. Factor f(r).
-4*r*(r - 1)*(r + 4)*(7*r + 2)
Let l(x) be the first derivative of -x**6/180 + x**5/60 - 7*x**3/3 - 10. Let c(j) be the third derivative of l(j). Suppose c(r) = 0. What is r?
0, 1
Suppose -l + 4*t - 20 = -5*l, -3*t + 19 = 4*l. Factor 8 + 3*r - 11*r + 4*r - 8*r**2 + l*r**2.
-4*(r - 1)*(r + 2)
Let d = -28 + 40. Suppose 4*r + 4 = d. Solve -4*h**2 - 3 + 6*h**r + h**2 = 0.
-1, 1
Suppose 1 = h - 3. Suppose -i - h = -3*i. Find c such that 2*c + 16 - c**3 + c**i - 16 = 0.
-1, 0, 2
Let w = 18 + -20. Let p = w + 6. Let 13*i**4 - 12*i**5 + 2*i**5 - p*i**3 + i**4 = 0. What is i?
0, 2/5, 1
Suppose -2*p + 5*k + 344 = 0, -18*k = -3*p - 13*k + 506. Determine g, given that 147*g**5 + 24/7*g - 276/7*g**2 + p*g**3 + 0 - 273*g**4 = 0.
0, 2/7, 1
Let t(y) = 6*y**3 - 13*y - 76 + 80 + 2*y**3 - 9*y**4. Let h(n) = -28*n**4 + 24*n**3 - 40*n + 12. Let f(w) = 5*h(w) - 16*t(w). Let f(b) = 0. Calculate b.
-1, 1
Let u be 3 - (2 + 25735/(-75)). Let j = u - 344. Let 2/15 - j*z**2 + 0*z = 0. Calculate z.
-1, 1
Let v(f) be the first derivative of 4*f**3/3 - 14*f**2 - 72*f + 123. Factor v(t).
4*(t - 9)*(t + 2)
Let i(a) be the second derivative of 4*a**6/5 + 57*a**5/20 - 9*a**4/2 - 9*a**3/2 - 565*a. Let i(v) = 0. What is v?
-3, -3/8, 0, 1
Factor -8/3*j - 3*j**2 + 0 - 1/3*j**3.
-j*(j + 1)*(j + 8)/3
Let t = 22 - 28. Let r(w) = -2*w**3 - 12*w**2 - 2*w - 10. Let c be r(t). Factor 1/6*d**3 + 1/3*d**c + 5/6*d**5 + 0 + 0*d - 4/3*d**4.
d**2*(d - 1)**2*(5*d + 2)/6
Suppose 0 = j + 12 - 16. Factor 4*v**4 + 5*v**3 - j*v**2 + 8*v + 9*v**5 - 5*v**5 - 17*v**3.
4*v*(v - 1)**2*(v + 1)*(v + 2)
Let -4/3 + 2/3*r**2 - 2/3*r = 0. What is r?
-1, 2
Suppose -102 = -54*k + 20*k. Let c(y) be the first derivative of 0*y + 2*y**k + y**2 + 2/5*y**5 + 5 + 3/2*y**4. Factor c(n).
2*n*(n + 1)**3
Suppose -4*t - s - 33 = 0, -4*t - 5*s - 59 + 6 = 0. Let h be (-4)/(3 + t + 2). Determine g, given that -2*g**2 - 10*g - 13 - 12 - 2*g**h + 3*g**2 = 0.
-5
Let d(t) be the second derivative of 9/20*t**5 + 0*t**2 - 3/2*t**3 - 1/4*t**4 + 0 - 48*t + 1/10*t**6. What is k in d(k) = 0?
-3, -1, 0, 1
Let f be (7 - 4 - 12)/(2 - 1). Let x be ((-18)/15)/(f/(-10)) - -2. Factor -2/3 + 8*o**2 + x*o.
2*(3*o + 1)*(4*o - 1)/3
Suppose 366 - 318 = 12*l. Let v(p) be the third derivative of 1/270*p**5 - 1/18*p**l + 0 + 1/3*p**3 - 4*p**2 + 0*p. Find g such that v(g) = 0.
3
Suppose 30*h + 69 = 43 + 86. Let 1/2*u**3 + 3/2*u**4 + 0 + 1/2*u**5 - u - 3/2*u**h = 0. What is u?
-2, -1, 0, 1
Let p(w) be the second derivative of 2*w**7/21 + 298*w**6/15 + 1095*w**5 - 1875*w**4 - 142*w. Let p(l) = 0. What is l?
-75, 0, 1
Let c(y) be the second derivative of 1/3*y**4 + 6*y**2 - y - 8/3*y**3 + 0. Factor c(z).
4*(z - 3)*(z - 1)
Find u such that 1200*u**2 + 28/3*u**4 + 6912 - 152*u**3 - 4608*u - 2/9*u**5 = 0.
