 m(v) = -100*v**2 + 1476*v - 1376. Let f(r) = -35*r**2 + 493*r - 458. Let p(q) = -17*f(q) + 6*m(q). Find d, given that p(d) = 0.
1, 94
Let z(d) = -16*d**2 - 30*d + 64. Let y(c) = -18*c**2 - 31*c + 64. Let p(u) = 6*y(u) - 7*z(u). Factor p(m).
4*(m - 2)*(m + 8)
Let i = -615 + 620. Factor 9 - 4*d**4 - d**3 - d**5 - 5*d**5 + 5*d**i + 14*d**2 + 4*d + 16*d - 1.
-(d - 2)*(d + 1)**2*(d + 2)**2
Let p(h) = 86*h**2 + 58*h + 2. Let j be p(-3). Suppose -605*n + j*n = 0. Factor n*s + 1/3*s**2 - 1/3.
(s - 1)*(s + 1)/3
Let j(d) = d**2 - d - 4. Let l(b) = 5*b**2 - 5*b - 18. Suppose 5*s - 6 = q, -20*q + 2*s + 12 = -16*q. Let f(m) = q*j(m) - l(m). Factor f(h).
-(h - 2)*(h + 1)
Let q(c) be the third derivative of c**8/112 - c**7/10 + 7*c**6/40 + 23*c**5/20 - 11*c**4/2 + 10*c**3 - 3492*c**2 - 2. Determine t, given that q(t) = 0.
-2, 1, 2, 5
Let j(r) be the first derivative of -5*r + 1/4*r**4 - 18 + 11/2*r**2 - 7/3*r**3. Factor j(u).
(u - 5)*(u - 1)**2
Find v, given that -2/7*v**3 + 0 + 500/7*v**2 - 498/7*v = 0.
0, 1, 249
Let b(o) be the second derivative of -1/12*o**4 + 5/24*o**3 + 63*o + 1/80*o**5 - 1/4*o**2 + 0. Solve b(y) = 0.
1, 2
Let t(v) be the first derivative of v**4/78 + 2*v**3/13 - 7*v**2/13 + 30*v + 54. Let z(p) be the first derivative of t(p). Factor z(m).
2*(m - 1)*(m + 7)/13
Let c(z) = -z**3 - 19*z**2 + 55*z + 31. Let u be c(-20). Let d = -2003/3 - u. Let 16/3*g**2 + d*g**3 + 0 + 4*g = 0. What is g?
-3, -1, 0
Let f = 2111/1560552 - 2/3981. Let o(n) be the third derivative of 0 + 0*n + 0*n**7 + 1/420*n**6 + 0*n**3 + 0*n**5 - f*n**8 - 6*n**2 + 0*n**4. Factor o(c).
-2*c**3*(c - 1)*(c + 1)/7
Let x(m) be the third derivative of -m**6/180 + 29*m**5/90 + 43*m**4/12 + 11*m**3 + 122*m**2. Find g, given that x(g) = 0.
-3, -1, 33
Suppose -33*d - 56*d = 76*d - 330. Let -6/11*l**d + 0 - 2/11*l**3 - 4/11*l = 0. Calculate l.
-2, -1, 0
Let a(j) = -2*j**5 - 8*j**4 - 20*j**3 + j**2 + 5. Let t(h) = -h**5 - 4*h**4 - 11*h**3 + h**2 + 3. Let z(l) = -6*a(l) + 10*t(l). Solve z(s) = 0 for s.
-2, -1, 0
Suppose -164/5*r**3 + 182/5 + 1/5*r**5 + 163/5*r + 4*r**4 - 202/5*r**2 = 0. What is r?
-26, -1, 1, 7
Let i(g) = -8*g**5 + 41*g**4 + 96*g**3 + 7*g**2 - 82*g - 48. Let q(b) = b**5 - 2*b**4 - 2*b**3 + b**2 - b + 1. Let k(d) = -i(d) - 3*q(d). Solve k(s) = 0.
-1, 1, 9
Let w(q) = 23*q**4 - 131*q**3 + 3*q**2 + 85*q. Let y(b) = 22*b**4 - 127*b**3 + 3*b**2 + 86*b. Let a(o) = 4*w(o) - 5*y(o). Factor a(g).
-3*g*(g - 6)*(g - 1)*(6*g + 5)
Let -1/4*l**2 - 277729 - 527*l = 0. What is l?
-1054
Let c(j) be the third derivative of j**8/84 - 4*j**7/21 - 61*j**6/15 - 124*j**5/5 - 141*j**4/2 - 108*j**3 - 11*j**2 - 143. Determine t, given that c(t) = 0.
-3, -1, 18
Let c = 562 + 48. Let w = 3062/5 - c. Factor -2/5*i**3 - 2*i + w*i**2 + 0.
