c(i) = -9*i**2 + 20*i - 11. Let z(d) = -17*d**2 + 19*d - 19*d - 23 + 21*d + 19*d. Let v(h) = 7*c(h) - 4*z(h). Factor v(x).
5*(x - 3)*(x - 1)
Let w(n) be the first derivative of 9/5*n**5 - 4*n**3 + 0*n**4 - 16 + 1/2*n**6 + 0*n**2 + 0*n. Determine j so that w(j) = 0.
-2, 0, 1
Determine j, given that -440*j + 15/2*j**5 + 865/2*j**3 + 235/2*j**4 - 555/2*j**2 + 160 = 0.
-8, -1, 1/3, 1
Factor -17 - 21*n**3 - 3*n**4 + 24*n**2 + 0*n**2 + 17.
-3*n**2*(n - 1)*(n + 8)
Let f(r) be the second derivative of -r**6/15 + 17*r**5/30 - 7*r**4/18 - 17*r**3/9 + 10*r**2/3 - 31*r. Determine w so that f(w) = 0.
-1, 2/3, 1, 5
Let t(a) be the third derivative of a**8/6720 - a**7/840 + a**6/360 - 23*a**4/24 - 19*a**2. Let p(w) be the second derivative of t(w). Solve p(l) = 0 for l.
0, 1, 2
Let f(u) be the third derivative of u**8/168 - u**7/35 - u**6/12 + u**5/10 + u**4/3 + 4*u**2 + 3. Factor f(d).
2*d*(d - 4)*(d - 1)*(d + 1)**2
Let j = -43/110 + 827/990. Factor 1/9*q**5 + 1/9*q**3 - 10/9*q**2 - j*q + 8/9 + 4/9*q**4.
(q - 1)**2*(q + 2)**3/9
Let z(p) = -9*p**4 - 28*p**3 + 59*p**2 - 158*p + 32. Let l(h) = 4*h**4 + 14*h**3 - 30*h**2 + 76*h - 16. Let u(w) = -13*l(w) - 6*z(w). Let u(r) = 0. What is r?
1, 2
Let w(u) be the second derivative of -u**5/20 + u**4/2 - 7*u**3/6 - u**2 + 6*u. Let m be w(4). Factor 3*k**2 - k**2 - k**m - k.
k*(k - 1)
Let o(g) be the third derivative of -g**5/60 + 13*g**4/3 + g**2 - g. Factor o(p).
-p*(p - 104)
Factor 586*c**3 + 20*c**2 + 18*c + 140*c + 832 + 194*c - 590*c**3.
-4*(c - 13)*(c + 4)**2
Solve -3 - 6*l + 2*l - 89*l**2 + 88*l**2 = 0 for l.
-3, -1
Factor -25*j**2 - 231*j**3 - 10*j + 5*j**5 + 5*j**4 + 106*j**3 + 110*j**3.
5*j*(j - 2)*(j + 1)**3
Let y = 44 - 42. Factor 2*d**3 + 8*d**y + 128 - 128.
2*d**2*(d + 4)
Let u(k) = 30*k**3 + 12*k**2 + 18*k - 32. Let i(t) = 7*t**3 - t**2 + 1. Let j(l) = 4*i(l) - u(l). Factor j(o).
-2*(o - 1)*(o + 3)*(o + 6)
Let g(k) be the first derivative of k**4/2 + 16*k**3 + 144*k**2 + 107. Factor g(v).
2*v*(v + 12)**2
Let o(q) be the first derivative of q**3/6 - 9*q**2/4 + 206. Factor o(i).
i*(i - 9)/2
Let j(r) be the first derivative of -5*r**6/24 + r**5/12 - 9*r**2/2 + 15. Let c(i) be the second derivative of j(i). Factor c(l).
-5*l**2*(5*l - 1)
Suppose 5*a = -0*a. Suppose -2 = -m - a*m. Factor -3*x**2 + 1 - 2 + 10 - 8*x + m*x.
-3*(x - 1)*(x + 3)
Suppose -4*u + 60 = 5*z, -3*u + 14 + 3 = 2*z. Determine w, given that -8*w**3 - 3*w + 14*w - 4*w**5 + 16*w**4 + w - z*w**2 = 0.
-1, 0, 1, 3
Factor 1500*p - 12500/3 - 135*p**2.
-5*(9*p - 50)**2/3
Let v be (-1)/((-106)/(-105) + -1). Let d = -419/4 - v. Determine h so that 0 + 1/8*h**3 + 1/8*h + d*h**2 = 0.
-1, 0
Let q(y) = y**3 + 45*y**2 - 46*y - 19. Let l(s) = 9*s**2 - 9*s - 4. Let t(h) = -33*l(h) + 6*q(h). Factor t(z).
