89.
2*(r - 2)*(r - 1)
Suppose -45*l = 11*l. Let f(a) be the second derivative of -1/6*a**4 + 0 + l*a**2 - 8*a + 0*a**3 - 1/20*a**5. Suppose f(r) = 0. What is r?
-2, 0
Let s(y) be the first derivative of 2*y**3/15 - 126*y**2/5 + 7938*y/5 + 224. Factor s(u).
2*(u - 63)**2/5
Factor -3448*n**2 - 19 - 5*n + 5*n**3 + 3473*n**2 - 6.
5*(n - 1)*(n + 1)*(n + 5)
Let g(o) be the first derivative of o**5/5 + o**4/4 + o**3/3 + o - 16. Let s(v) = 12*v**4 + 6*v**3 + 8*v**2 + 4*v + 10. Let n(f) = 10*g(f) - s(f). Factor n(a).
-2*a*(a - 2)*(a - 1)*(a + 1)
Suppose -4 = -3*j + 5*p, -5*j + p = -0*p - 14. Find m such that -7 - 1 + 6*m**2 - 5 - 2*m**j + 5 = 0.
-1, 2
Let s(h) = -9*h**4 - 13*h**3 + h**2 - 2*h. Let j be ((-14)/(-3))/((-12)/18). Let m(a) = -4*a**4 - 6*a**3 - a. Let g(b) = j*m(b) + 3*s(b). Factor g(u).
u*(u + 1)**3
Let k(p) = -5*p**2 + 1835*p + 167450. Let o(d) = 2*d**2 - d - 1. Let u(g) = -k(g) - 5*o(g). Factor u(f).
-5*(f + 183)**2
Suppose -3*o = -7*v + 3*v - 874, 5*v = o - 306. Let r be (-10)/6 + o/156. Determine g so that -r*g**4 + 1/6*g**2 + 0 - 1/6*g**3 + 1/6*g = 0.
-1, 0, 1
Let a(n) = -25*n**3 - 67*n**2 + 145*n - 33. Let y(o) = 24*o**3 + 69*o**2 - 144*o + 36. Let l(p) = -3*a(p) - 4*y(p). Suppose l(f) = 0. What is f?
-5, 3/7, 1
Find c such that 54/7*c**2 + 24/7 - 60/7*c - 3*c**3 + 3/7*c**4 = 0.
1, 2
Let t(i) be the second derivative of 3*i**4/4 + 7*i**3/6 + 3*i**2/2 + 8*i. Let x(g) = -4*g**2 - 4*g - 2. Let w(o) = -4*t(o) - 10*x(o). Factor w(u).
4*(u + 1)*(u + 2)
Suppose -j + 8 = 6. Suppose -99*u**j - 13 + 104*u**2 - 40*u - 7 + 10*u**3 = 0. What is u?
-2, -1/2, 2
Let t(s) be the first derivative of -12*s - 10/3*s**3 + 5 - 17*s**2. Factor t(q).
-2*(q + 3)*(5*q + 2)
Factor -128/7 - 104/7*p**2 - 192/7*p - 2/7*p**4 - 24/7*p**3.
-2*(p + 2)**2*(p + 4)**2/7
Let k(i) be the first derivative of 4*i**3/3 + 96*i**2 + 368*i - 613. Factor k(j).
4*(j + 2)*(j + 46)
Let c(a) be the second derivative of a**5/10 - 7*a**4/6 + 14*a**3/3 - 8*a**2 + 39*a - 2. Solve c(z) = 0 for z.
1, 2, 4
Let u(h) = -h**3 + 6*h**2 + 3. Let l be u(6). Let n be 9 - (-3 + 280/24). What is z in 5/3*z + 1/3*z**4 - z**2 - 2/3 - n*z**l = 0?
-2, 1
Let t(k) = -2*k + 1. Let r(d) be the second derivative of -d**4/12 - d**3/6 + 2*d**2 - 23*d. Let c(b) = -2*r(b) - 4*t(b). Factor c(z).
2*(z - 1)*(z + 6)
Factor -6*z**2 + 0*z**2 + z**2 - 159 - 75*z + 0*z**2 + 329.
-5*(z - 2)*(z + 17)
Let o be 81/135 - (-374)/(-690). Let h = 593/483 + o. Find w such that 18/7*w**2 + h*w**4 - 24/7*w**3 - 3/7 + 0*w = 0.
-1/3, 1
Let v(m) be the first derivative of 3*m**5/20 - m**3/2 - m + 1. Let b(z) be the first derivative of v(z). Factor b(y).
3*y*(y - 1)*(y + 1)
Let x(n) = 18*n + 29. Let f be x(9). Factor 3*q**2 - f*q**3 + q - 3*q + 190*q**3.
