-3*b + 3. Let m(t) be the first derivative of -84*t**3 + 7*t - 1 + 20*t + 85*t**3 - 9*t**b. What is q in m(q) = 0?
3
Factor 1280*x**2 + 45 - 137*x + 372*x + 245*x.
5*(16*x + 3)**2
Let l be ((1 - 3) + -4)/(-2). What is b in b**5 + 4*b**l - b**4 - 4*b**4 - 3*b**4 + 3*b**5 = 0?
0, 1
Let i(l) be the third derivative of l**8/10080 + l**7/3780 - l**6/135 - l**5/15 - l**4/8 + 22*l**2. Let x(z) be the second derivative of i(z). Factor x(b).
2*(b - 3)*(b + 2)**2/3
Let z(h) = 4*h**4 + 28*h**3 - 32*h**2 - 9*h - 3. Let w(a) = -4*a**4 - 28*a**3 + 32*a**2 + 6*a + 2. Let c(d) = 3*w(d) + 2*z(d). Determine k so that c(k) = 0.
-8, 0, 1
Let w be ((-400)/96*12/30)/((-10)/4). Factor -w*l**3 + 14/3*l - 8/3 - 4/3*l**2.
-2*(l - 1)**2*(l + 4)/3
Factor 5/4*r**3 + 0 - 15/2*r**2 + 45/4*r.
5*r*(r - 3)**2/4
Let u(n) be the third derivative of n**5/120 + 13*n**4/24 + 169*n**3/12 - 20*n**2 + 2*n. Factor u(b).
(b + 13)**2/2
Let h = -26 + 21. Let f(x) = x**4 + 6*x**3 + 9*x**2 + 10*x. Let i(v) = -2*v**4 - 12*v**3 - 19*v**2 - 20*v - 1. Let d(j) = h*f(j) - 3*i(j). Factor d(y).
(y + 1)**3*(y + 3)
Let n(q) be the third derivative of -1/120*q**5 + 4*q**2 + 5 + 0*q**4 + 0*q**3 + 0*q + 1/240*q**6. Factor n(u).
u**2*(u - 1)/2
Let m(g) be the third derivative of -g**6/540 - g**5/6 - 161*g**4/36 + 529*g**3/27 + 99*g**2. Solve m(o) = 0 for o.
-23, 1
Let u(o) = -23*o - 2. Let m be u(-1). Suppose 13*q**2 - m*q + 2*q**2 - 3*q**2 - 6 = 0. What is q?
-1/4, 2
Determine q, given that 16/7*q**3 - 12/7*q + 46/7*q**2 + 0 + 8/7*q**5 - 34/7*q**4 = 0.
-1, 0, 1/4, 2, 3
Suppose 54*r - 58*r - 20 = 2*b, 0 = -2*b + r + 10. Factor -2/3*w**4 + 10/3*w**3 - 6*w**b + 14/3*w - 4/3.
-2*(w - 2)*(w - 1)**3/3
Let z(q) = -q**2 + 3*q + 20. Suppose -4*v + a = -28, 2*v + a - 9 = -1. Let s be z(v). Determine l so that 0 + 0*l - 4/11*l**s + 14/11*l**4 + 10/11*l**3 = 0.
-1, 0, 2/7
Let z be ((-6)/(-2) + -4)*0. Suppose z = -6*t + t + 35. Factor 27*p**2 - 48 - t*p**2 + 4*p**2 - 3*p**4.
-3*(p - 2)**2*(p + 2)**2
Let s be (1/(-5))/((-1989)/2210). Factor 0 - 2/9*q**3 + s*q**2 + 4/9*q.
-2*q*(q - 2)*(q + 1)/9
Let k(a) be the first derivative of -3*a**4/8 + 8*a**3 + 33*a**2/4 - 1089*a + 654. Determine h so that k(h) = 0.
-6, 11
Let f be (-6)/2 - (13 + 2)/(-5). Let t(p) = p**2 + 2*p. Let j be t(0). Determine o so that -1/5*o**4 + f*o**2 + 0 - 1/5*o**5 + 0*o**3 + j*o = 0.
-1, 0
Suppose 57*b**4 + 6*b**5 - 31*b + 22*b**3 + 36*b**3 - 10*b - 78*b**2 - 7*b + 5*b**3 = 0. What is b?
-8, -2, -1/2, 0, 1
Let j(l) be the second derivative of -l**8/4032 - l**7/756 + 7*l**4/3 + 13*l. Let a(i) be the third derivative of j(i). What is b in a(b) = 0?
-2, 0
Let c(u) = -u**3 + 5*u**2 + 6*u + 4. Let k be c(6). Suppose 2*l**2 - 2*l**4 + 0*l**4 + 3*l**3 - 6*l**2 + 3*l**k = 0. What is l?