3*(z - 3)*(z - 2)*(2*z + 1)
Let u be (-1 + 4)*5/5. Let d(k) = -k**3 + 5*k**2 - 4*k + 6. Let y be d(u). What is p in 12*p**3 + 6*p**5 - 2*p**2 - y*p**4 - 2*p**5 - 3*p**2 + p**2 = 0?
0, 1
Suppose n - 3*d = 8, 4*n + 5*d - 5 = 2*n. Let l = n - 3. Determine q, given that -2/9*q**l + 0 + 2/9*q = 0.
0, 1
Let d(n) = -5*n**3 + n**2 - n - 1. Let z be d(-1). Let r be 2/z - 28/12 - -4. Factor -4/7*p**3 + 0 - 2/7*p**4 + 2/7*p**r + 4/7*p.
-2*p*(p - 1)*(p + 1)*(p + 2)/7
Factor 5/3*r + 2 + 1/3*r**2.
(r + 2)*(r + 3)/3
Let h = 6648/7 + -952. Let o = h + 76/21. Find v such that 0 + 0*v + o*v**3 + 2/3*v**4 + 0*v**2 = 0.
-2, 0
Let z = 60 + -58. Factor -4*u**3 - 4*u**2 - 4*u**z + 0*u**2 + 12*u.
-4*u*(u - 1)*(u + 3)
Let w(g) be the third derivative of g**6/60 - 7*g**5/30 + 11*g**4/12 - 5*g**3/3 + 164*g**2. Factor w(h).
2*(h - 5)*(h - 1)**2
Let w = 8858/35 - 253. Let b(o) be the first derivative of -3/14*o**2 + 0*o + 5 + 3/28*o**4 + 1/7*o**3 - w*o**5. Factor b(d).
-3*d*(d - 1)**2*(d + 1)/7
Factor 970*w**4 + 841*w**2 - 3332*w**3 + 1679*w**2 + 420*w - 1108*w - 284*w**4 + 64.
2*(w - 4)*(7*w - 2)**3
Solve o**2 + 3*o + 0 + 1/4*o**4 - 7/4*o**3 = 0.
-1, 0, 2, 6
Let z(b) = 10*b**2 + 615*b + 9005. Let n(l) = -15*l**2 - 924*l - 13508. Let c(a) = 5*n(a) + 8*z(a). Factor c(u).
5*(u + 30)**2
Let x(y) be the first derivative of y**6/24 + 3*y**5/10 - 9*y**4/16 - 7*y**3/6 + 41. Find m such that x(m) = 0.
-7, -1, 0, 2
Let n = 29 + -49. Let h = 22 + n. Find q, given that 1/4 + 1/4*q - 1/4*q**3 - 1/4*q**h = 0.
-1, 1
Factor 2/7*j**5 + 0*j**2 + 2/7*j**3 + 0*j + 0 + 4/7*j**4.
2*j**3*(j + 1)**2/7
Let i(q) be the first derivative of 1/6*q**2 + 2/9*q**3 - 4 + 0*q + 1/12*q**4. Factor i(z).
z*(z + 1)**2/3
Let k(o) = o**4 + 7*o**3 - 13*o**2 + 5. Let v(y) = -y**3 + y**2 - 1. Let g(b) = -4*k(b) - 20*v(b). Factor g(t).
-4*t**2*(t - 2)*(t + 4)
Suppose 13*g - 4 = -95. Let v(p) = -17*p**3 - 13*p**2 + 7*p. Let f(m) = 8*m**3 + 7*m**2 - 3*m. Let u(r) = g*f(r) - 3*v(r). Factor u(x).
-5*x**2*(x + 2)
Let m = -3209534/13 + 247092. Factor -2/13*h**5 - 4180/13*h**2 - 860/13*h**3 - 70/13*h**4 - 6050/13*h - m.
-2*(h + 1)**2*(h + 11)**3/13
Let y(j) be the third derivative of j**7/1155 + j**6/110 - 17*j**5/330 - j**4/22 + 16*j**3/33 - 71*j**2. Determine x so that y(x) = 0.
-8, -1, 1, 2
Suppose 3*z = -4*f, f - 19 = 8*z - 4*z. Determine u so that -9*u + 61*u + 7*u**2 + 13*u**2 + 8 - 37*u**f + 13*u**3 = 0.
-1, -1/6, 2
Suppose p + 4*p - 3*j = 24, 4*p - 27 = 5*j. Let z be (-70)/(-22) + 14/(-77). Determine l so that 8*l**p - 4*l**z - 8*l**3 + 4*l + 8 - 8*l**2 = 0.
-2, -1, 1
Let c be -1 - (-33 + -4) - 1. Factor -c*m + 0*m + 80*m**3 + 0*m + 14*m**2 + 26*m**2 + 5.
5*(m + 1)*(4*m - 1)**2
Let j(q) be the first derivative of 4*q**5 + 5*q**4/4 - 20*q**3 - 55*q**2/2 - 10*q - 93. Factor j(m).