-q*(q - 2)*(q - 1)
Let -21*j**4 - 18*j**3 + 6*j + 142*j**5 - 279*j**5 + 21*j**2 + 149*j**5 = 0. What is j?
-1, -1/4, 0, 1, 2
Let j = -90 + 93. Suppose -4*w + 10 = 2*u, -15 = -17*w + 20*w - j*u. Factor 1/4*f**4 + w + 1/4*f - 1/4*f**2 - 1/4*f**3.
f*(f - 1)**2*(f + 1)/4
Factor 2/15*x**3 + 0 - 4/15*x**2 - 16/15*x.
2*x*(x - 4)*(x + 2)/15
Factor -4 - 10921*w**2 - 6 + 12*w + 10919*w**2.
-2*(w - 5)*(w - 1)
Suppose 2/11*f**4 + 2/11*f**5 - 2/11*f**2 - 72/11 + 96/11*f - 26/11*f**3 = 0. What is f?
-3, 1, 2
Let u(b) be the second derivative of b**5/80 - 5*b**4/48 - b**3/2 + 9*b**2/2 - 211*b. Suppose u(t) = 0. What is t?
-3, 2, 6
Factor -38*f - 34*f + 8*f**2 - 4*f**2 + 74*f - 4*f**4 - 2*f**5.
-2*f*(f - 1)*(f + 1)**3
Suppose 4*j + 6*i = 5*i + 66, -2*i = 4. Suppose 4*g - 12 = -4*m, 3*g = -m + j - 6. Determine u so that 16/9*u**3 - 44/9*u**2 - 2 + 16/3*u - 2/9*u**g = 0.
1, 3
Let s(y) be the second derivative of -y**8/560 + y**7/280 - 4*y**3/3 + 18*y. Let m(v) be the second derivative of s(v). Factor m(g).
-3*g**3*(g - 1)
Suppose m - 5 = 0, -22*l + 17 = -24*l + 5*m. Factor 6/5*j**l + 0*j + 3/5*j**2 + 0 - 9/5*j**3.
3*j**2*(j - 1)*(2*j - 1)/5
Let a(t) be the second derivative of t**8/1008 + t**7/315 + t**6/360 + 8*t**2 - 5*t. Let m(g) be the first derivative of a(g). Find y, given that m(y) = 0.
-1, 0
Suppose -4*k + 21 = j, -4*k + 31 = 4*j - j. Suppose 3*w = -5*v + 8*w, 0 = w. Solve -2*g**2 - k*g**3 + v*g**3 - 2*g**4 - 66 + 66 = 0.
-1, 0
Let t(a) be the third derivative of -1/32*a**4 + 0*a - 1/80*a**5 - 1/480*a**6 + 0 - 1/24*a**3 + 16*a**2. Factor t(w).
-(w + 1)**3/4
Let q(i) be the first derivative of 8 - 1/16*i**4 + 0*i**2 + 6*i + 1/120*i**6 + 1/12*i**3 + 0*i**5. Let k(w) be the first derivative of q(w). Solve k(j) = 0.
-2, 0, 1
Let z = 9 + -4. Suppose 3*a + 17*p = 18*p + 16, 4*a = -4*p. Let -4/11*h**2 - 4/11*h**3 - 2/11*h**z + 6/11*h + 6/11*h**a - 2/11 = 0. Calculate h.
-1, 1
Let s = 4 - -6. Suppose 2*z - s = -0*z. Factor -4*f**4 - 3*f**3 + 4*f**5 + 4*f**4 - f**z.
3*f**3*(f - 1)*(f + 1)
Let i(v) be the third derivative of v**8/560 - v**6/100 + v**4/40 + 496*v**2. Determine r, given that i(r) = 0.
-1, 0, 1
Let j(m) be the third derivative of -m**8/3696 + m**7/330 - m**6/120 + m**5/132 - m**2 + 64*m. Let j(n) = 0. Calculate n.
0, 1, 5
Let d(j) be the second derivative of j**6/96 + 7*j**5/240 + j**4/48 + 25*j**2/2 + 19*j. Let a(z) be the first derivative of d(z). Factor a(p).
p*(p + 1)*(5*p + 2)/4
Let f(a) be the third derivative of a**5/210 - 5*a**4/28 + a**2. Let f(c) = 0. What is c?
0, 15
Factor -5*g**2 + 19*g - 5944 + 16*g + 6034.
-5*(g - 9)*(g + 2)
Let x(d) be the third derivative of d**7/105 + 13*d**6/20 + 133*d**5/10 + 361*d**4/12 - 95*d**2. Factor x(b).
2*b*(b + 1)*(b + 19)**2
Let n be (-21 - -9)*5/(-20). Factor 1/3*v**n + 2/3*v**2 + 1/3*v + 0.
v*(v + 1)**2/3
Factor -3*p - 1/5*p**2 + 16/5.
