + 6*d**2 + 3*d + 2*d**3 + 47 + 3*d - 23 = 0. What is d?
-1
Determine t, given that 16/5 - 4/5*t**3 + 32/5*t - t**4 + 16/5*t**2 - 1/5*t**5 = 0.
-2, -1, 2
Let c be 60/((-36)/(-9)) - 8. Let k(n) be the first derivative of -c + 0*n - 2/27*n**3 - 4/9*n**2. Factor k(r).
-2*r*(r + 4)/9
Let g(s) be the second derivative of 200*s**6/3 + 10*s**5 - 665*s**4/4 - 100*s**3/3 - 5*s**2/2 + 23*s. Solve g(f) = 0 for f.
-1, -1/20, 1
Let y(a) be the second derivative of a**6/30 - 3*a**5/10 - a**4/12 + a**3 + 504*a. Solve y(r) = 0 for r.
-1, 0, 1, 6
Let a(b) = -3*b**2 + 12*b + 1. Let l(y) = 7*y**2 - 1. Let j(t) = -a(t) - l(t). Factor j(s).
-4*s*(s + 3)
Let p(n) = n**2 - 149*n + 294. Let h be p(147). Solve -2/5*v**5 - 54/5*v**2 - 54/5*v**3 + h*v - 18/5*v**4 + 0 = 0 for v.
-3, 0
Let p(a) = 4*a**3 + 8*a**2 + 8*a + 2. Let b(l) = -24*l**2 + 5*l - 14*l - 4 - 14*l - 1 - 13*l**3. Let x(k) = -2*b(k) - 7*p(k). Factor x(f).
-2*(f + 1)**2*(f + 2)
Let h = -13 - -19. Let z = h + -2. Solve 12 + 12*t - 4*t**3 + 18*t**3 + 10*t**3 + 32*t + 56*t**2 - 4*t**5 - z*t**4 = 0.
-1, 3
Let n = 4/45 - -1/9. Let o be 2 - (3 + 5 - 2) - 110/(-25). Solve -n*q**2 + 3/5*q - o = 0.
1, 2
Let b(q) = -5*q**2 - 29*q. Let d be 21/(-14) + (-111)/(-6). Let t(l) = -2*l**2 - 10*l. Let j(v) = d*t(v) - 6*b(v). Determine s so that j(s) = 0.
0, 1
Suppose -2*m - 9 = -5*p, 0*m = m + 2*p - 9. Let r(g) be the first derivative of -1/16*g**4 - 3 + 1/2*g + 0*g**m + 3/8*g**2. Factor r(n).
-(n - 2)*(n + 1)**2/4
Let j(p) be the second derivative of 27/2*p**2 - 1/4*p**4 - 4*p**3 + 0 + 25*p. Factor j(h).
-3*(h - 1)*(h + 9)
Factor -72/7*a + 0 - 4/7*a**2.
-4*a*(a + 18)/7
Factor 0 - 2/11*p**2 - 12/11*p.
-2*p*(p + 6)/11
Let v(w) be the third derivative of -7*w**8/60 - 13*w**7/30 - 17*w**6/30 - 3*w**5/10 + 17*w**3/6 - w**2. Let i(x) be the first derivative of v(x). Factor i(t).
-4*t*(t + 1)*(7*t + 3)**2
Suppose 12 = 4*x + 4. Let h be 24 - 20 - (-16)/12*-3. Find q, given that -1/3*q**4 + 0*q + h*q**x + 2/3*q**3 + 0 = 0.
0, 2
Let u(r) be the first derivative of 20*r**3/3 + 715*r**2/2 - 180*r - 367. Factor u(j).
5*(j + 36)*(4*j - 1)
Let l = 27/7 + -101/28. Suppose 56 = -3*y + 31*y. Suppose -1/4*c - l*c**y + 0 = 0. Calculate c.
-1, 0
Factor 2/7*b**4 + 18/7*b**3 - 36/7 - 6/7*b**2 - 58/7*b.
2*(b - 2)*(b + 1)**2*(b + 9)/7
Let r(o) be the third derivative of o**8/336 + 2*o**7/35 + 17*o**6/120 - o**5/2 - 553*o**2. Factor r(l).
l**2*(l - 1)*(l + 3)*(l + 10)
Factor r + 12 + 7 + 109*r**2 - 3 + 11*r - 113*r**2.
-4*(r - 4)*(r + 1)
Let y(i) = 12*i - 4. Let v be y(3). Suppose 4 = 4*q - v. Let q*t - 10*t - 2*t + 0*t + 2 + t**2 = 0. Calculate t.
1, 2
Let c = -1815 + 9077/5. Let l(d) be the first der