5*(m - 2)*(m + 1)**2*(4*m + 1)
Let g(m) be the third derivative of 0 - 3*m**2 - 5/84*m**4 + 0*m - 1/7*m**3 + 4/105*m**5. Suppose g(n) = 0. Calculate n.
-3/8, 1
Let w = -979 - -979. Let q(p) be the second derivative of -3/10*p**5 - 1/4*p**4 + 0*p**3 + w*p**2 - 13*p - 1/10*p**6 + 0. Factor q(j).
-3*j**2*(j + 1)**2
Factor -2/3*d**3 + 16/3*d - 2/3*d**2 + 8.
-2*(d - 3)*(d + 2)**2/3
Let o(w) = -w**2 - 3*w + 14. Let u be o(-6). Let y be -3*(12/3)/u. Factor -2 - x + 2 - 2*x**y - 6*x**2 - 3*x.
-2*x*(x + 1)*(x + 2)
Let l(a) be the third derivative of -a**7/280 - a**6/30 - a**5/8 - a**4/4 + 4*a**3 - 8*a**2. Let j(v) be the first derivative of l(v). Factor j(t).
-3*(t + 1)**2*(t + 2)
Suppose 2*h + 5 = h - 3*c, -4*c = h + 9. Suppose -h = -2*u - 5. Let 1/2*w**2 - 1/2*w - u = 0. What is w?
-1, 2
Let o(p) = 3*p + 48. Let y be o(-15). Let -20 + 6*i + y*i + 4*i**2 + 9*i - 2*i = 0. What is i?
-5, 1
Determine d, given that -4/3*d**3 - 2/3*d**2 + 0 - 2/3*d**4 + 0*d = 0.
-1, 0
Suppose 9*d - 1 - 26 = 0. Factor d*o**3 - 7*o**3 + 5*o**5 + 4*o**2 - 2 - o**5 - 2*o**4 - 2*o**5 + 2*o.
2*(o - 1)**3*(o + 1)**2
Let n be 15 + -9 + -7 - 4/(-3). Solve 1/3 - n*y**2 + 0*y = 0.
-1, 1
Let h(u) = -u**3 - 12*u**2 - 7*u + 47. Let x be h(-11). Let l(o) be the first derivative of -5 + 0*o + o**2 + 1/3*o**x. Factor l(v).
v*(v + 2)
Suppose 5*v + 16 = 9*v. Let a be ((-88)/2002)/(v/(-14)). Suppose -2/13*x**3 + 0 + a*x**2 + 0*x = 0. Calculate x.
0, 1
Let y = -66 - -4. Let q = -59 - y. Find d such that 0 + 0*d + 0*d**2 + 0*d**q + 2/7*d**4 - 2/7*d**5 = 0.
0, 1
Let g = 287/2400 - 11/96. Let j(a) be the third derivative of 0 + 3/10*a**3 + 0*a - a**2 + 1/100*a**5 + g*a**6 - 1/8*a**4. What is n in j(n) = 0?
-3, 1
Let r(y) = y**2 + 9*y - 7. Let c be r(-10). Suppose -b + 28 = c*b. Factor -4*n**4 + 2 - 10*n**3 + 0*n + 5*n - 13*n**2 - 3*n + b*n**2.
-2*(n + 1)**3*(2*n - 1)
Let w(y) = -12*y**3 + 125*y + 332 - 62 - 185*y**2 + 42*y**3. Let c(m) = 5*m**3 - 31*m**2 + 21*m + 45. Let h(j) = 35*c(j) - 6*w(j). Factor h(z).
-5*(z - 3)**2*(z + 1)
Let r be 15/6*(-12)/(-15). Suppose 5*s - 2 = -5*k + 13, r*k = s. Find l, given that -16*l + 5 + 1 + s - 10*l**2 = 0.
-2, 2/5
Let z(a) be the first derivative of 4/3*a**3 + 8 + 4*a - 4*a**2. Factor z(n).
4*(n - 1)**2
Let h(w) be the third derivative of w**7/350 + w**6/50 + w**5/50 - w**4/10 - 3*w**3/10 - 111*w**2. Factor h(n).
3*(n - 1)*(n + 1)**2*(n + 3)/5
What is w in 3*w**5 + 6*w**2 + 0*w**2 + 10*w**3 + 2*w**4 - 2*w**5 - 3*w**5 = 0?
-1, 0, 3
Let b(r) = 5*r**3 - 7*r**2 + 2*r + 7. Let v(c) = -2*c**3 + 3*c**2 - c - 3. Let f be (-28)/(1 + (-1 - -2)). Let l(p) = f*v(p) - 6*b(p). Factor l(u).
-2*u*(u - 1)*(u + 1)
Find s, given that -8/7*s**3 - 8/7 + 20/7*s**2 - 4/7*s = 0.
-1/2, 1