-2*i*(i - 5)*(i - 1)/5
Let f(w) be the second derivative of w**6/180 - w**5/6 - 37*w**3/6 - w**2 - 11*w - 3. Let n(h) be the second derivative of f(h). Let n(i) = 0. Calculate i.
0, 10
Let n(a) be the third derivative of -7*a**6/150 + 17*a**5/5 - 396*a**4/5 + 648*a**3/5 - 88*a**2. Solve n(h) = 0 for h.
3/7, 18
Suppose 0 = -b + 1 + 2. Suppose -b*h - 19 + 5 = -4*a, 10 = 3*a - 2*h. Factor 3*k**2 + k**2 + 0*k**a - k**2 + 21*k.
3*k*(k + 7)
Let i(j) be the first derivative of 9/4*j**3 + 9/20*j**5 + 12*j**2 - 111/16*j**4 - 9*j - 110 + 5/8*j**6. Determine f, given that i(f) = 0.
-3, -1, 2/5, 1, 2
Let z(o) be the second derivative of -264*o - 3/80*o**5 - 1/40*o**6 - 11/8*o**3 + 0 + 9/16*o**4 + 3/2*o**2. Factor z(a).
-3*(a - 1)**3*(a + 4)/4
Suppose 343*a - 865*a - 571*a + 60*a = -2066. Factor -2/7 + 45/7*d**3 - 45/7*d + 2/7*d**a.
(d - 1)*(d + 1)*(45*d + 2)/7
Let g(d) = d**3 - 3*d**2 - 4*d + 2. Let h(c) = -c**2 - 4*c + 4. Let p be h(-4). Let v be g(p). What is m in -m**3 + 22 - 6*m**4 + m**v - 22 + m**5 + 5*m**4 = 0?
-1, 0, 1
Let w(h) be the second derivative of -154*h + 0 - 672*h**2 - 8*h**3 - 1/28*h**4. Factor w(s).
-3*(s + 56)**2/7
Suppose -55 = 21*u - 18*u + 7*g, g = 3*u - 25. Factor 9*n**3 + 10*n**2 - 1/2*n**u + 7/2*n + 0 + 2*n**4.
-n*(n - 7)*(n + 1)**3/2
Suppose 7*j - 5*j = 60. Suppose -19*t + j = -4*t. Factor -2/19*o**t + 0 - 6/19*o.
-2*o*(o + 3)/19
Let c(q) = -2*q**2 - 18*q - 97. Let p(d) = -5*d**2 - 47*d - 193. Let z(u) = -7*c(u) + 3*p(u). Factor z(i).
-(i - 5)*(i + 20)
Let i = 659/3443 + -3/313. Factor i*n**2 - 10/11*n + 8/11.
2*(n - 4)*(n - 1)/11
Let z(y) = 29*y**3 - 191*y**2 + 4*y + 158. Let s(k) = 8*k**3 - 48*k**2 + k + 39. Let n(l) = -11*s(l) + 3*z(l). Determine a so that n(a) = 0.
-45, -1, 1
Suppose 2*w + 10 = 0, -j + 5 = -w - 2. Factor 91 - 9*t**j + 5*t**3 - 15*t - 9*t**2 - 1 - 2*t**2.
5*(t - 3)**2*(t + 2)
Let x = -1708 + 1704. Let n be (-6)/8 + (-1)/(x/12). Suppose 15/8 + n*k + 3/8*k**2 = 0. What is k?
-5, -1
Suppose 0 = 30*l + 2939 - 2969. Let k(y) = -5 + y**4 + 2 + 2. Let d(g) = 24*g**4 + 20*g**3 - 30*g**2 - 20*g + 6. Let n(z) = l*d(z) + k(z). Factor n(t).
5*(t - 1)*(t + 1)**2*(5*t - 1)
What is i in 146/11*i - 2/11*i**2 + 948/11 = 0?
-6, 79
Let y(b) = 52*b**2 + 8171*b - 8339531. Let q(o) = 138*o**2 + 24512*o - 25018592. Let u(a) = -3*q(a) + 8*y(a). Factor u(n).
2*(n - 2042)**2
Let g(o) be the second derivative of o**4/12 + 3*o**3/2 + 9*o**2 - o + 191. Find x, given that g(x) = 0.
-6, -3
Let o(n) be the second derivative of -n**7/8 + 3*n**6/20 + 21*n**5/80 - 3*n**4/8 + 868*n. Suppose o(f) = 0. Calculate f.
-1, 0, 6/7, 1
Suppose -4*a - 11*t = -12*t - 18, -4*a - 2*t + 24 = 0. Let c(i) be the first derivative of 5*i**2 - 5*i + 0*i**3 + i**a - 9 - 5/2*i**4. Factor c(u).