-4, 0, 1
Let y(v) be the third derivative of 0*v + 0*v**3 - 7/660*v**6 + 0 - 4/231*v**7 - 1/168*v**8 + 1/165*v**5 + 0*v**4 + 5*v**2. Find d, given that y(d) = 0.
-1, 0, 2/11
Let w(q) be the third derivative of -q**7/420 - q**6/30 - 7*q**5/120 - 11*q**2. Determine u so that w(u) = 0.
-7, -1, 0
Let -404 - 5*x**2 - 77*x - 1621 - 13*x + 4*x**2 = 0. What is x?
-45
Let x = -182 - -184. Let h(c) be the second derivative of 5*c - 1/12*c**4 + 1/40*c**5 - 1/12*c**3 + 1/2*c**x + 0. Solve h(j) = 0 for j.
-1, 1, 2
Let m(b) be the third derivative of -b**5/210 - 3*b**4/28 + 10*b**3/21 + 632*b**2. Factor m(q).
-2*(q - 1)*(q + 10)/7
Let v = -1/2 + 107/210. Let c(m) be the second derivative of -v*m**6 + 8*m + 1/42*m**4 + 0 + 2/21*m**3 - 1/35*m**5 + 0*m**2. Suppose c(a) = 0. What is a?
-2, -1, 0, 1
Solve -6/13*k**4 - 6/13 + 12/13*k**2 + 4/13*k**3 - 2/13*k**5 - 2/13*k = 0.
-3, -1, 1
Let u(d) be the second derivative of d**6/120 + 17*d**5/60 + 10*d**4/3 + 32*d**3/3 - 9*d**2 - 13*d. Let r(c) be the first derivative of u(c). Factor r(h).
(h + 1)*(h + 8)**2
Let h(p) = -5*p**3 + p**2 + p - 1. Let b be h(-1). Factor 0 - u**5 - 2*u**2 - 4*u**3 + 0*u**5 + 5*u + 0*u**2 + 4*u**b - 2.
-(u - 2)*(u - 1)**3*(u + 1)
Let m(g) = -11*g + 13. Let a be m(-9). Let s be a/21*(-6)/(-4). Let 5*z**2 - z + 12 - 19*z + s = 0. Calculate z.
2
Let v(c) = 2*c**2 + 59*c + 138. Let o be v(-27). Suppose 1/5*x**4 + 0*x**2 + 0 + 0*x + 0*x**o = 0. Calculate x.
0
Let k(r) be the first derivative of 5*r**9/3024 + r**8/336 - r**7/28 - r**6/18 + r**5/3 + 10*r**3/3 - 4. Let x(u) be the third derivative of k(u). Factor x(s).
5*s*(s - 2)*(s - 1)*(s + 2)**2
Let y(r) be the second derivative of r**4/12 - 19*r**3/6 + 66*r. Let y(p) = 0. Calculate p.
0, 19
Let o be 2 - (440/99 - 4). Solve 10/9*a**3 + 8/9 - o*a**2 - 16/9*a = 0.
-1, 2/5, 2
Let r(d) = -278*d + 558. Let k be r(2). Factor 0 - 24/5*q**k + 4/5*q**3 + 4*q.
4*q*(q - 5)*(q - 1)/5
Let d(z) be the first derivative of -3*z**5/100 + z**4/20 + 16*z - 7. Let j(f) be the first derivative of d(f). Suppose j(s) = 0. What is s?
0, 1
Let q(o) be the third derivative of -13*o**5/240 + 7*o**4/96 + o**3/4 + 321*o**2. Determine j, given that q(j) = 0.
-6/13, 1
Let p(x) be the third derivative of x**5/15 + x**4/6 - 8*x**3 - 10*x**2 + 4*x. Factor p(b).
4*(b - 3)*(b + 4)
Solve 62/7*o**3 + 0 - 2/7*o**4 - 374/7*o**2 - 1734/7*o = 0.
-3, 0, 17
Solve -112*u - 2*u**4 + 77 + 83 + 112*u**2 - 68*u - 93*u + 9*u - 6*u**3 = 0.
-10, 1, 2, 4
Let z(d) be the first derivative of d**5/35 + 2*d**4/21 - 2*d**3/21 - 4*d**2/7 - 8*d + 2. Let n(y) be the first derivative of z(y). Factor n(i).
4*(i - 1)*(i + 1)*(i + 2)/7
Let r(t) be the third derivative of 3*t**7/175 + 43*t**6/300 + 31*t**5/75 + t**4/3 - 8*t**3/15 - t**2 - 40*t. Suppose r(z) = 0. What is z?
-2, -1, 2/9
Let l(z) be the second derivative of 80*z**4/3 + 280*z**3/3 + 245*z**2/2 - 2*z + 11. Factor l(d).