6, 12
Let o be ((-12)/(-95))/(5 - 984/200). Let p = o - 3/38. Find z such that 0 + p*z**2 + 0*z = 0.
0
Let z(m) be the second derivative of -27*m**5/20 - 13*m**4 + 75*m**3/2 - 21*m**2 - 12*m - 4. Factor z(h).
-3*(h - 1)*(h + 7)*(9*h - 2)
Suppose -12*a + 24 = -0*a. Factor -20*m + 5*m**4 - 38*m**2 - 469*m**3 + 40 + 8*m**a + 474*m**3.
5*(m - 2)*(m - 1)*(m + 2)**2
Let l = 1435/106 - 2/53. Let k(z) be the second derivative of l*z**2 + 0 + 4*z + 3*z**3 + 1/4*z**4. Determine m so that k(m) = 0.
-3
Let a be (-1)/(-4 - 15/(-4)). Factor -4*n + 0*n**5 + 5*n**4 - n**4 - 8*n**2 + 4*n**5 + a*n**4.
4*n*(n - 1)*(n + 1)**3
Let y = -76 + 78. Factor -8*p + 9*p**2 - 2*p**4 - 10*p**2 - 12*p**3 - 17*p**y.
-2*p*(p + 1)**2*(p + 4)
Determine f, given that 78/7 - 6/7*f**3 - 87/7*f**2 - 111/7*f = 0.
-13, -2, 1/2
Let -224*s - 2/7*s**3 + 0 + 16*s**2 = 0. What is s?
0, 28
Let r(i) = -2*i**4 - 2*i**3 + 25*i**2. Suppose d = -5*t - 22, 3*d + 0*d - 5*t = -6. Let n(u) = -u**4 - u**3 + 8*u**2. Let s(j) = d*n(j) + 2*r(j). Factor s(a).
3*a**2*(a - 1)*(a + 2)
Let f(c) = c - 8. Let u(y) = -3*y + 25. Let i(z) = 17*f(z) + 6*u(z). Let w be i(11). Solve -n**2 + 3*n - 5*n**3 + 0 + 1 + w*n**3 - n**3 = 0.
-1, -1/3, 1
Let u(v) = -12*v**5 - 4*v**4 + 4*v**3 + 48*v**2 + 18*v - 14. Let d(k) = -k**5 + k**4 + k**3 + k**2 + k + 1. Let x(w) = 20*d(w) - 2*u(w). What is j in x(j) = 0?
-6, -2, -1, 1
Let a(x) be the third derivative of 5/48*x**8 - 3/8*x**6 + 5/42*x**7 + 0*x + 5/12*x**4 - 5/12*x**5 + 0 - 20*x**2 + 0*x**3. Find y such that a(y) = 0.
-1, 0, 2/7, 1
Let s = 202 - 418. Let k be -3 - s/52 - 1. Suppose 2/13*b**3 - 2/13*b**2 - k*b + 2/13 = 0. Calculate b.
-1, 1
Let g be (-76)/(-364)*(7 + -8). Let w = 1/13 - g. Factor -w*s**2 - 2/7 + 4/7*s.
-2*(s - 1)**2/7
Let w(x) = 3*x**3 + 94*x**2 + 964*x + 1536. Let f(l) = 12*l**3 + 378*l**2 + 3855*l + 6144. Let g(a) = -4*f(a) + 15*w(a). Find v, given that g(v) = 0.
-16, -2
Solve -2/11*b**2 + 2/11 - 2/11*b**3 + 2/11*b = 0 for b.
-1, 1
Let x(y) be the third derivative of y**7/1764 - y**6/360 + y**5/210 - 17*y**4/24 + 10*y**2. Let t(i) be the second derivative of x(i). Factor t(l).
2*(l - 1)*(5*l - 2)/7
Factor -126*w**2 - 2704 + 22*w - 230*w + 122*w**2.
-4*(w + 26)**2
Let x(r) be the first derivative of -2*r**2 - 14 + 1/2*r**4 + 2/3*r**3 + 0*r. Factor x(a).
2*a*(a - 1)*(a + 2)
Let d = 2/5397 - 692617/5397. Let t = 129 + d. Factor 0 - t*y**4 + 2/3*y**2 - 4/3*y + 4/3*y**3.
-2*y*(y - 2)*(y - 1)*(y + 1)/3
Let w(u) be the third derivative of u**8/1008 - u**7/630 - u**6/60 + u**2 + 115*u. Factor w(p).
p**3*(p - 3)*(p + 2)/3
Let o(q) be the first derivative of -6 + 0*q + 2/3*q**2 - 2/9*q**3. Factor o(k).
