 8*f**2 + 20*f - 12. Let d(h) = 9*h**2 + 24*h - 13. Let w(c) = a*d(c) + 7*t(c). Find x such that w(x) = 0.
-1, 3
Let y be 1134/234 - (0 + (-6)/39). What is w in 4*w - 3*w**2 + 176*w**3 + 3*w**4 - y*w**2 - 175*w**3 = 0?
-2, 0, 2/3, 1
Suppose 22 + 282 = -19*l. Let g be 7/10 + (-8)/l + 0. Suppose -2/5*f**2 - 2*f - g + 2/5*f**3 = 0. What is f?
-1, 3
Let h(o) be the second derivative of -o**6/75 + 11*o**5/50 + 2*o**4/5 - 1468*o. Factor h(g).
-2*g**2*(g - 12)*(g + 1)/5
Let g(c) be the first derivative of -c**4/4 - 3*c**3 - 13*c**2 - 24*c - 3035. Let g(d) = 0. What is d?
-4, -3, -2
Let i(d) be the third derivative of -d**5/30 + 7*d**4/24 - d**3/3 - 11*d**2. Let u be i(3). Factor 803*j + 2*j**4 + 3 - 4*j**2 - u - 803*j.
2*(j - 1)**2*(j + 1)**2
What is k in 159/7*k**2 - 1008 + 3/7*k**3 + 264*k = 0?
-28, 3
Let n = 35917/18 - 17957/9. Find z such that 4/3*z + n*z**3 + 8/3 - 7/6*z**2 = 0.
-1, 4
Let c(i) be the first derivative of -10*i**3/33 + 263*i**2/11 - 312*i/11 - 12099. Factor c(b).
-2*(b - 52)*(5*b - 3)/11
Let w be -1 - (-6 - 1 - -3*284/144). Let h(i) be the second derivative of 3/20*i**5 - 1/30*i**6 + 8*i - 1/3*i**3 + 0*i**2 + 0 + w*i**4 - 1/42*i**7. Factor h(s).
-s*(s - 1)**2*(s + 1)*(s + 2)
Let s(q) be the first derivative of -13*q + 1/6*q**3 - 1/12*q**4 - 4 + 0*q**2. Let w(c) be the first derivative of s(c). Factor w(x).
-x*(x - 1)
Let a(h) be the second derivative of -5*h**4/12 - 595*h**3/6 - 295*h**2 + 2*h - 260. Factor a(q).
-5*(q + 1)*(q + 118)
Let s = -554 - -563. Let c be s - (378/(-6))/(-7). Let 0 + 4/7*z**3 - 4/7*z**5 + 0*z + 0*z**4 + c*z**2 = 0. What is z?
-1, 0, 1
Let a(v) = 9*v**3 + 2*v**2 - 4*v - 24. Let r(n) = -25*n**3 - 7*n**2 + 12*n + 72. Let i(b) = -33*a(b) - 12*r(b). Factor i(q).
3*(q - 2)*(q + 2)*(q + 6)
Let t = 974 - 992. Let b be t/(-45)*(5 - (-75)/18). Determine j, given that b*j - 1/6*j**2 - 121/6 = 0.
11
Suppose 500*g - 8 = 495*g - 4*t, -4 = -4*g - 4*t. Solve 45/4*f**2 + 3/4*f**g - 21/4*f**3 - 27/4*f + 0 = 0.
0, 1, 3
Let w = 112450 - 40376. Factor -w*d + 4*d**3 + 71862*d - 282*d**2 + 74*d**2.
4*d*(d - 53)*(d + 1)
Let p = -46 - -22. Let t = 35 + p. Suppose -4*o**5 + 5*o**3 - t*o**3 + 10*o**3 = 0. What is o?
-1, 0, 1
Let v(r) be the third derivative of 7*r**5/30 + 5*r**4/12 - r**3/3 + 163*r**2. Let y(o) = o**2 + o - 2. Let f(k) = -3*v(k) - 3*y(k). Factor f(l).
-3*(l + 1)*(15*l - 4)
Let f = -853255 + 853257. Let 1/7*j**f + 0 + 59/7*j = 0. What is j?
-59, 0
Let j(i) be the first derivative of -25*i**6/48 - 13*i**5/8 - 23*i**4/16 + i**3/12 + 7*i**2/16 - i/8 + 179. Factor j(d).
-(d + 1)**3*(5*d - 1)**2/8
Suppose 0 = -u - f - 3, u - f = -2*u + 11. Factor 508*a - 59*a**2 + u*a**3 - 16*a**2 + 19*a**2 - 116*a.
2*a*(a - 14)**2
Let j(h) be the first derivative of -h**5/10 + 87*h**4/8 - 1006*h**3/3 + 1239*h**2 + 3528*h - 1723. Determine r, given that j(r) = 0.