5*(u - 1)**3*(u + 1)
Let z be (182/35)/(12/(-20) + 1). Let i(s) = s**3 - 14*s**2 + 14*s - 9. Let h be i(z). Factor h*n**2 + 4/3*n**4 + 4/3*n**5 + 0 - 20/3*n**3 + 0*n.
4*n**2*(n - 1)**2*(n + 3)/3
Let m(u) = u**3 - 9*u**2 + 13*u - 9. Let l be m(8). Let a = -26 + l. Suppose -1406 + 7*y**2 - a*y + 1406 + 18*y**2 = 0. What is y?
0, 1/5
Determine s so that 8/5 - 8/15*s - 14/15*s**2 - 2/15*s**3 = 0.
-6, -2, 1
Suppose 74/3 - 109/9*l - 1/9*l**2 = 0. What is l?
-111, 2
Let y(c) be the second derivative of -6*c**2 + 0 + 60*c - 3/5*c**5 + 3/4*c**4 + 2*c**3 + 1/10*c**6. Factor y(g).
3*(g - 2)**2*(g - 1)*(g + 1)
Let r = 49621/9 - 5500. Let v(b) be the second derivative of -1/54*b**4 - 4*b - 22/27*b**3 - r*b**2 + 0. Factor v(l).
-2*(l + 11)**2/9
Let s be 44/(-6) - (4 - 65/15). Let l(d) = d**3 + 5*d**2 - 18*d - 26. Let m be l(s). Determine k so that 9*k**2 - 3*k + 2*k**3 + 3*k**4 - m*k**3 - 9*k**3 = 0.
0, 1
Let s(z) be the second derivative of 0 - 1/48*z**4 + 1/8*z**3 + 170*z + 0*z**2. Factor s(i).
-i*(i - 3)/4
Let w = 171013 + -513037/3. Let -23/3*p**4 - 6*p**2 + 1/3 - w*p - 2*p**5 - 32/3*p**3 = 0. What is p?
-1, 1/6
Determine m so that 76/5*m**2 + 2/5*m**4 - 78/5 + 32/5*m - 32/5*m**3 = 0.
-1, 1, 3, 13
Let g be (-41285)/61389 + 42/54. Factor 0*p**2 - g*p**3 - 24/19 + 26/19*p.
-2*(p - 3)*(p - 1)*(p + 4)/19
Let k = 6261/5 - 1252. Factor -k*x + 1/5*x**3 - 1/10*x**4 + 1/10 + 0*x**2.
-(x - 1)**3*(x + 1)/10
Let a = -19632 - -59494/3. Let t = a + -199. Factor 0 + 0*d - t*d**4 - 2/3*d**3 + 0*d**2.
-d**3*(d + 2)/3
Let d(i) be the third derivative of -i**8/30240 - i**7/7560 + i**6/540 - 29*i**5/15 - 70*i**2. Let m(f) be the third derivative of d(f). Factor m(q).
-2*(q - 1)*(q + 2)/3
Let f = -101 - -115. Let a be 4/(-14) - (-4)/f. Factor a + b - 3*b**2 - 7/4*b**3.
-b*(b + 2)*(7*b - 2)/4
Let z be ((-104)/(-6) - -7) + (-4)/(-6). Determine a so that -25 + 18*a**2 - z*a**2 + 1 + 86*a = 0.
2/7, 12
Find t, given that 756/5*t**3 - 193536/5*t - 3/5*t**4 - 46092/5*t**2 - 196608/5 = 0.
-2, 128
Suppose 39*n**3 + 53*n - 21*n**2 + 112*n - 17*n**2 - 6 - 46*n**2 - 114*n = 0. What is n?
2/13, 1
Let o(b) = -7*b**3 - 15*b**2 - 6*b - 26. Let p(t) = t**3 + t**2 - t - 1. Let r(f) = -o(f) - 6*p(f). Let h be r(-8). Factor 4*z - 1 + z**3 - 3*z**2 - z + h*z**2.
(z - 1)**3
Let d = -371 - -561. Suppose -2*y - 2*m + 74 = -5*m, -5*m = -5*y + d. Factor 3*x**2 - 41*x + y*x - 4*x**2.
-x*(x + 1)
Let r(j) be the first derivative of -j**6/240 - j**5/15 + 5*j**4/12 - 87*j**2/2 + 14. Let p(n) be the second derivative of r(n). Suppose p(v) = 0. Calculate v.
-10, 0, 2
Let m(q) be the first derivative of -7*q**4/18 + 50*q**3/27 + 16*q**2/9 - 32*q/9 + 2179. Factor m(j).
-2*(j - 4)*(j + 1)*(7*j - 4)/9
Let l(t) be the first derivative of t**6/2 - 3*t**5/5 - 3*