5*(8*d + 7)**2
Let g = 1144 - 1141. Let g*v**5 - 3*v**2 + 21/2*v**3 + 0 + 0*v - 21/2*v**4 = 0. Calculate v.
0, 1/2, 1, 2
Let p(y) be the first derivative of 2/9*y**3 + 0*y**2 + 2/15*y**5 + 1/3*y**4 + 11 + 0*y. Suppose p(r) = 0. Calculate r.
-1, 0
Let o = 3624/3425 + 3/137. Let x(r) be the first derivative of 9/4*r**4 + o*r**5 + 3/10*r**2 + 7/5*r**3 + 0*r + 4. Find f, given that x(f) = 0.
-1, -1/3, 0
Let q be -7 + (33/2)/((-18)/(-8)). Solve -2/3*b**2 + 1/3*b**3 + q*b**4 + 0 + 0*b = 0.
-2, 0, 1
Suppose 3*f + 4*o - 81 = -2, -1 = -f + 5*o. Let w be (5 + (-117)/f)/((-12)/14). Suppose -w + 2/3*y**2 - 1/3*y + 1/3*y**3 = 0. Calculate y.
-2, -1, 1
Suppose -45*l = -49*l + 2*v + 40, -l + 2*v + 13 = 0. Factor 9/2*h**4 + l*h**2 - 39/4*h**3 + 0 - 3*h - 3/4*h**5.
-3*h*(h - 2)**2*(h - 1)**2/4
Let c = 166904/4249 - -3/607. Let i = c - 39. Factor -10/7*w + 4/7 - i*w**3 + 8/7*w**2.
-2*(w - 2)*(w - 1)**2/7
Suppose -t - 21*x = -25*x + 11, -t - x = -9. Factor 3/5*n**t + 6/5 - 3*n + 12/5*n**3 - 12/5*n**4 + 6/5*n**2.
3*(n - 2)*(n - 1)**3*(n + 1)/5
Let k(u) be the third derivative of 49/24*u**6 + 0*u + 21/2*u**5 + 0 + 3*u**2 + 25/2*u**4 + 20/3*u**3. Let k(i) = 0. What is i?
-2, -2/7
Let 4*l**3 + 18*l**2 + 2*l**2 + 10 + l**3 + 0*l**3 + 25*l = 0. What is l?
-2, -1
Let b be (-4)/8*((-14)/(-28))/((-1)/6). Solve b*x**2 - 9/2 + 3*x = 0 for x.
-3, 1
Let j(f) be the second derivative of f**3/3 - 3*f**2/2 + 3*f. Let x be j(3). What is a in 0*a + 10*a**x - 16*a**3 - 3*a**2 - 3*a**4 + 0*a = 0?
-1, 0
Let o(a) be the first derivative of 1/2*a**2 + 7/720*a**6 + 1 + 0*a + 0*a**3 + 1/72*a**4 + 1/40*a**5. Let r(f) be the second derivative of o(f). Factor r(h).
h*(h + 1)*(7*h + 2)/6
Solve 4*s**2 - 63*s + 16 - 13 + 18*s + 8 = 0.
1/4, 11
Let z(r) be the third derivative of -3*r**8/280 - 2*r**7/75 + 17*r**6/300 + 7*r**5/75 - 2*r**4/15 + 6*r**2. Determine k so that z(k) = 0.
-2, -1, 0, 4/9, 1
Factor -99/2*o**2 + 39/2*o**3 - 3/2*o**4 - 15 + 93/2*o.
-3*(o - 10)*(o - 1)**3/2
Let d(g) be the second derivative of g**5/30 - 2*g**4/9 + 4*g**3/9 - 40*g. Factor d(b).
2*b*(b - 2)**2/3
Let t = -24 - -30. Solve 4*v + t*v + 5*v**4 + 10*v**2 - 11*v**2 - 14*v**2 = 0 for v.
-2, 0, 1
Let p = -9439 - -9442. Factor -1/4 - 9/8*h + 3/8*h**4 + 1/8*h**p - 9/8*h**2.
(h - 2)*(h + 1)**2*(3*h + 1)/8
Let z be (-1 + (-8)/(-6))*694/1041. Factor 0 + 4/9*d**3 + z*d**4 + 0*d + 2/9*d**2.
2*d**2*(d + 1)**2/9
Let y(o) = -o**2 - o + 1. Let n(k) = -18*k**2 - 18*k + 21. Let s = 15 + 0. Let v(b) = s*y(b) - n(b). Factor v(f).
3*(f - 1)*(f + 2)
Let m be 4/4 + -3 - 48/(-14). Factor 4/7*k - 6/7*k**3 + 0 - m*k**2.
-2*k*(k + 2)*(3*k - 1)/7
Factor 2