-2*k*(k - 2)/3
Suppose -3*q = 3*p - 27, -3*p + 5*q - 11 - 2 = 0. Suppose 9*h - h - 128 = 0. What is i in 12*i - 20*i - p*i**4 - 15*i**2 + h + i**4 + 2*i**4 + 8*i**3 = 0?
-1, 1, 4
Solve -1880*h**2 + 1740*h**3 - 392*h**2 - 36*h**4 + 210*h + 542*h = 0 for h.
0, 2/3, 47
Suppose 12 = 2*j - 10. Let z be (-6)/9 + j/3. Factor -3*m**2 + 6*m**3 - 5*m + 5*m - 6*m**4 + z*m**4.
-3*m**2*(m - 1)**2
Let w = -13191/4 - -3274. Let u = w + 101/4. Factor -1/2*k**3 - u*k**2 - k + 0.
-k*(k + 1)*(k + 2)/2
Suppose 4*i - 3*i - 8 = 0. Suppose -12*l = -i*l - 12. What is j in l*j**2 + 2*j - 6*j**2 + j = 0?
0, 1
Find n, given that 46*n**2 - 20*n**3 - 108*n - 2*n**4 + 80*n + 5*n**4 - n**4 = 0.
0, 1, 2, 7
Let c = 11 - 15. Let p be 12/3 - (c - -4). Factor -x**3 + 0*x**4 + 3*x**p + 0*x**2 + 3*x**5 - 2*x**3 - 3*x**2.
3*x**2*(x - 1)*(x + 1)**2
What is q in -1/4*q**3 - 7/4*q**2 - 2 - 7/2*q = 0?
-4, -2, -1
Let h(x) be the first derivative of -x**4/3 + 8*x**3/3 - 6*x**2 - 17*x - 13. Let p(z) be the first derivative of h(z). Suppose p(g) = 0. What is g?
1, 3
Suppose 8 = -12*n + 16*n. Determine b, given that -7*b**2 - 2*b**3 - b**3 + 9*b + b**n = 0.
-3, 0, 1
Suppose 46*s = 56*s. Let k(y) be the third derivative of 0 + 0*y + 0*y**3 - 1/330*y**6 - 1/1155*y**7 + s*y**4 - 1/330*y**5 + 5*y**2. Solve k(w) = 0.
-1, 0
Determine h so that 0 + 20/7*h + 4/7*h**2 = 0.
-5, 0
Suppose 9*j - 13*j - z + 15 = 0, 3*j - z - 6 = 0. Let v(a) be the first derivative of 0*a + 9/2*a**2 - 4*a**3 + 3/4*a**4 + j. Factor v(t).
3*t*(t - 3)*(t - 1)
Let r(f) = 3*f - 13. Let x be r(5). Factor -20*q**2 - 13*q**2 + q**3 - 15*q**3 - 22*q - 4 + q**x.
-2*(q + 1)**2*(7*q + 2)
Let j(k) = 4*k**2 - 150*k + 179. Let x(s) = -s**2 + 30*s - 35. Let h(c) = -2*j(c) - 11*x(c). Find f such that h(f) = 0.
1, 9
Let i(c) = -c**3 + 7*c**2 + 6. Let u be i(7). Let w(k) = -k**2 + 6*k + 3. Let n be w(u). Let o**2 + n*o - o + 5*o - 5*o = 0. What is o?
-2, 0
Let y(a) be the third derivative of -25*a**8/588 - 62*a**7/147 - 37*a**6/30 - 11*a**5/7 - 6*a**4/7 - 78*a**2 - 1. Suppose y(r) = 0. What is r?
-4, -1, -3/5, 0
Suppose 5*z + 44 = 3*h - 21, 0 = -3*h - 3*z + 57. Let x be (-8 + 148/h)/(18/(-20)). Factor 6 + x*q**2 + 4*q.
2*(q + 3)**2/3
Let p(c) be the first derivative of -25*c**6/24 + 95*c**5/12 - 40*c**4/3 + 10*c**3 - 6*c**2 + 9. Let i(s) be the second derivative of p(s). Factor i(v).
-5*(v - 3)*(5*v - 2)**2
Suppose 23/4*k**3 - 5/4*k**4 - 9/2 - 51/4*k - 5/4*k**2 = 0. Calculate k.
-1, -2/5, 3
Let h(g) be the first derivative of g**4/2 + 40*g**3/3 - 67*g**2 + 92*g - 41. Suppose h(t) = 0. Calculate t.
-23, 1, 2
Let q(u) be the first derivative of u**5 - 25*u**4/2 - 115*u**3/3 + 600*u**2 + 2880*u + 249. Factor q(v).
5*(v - 8)**2*(v + 3)**2
Let l(p) = -p**2 + 19*p + 47. Let w be l(21). Suppose -33*o**2 + 9 - 2*o**w + 4*o**4 + o**3 + 7 + 13*o**2 - 8*o + 9*o**3 = 0