-1, 4, 42
Let b(o) be the second derivative of o**6/15 - 37*o**5/5 + 336*o**4 - 24064*o**3/3 + 106496*o**2 + 2748*o. Factor b(a).
2*(a - 26)*(a - 16)**3
Suppose 60 = -4*k + 5*p, 5*p - 2*p = -12. Let t be k - -24 - (1 - 0). Factor 566 - 566 + 3*m**t - 3*m.
3*m*(m - 1)*(m + 1)
Let a = 1396473 + -1396465. Solve 0 + 56*h + 2/7*h**3 - a*h**2 = 0.
0, 14
Let x(k) be the third derivative of k**5/30 + 5*k**4/3 + 2*k**2 - 45*k. Factor x(l).
2*l*(l + 20)
What is w in 1032/5*w**2 + 4/5*w**4 - 1376/5 + 356/5*w**3 - 16/5*w = 0?
-86, -2, 1
Solve 8/3 - 47/6*p + 1/3*p**3 + 29/6*p**2 = 0 for p.
-16, 1/2, 1
Let u = 2/2626795 + 5253572/23641155. Suppose 2*i = -3*i. Factor i*t - u*t**2 + 8/9.
-2*(t - 2)*(t + 2)/9
Suppose 47 = -4*f - 5*y + 52, 2*f - 4*y + 4 = 0. Suppose -5*h = -f*h. Factor -1/6*d**5 - 1/3*d**4 - 1/6*d**3 + h + 0*d**2 + 0*d.
-d**3*(d + 1)**2/6
Let r(d) be the first derivative of 2*d**6/3 - 4*d**5/5 - 5*d**4 + 4*d**3/3 + 16*d**2 + 16*d - 529. Let r(u) = 0. What is u?
-1, 2
Let q = 2/14825 + 14817/59300. Factor 3*h**2 - 2*h - 3/2*h**3 + 0 + q*h**4.
h*(h - 2)**3/4
Let j be 8/(-12) + 22/24. Let u be (-228)/152 - -5*5/((-50)/(-4)). Factor -u*c**3 + 0 + 1/4*c**2 + j*c**4 + 0*c.
c**2*(c - 1)**2/4
Let z be 2*-5*(28 - 13769/490) + 2 + 0. Factor -3/2*v**2 + 6 - 2*v + 1/2*v**z.
(v - 3)*(v - 2)*(v + 2)/2
Let n(r) = -4*r**2 - 47*r - 93. Let v(o) = 6*o**2 + 48*o + 92. Let w(b) = -4*n(b) - 3*v(b). Find h such that w(h) = 0.
-2, 24
Let q(t) be the first derivative of -5*t**4 + 6325*t**3/3 + 2380*t**2 - 1585*t - 1780. Factor q(k).
-5*(k - 317)*(k + 1)*(4*k - 1)
Let s be (-4534)/(-10) - 30/(-50). Find p, given that -4*p**2 + 194*p - s*p - 144 + 212*p = 0.
-6
Let v = 237836 - 237836. Factor 1/5*f**5 + 0*f + 0*f**3 + 3/5*f**4 + v - 4/5*f**2.
f**2*(f - 1)*(f + 2)**2/5
Suppose -45 = 6*k + 3. Let h be k/(-12) + (-20)/(-6). Solve 4*i - 87*i**h + 21*i**4 + 26*i**2 + 42*i**4 + 34*i**3 = 0 for i.
-1/3, -1/4, 0, 2
Let z(k) be the first derivative of -3*k**5/40 - 27*k**4/16 + 45*k**3/8 + 141*k**2/8 - 45*k - 855. Find o, given that z(o) = 0.
-20, -2, 1, 3
Find q, given that -2312 - 2/9*q**2 - 136/3*q = 0.
-102
Let o be (162/4)/(-3)*(-2160)/324. Let g be (8 + (-700)/o)*2/2. Let 32/9 - 16/9*n + g*n**2 = 0. What is n?
4
Solve 2638/3*c**2 - 1176 - 210*c**3 - 112*c - 26*c**4 - 2/3*c**5 = 0.
-21, -1, 2
Suppose -4*w - 1 + 21 = 0. Suppose 4 = w*s - 3*y, 5*s - 16 = -6*y + 3*y. Suppose 0 - 2 + 2*i**s - 4*i - 4*i + 8 = 0. What is i?
1, 3
Let f(l) be the third derivative of -l**7/189 + 11*l**6/135 - 7*l**5/90 - 43*l**4/54 - 16*l**3/27 - 2172*l**2. Let f(q) = 0. Calculate q.
-1, -1/5, 2, 8
Let c(x) be the first derivative of x**5/4 + 5*x**4/4 + 25*x**3/12 + 5*x**2/4 + 931. Factor c(a).