-(p - 1)*(p + 16)/5
Factor -3*c - 6/5*c**2 - 6/5.
-3*(c + 2)*(2*c + 1)/5
Let u(d) be the first derivative of -5*d**9/3024 + d**7/56 + d**6/36 - d**3/3 + 11*d**2/2 - 13. Let g(c) be the third derivative of u(c). Factor g(f).
-5*f**2*(f - 2)*(f + 1)**2
Suppose -o = 2 - 4. Find j, given that 31*j**3 - 9*j**2 - 16*j**4 + j**o + 4*j**5 - 11*j**3 = 0.
0, 1, 2
Let w(n) be the first derivative of -n**3 + 51*n**2 - 101. Factor w(b).
-3*b*(b - 34)
Let m be 124/36 + (-28)/63. Let o(u) be the first derivative of -3/40*u**5 + 1/16*u**4 + 0*u - 5/48*u**6 + 0*u**2 + 0*u**m + 2. What is b in o(b) = 0?
-1, 0, 2/5
Let x(z) be the second derivative of z**7/14 + 2*z**6/5 + 9*z**5/20 + 85*z. Factor x(n).
3*n**3*(n + 1)*(n + 3)
Factor 4/7*m**3 - 2/7*m**2 + 0 - 4/7*m + 2/7*m**4.
2*m*(m - 1)*(m + 1)*(m + 2)/7
Let c = -6317/7 + 938. Let h = c - 244/7. Factor 4/7*x**2 - h*x + 1/7.
(x - 1)*(4*x - 1)/7
Let j(n) be the second derivative of n**6/12 - n**5/8 - 5*n**4/4 + 545*n. Suppose j(w) = 0. Calculate w.
-2, 0, 3
Let g be (6/(-4))/((-1)/2). Let t(x) = -10*x**2 + 118*x + 26. Let v be t(12). Factor -2/5*i**g + 4/5*i**v + 2/5*i - 4/5.
-2*(i - 2)*(i - 1)*(i + 1)/5
Suppose -4*y + 7*x + 17 = 10*x, 16 = 2*y + 4*x. Suppose 90/7*k**y - 50/7*k**3 - 48/7*k + 8/7 = 0. What is k?
2/5, 1
What is l in 2*l**2 + 14*l - 3*l**2 - l**2 - 75 + 55 = 0?
2, 5
Let r(j) be the first derivative of 0*j**4 + 2/13*j**2 + 1 + 0*j + 2/65*j**5 - 2/13*j**3. Factor r(n).
2*n*(n - 1)**2*(n + 2)/13
Let r(m) = m**2 + 21*m. Let v(j) be the second derivative of 2*j**3/3 + 12*j. Let k(l) = 2*r(l) - 11*v(l). Determine y so that k(y) = 0.
0, 1
Let f(i) = 2*i**4 + 8*i**3 + 4*i**2 - 2*i - 6. Let x(v) = v**3 + v**2 - 1. Let b(q) = f(q) - 6*x(q). Let b(l) = 0. What is l?
-1, 0, 1
Suppose 0 = 16*z - 37*z. Factor z - 9/2*x**2 - 2*x.
-x*(9*x + 4)/2
Let n(q) = 29*q**3 - 51*q**2 + 35*q - 5. Let s(i) = 28*i**3 - 52*i**2 + 35*i - 5. Let a(d) = 3*n(d) - 4*s(d). Factor a(m).
-5*(m - 1)**2*(5*m - 1)
Let n(r) be the second derivative of r**4/4 + 248*r**3 + 92256*r**2 + 637*r. Let n(g) = 0. What is g?
-248
Suppose -4*y = -2*j - 22, -5*j - 16 = -8*j - y. Factor j - 9/4*n - 3/4*n**2.
-3*(n - 1)*(n + 4)/4
Let v(z) be the second derivative of z**5/35 - 205*z**4/21 + 20806*z**3/21 + 21218*z**2/7 + 260*z + 1. Factor v(c).
4*(c - 103)**2*(c + 1)/7
Let a = -2737/166 + -1/83. Let s = 50/3 + a. Suppose -1/6*u - 5/6*u**2 + s - 1/2*u**3 = 0. What is u?
-1, 1/3
Suppose 2*c - 7 = 4*d - 19, -2*c + 3 = d. Factor 0 + 5/2*r**3 + c*r - 10*r**2.
5*r**2*(r - 4)/2
Let o = -31869/2 - -15935. Factor 3 - o*d**2 - 5/2*d.
-(d - 1)*(d + 6)/2
Solve 3/8*h**4 + 36 - 147/2*h + 48*h**2 - 87/8*h**3 = 0 for h.
1, 2, 24
Supp