5*a*(a + 1)**2*(a + 2)/4
Let t(m) = m**2 - 25*m + 70. Let h be (-1)/2 - (2058/28)/(-21). Let i be t(h). Solve -68/7*y**i + 0 + 0*y + 8/7*y**2 - 8*y**5 - 4/7*y**3 = 0.
-1, -1/2, 0, 2/7
Let d(u) = -u**3 + 2 - 6*u**3 - 6 + 19*u**2 - 16*u. Let g(j) = -j**3. Let r(l) = -146*l + 439. Let y be r(3). Let s(i) = y*d(i) - 2*g(i). Factor s(c).
-(c - 2)**2*(5*c + 1)
Let s(v) be the first derivative of -v**3 - 6*v**2 + 2016*v + 661. Determine k, given that s(k) = 0.
-28, 24
Let c be (-14 + (-1431)/(-108))*(174/(-126) - -1). What is d in 0*d + 72/7 - c*d**2 = 0?
-6, 6
Let o(i) be the third derivative of 1/588*i**8 + 0*i - 1/21*i**4 - 1/70*i**6 + 2/735*i**7 - 1/21*i**5 + 0 + 0*i**3 - 14*i**2. Factor o(j).
4*j*(j - 2)*(j + 1)**3/7
Let j(n) = n**2 + 23*n + 42. Let c be j(-21). Suppose 45*l - 36*l - 180 = c. Factor 28/3*o**3 - 16/3 - l*o**2 - 4/3*o**4 + 52/3*o.
-4*(o - 4)*(o - 1)**3/3
Let l(u) be the second derivative of u**8/2184 + 2*u**7/1365 - u**6/260 - 13*u**2 + 19*u. Let z(y) be the first derivative of l(y). Factor z(f).
2*f**3*(f - 1)*(f + 3)/13
Factor -72 - 244/7*k + 4/7*k**2.
4*(k - 63)*(k + 2)/7
Let p(r) be the first derivative of -2/3*r**3 + 0*r**2 + 14 - 1/6*r**4 + 8/3*r. Suppose p(k) = 0. Calculate k.
-2, 1
Factor -5/2*x**3 - 66 - 148*x + 83/2*x**2.
-(x - 11)*(x - 6)*(5*x + 2)/2
Suppose 0 = 7*u - 77 + 42. Determine s so that 243*s**u + 527 + 11280*s + 18916*s**3 - 9190*s**3 + 25560*s**2 + 7552*s**4 + 2573*s**4 + 16194*s**3 + 1345 = 0.
-39, -2/3
Let t(s) be the second derivative of -5*s**7/42 + 2*s**6/5 + 9*s**5/5 - 53*s**4/6 + 27*s**3/2 - 9*s**2 - 894*s. Determine g so that t(g) = 0.
-3, 2/5, 1, 3
Let k = 1294 + -6467/5. Let x(f) be the first derivative of 11 + 3/2*f**2 + k*f**3 + 1/20*f**4 - 5*f. Factor x(y).
(y - 1)*(y + 5)**2/5
Suppose 130*v - 4 = 129*v, 0 = -4*t - v + 4. Let n(c) be the second derivative of t*c**3 + 0 + 0*c**2 - 1/24*c**4 - 1/16*c**5 - 3*c - 1/60*c**6. Factor n(z).
-z**2*(z + 2)*(2*z + 1)/4
Let q(o) be the third derivative of 5*o + 30*o**3 + 0 - 11/12*o**5 + 1/42*o**7 + 4*o**2 + 1/12*o**6 - 5/2*o**4. What is t in q(t) = 0?
-3, 2
Let s(a) be the second derivative of 1/180*a**6 + 5/36*a**4 + 4/45*a**5 + 2*a + 0*a**2 - 1/6*a**3 + 0. Let c(g) be the second derivative of s(g). Factor c(w).
2*(w + 5)*(3*w + 1)/3
Determine i, given that 144/7 + 228/7*i - 6/7*i**4 + 18/7*i**2 - 72/7*i**3 = 0.
-12, -1, 2
Factor 114 - 20*n + 83*n + 4452*n**2 - 4449*n**2.
3*(n + 2)*(n + 19)
Let l(a) be the first derivative of 4*a**3/3 - 144*a**2 - 4234. Factor l(v).
4*v*(v - 72)
Let o(l) = 2*l**2 - 4*l + 2. Suppose 26 = 2*w + 2*z, -8 = 3*z + z. Let g(k) = 5 + 1 - w*k - 2 + 4 + 7*k**2. Let n(p) = 6*g(p) - 22*o(p). Factor n(x).
-2*(x - 1)*(x + 2)
Let l(y)