- 2)
Let t = 36 + -32. Suppose 3*s + 15 + 6 = t*c, -s = 2*c - 3. Factor 2/9*x + 0 - 4/9*x**2 + 2/9*x**c.
2*x*(x - 1)**2/9
Let n = 43 + -41. Factor -1 + 78*l**2 - 83*l**2 - 2 - n + 10*l.
-5*(l - 1)**2
Let c = -861/4 + 1723/8. Factor c*v**2 - 3/4*v + 9/8.
(v - 3)**2/8
Find s, given that 101*s**2 - 3*s**3 - 655 + 7*s**2 + 915 + 1474 - 1071*s = 0.
2, 17
Let a be (-16)/(-10) - (-2)/10*2. Suppose 4*x**3 + 50*x**4 - x - a*x**2 - 5*x + 2*x - 48*x**4 = 0. Calculate x.
-2, -1, 0, 1
Let a(w) = 19*w**2 - 717*w + 32403. Let j(g) = -43*g**2 + 1433*g - 64807. Let b(c) = 7*a(c) + 3*j(c). Suppose b(o) = 0. What is o?
90
Let r(d) be the first derivative of 4*d**6/9 - 224*d**5/15 + 205*d**4/6 + 170*d**3/9 - 184*d**2/3 + 104*d/3 + 208. Determine s so that r(s) = 0.
-1, 1/2, 2, 26
Let h(t) be the first derivative of -2*t**3/9 + 4*t**2/3 + 79. Factor h(m).
-2*m*(m - 4)/3
Suppose 3*a = 5*a - 30. Let r be (-20)/a - -1 - (-98)/24. Factor 3/4*o**3 + 3/4*o**4 - 9/4*o**2 - 3/2 - r*o.
3*(o - 2)*(o + 1)**3/4
Let j be -6*4*93/(-744). Factor 0*z + 0 - 6/5*z**j + 0*z**2.
-6*z**3/5
Let y(h) be the third derivative of h**8/80640 - h**7/4032 + h**6/480 + 29*h**5/60 + h**2. Let x(p) be the third derivative of y(p). Factor x(j).
(j - 3)*(j - 2)/4
Let k(c) be the second derivative of -c**4/48 + c**3/4 + 2*c**2 + 145*c. Solve k(u) = 0 for u.
-2, 8
What is o in 21*o**4 - 22*o**2 + 17*o**3 + 9/2*o**5 - 3 - 35/2*o = 0?
-3, -2, -1/3, 1
Let c(q) be the third derivative of -q**7/1050 + q**6/300 + q**5/100 - q**4/30 - 2*q**3/15 - 16*q**2. Factor c(d).
-(d - 2)**2*(d + 1)**2/5
Let p(y) be the second derivative of -6*y + 0 - 3/14*y**2 - 1/7*y**3 - 1/28*y**4. Find x, given that p(x) = 0.
-1
Let z(h) be the second derivative of -3*h**5/100 - 3*h**4/10 - 11*h**3/10 - 9*h**2/5 + 2*h + 46. Let z(w) = 0. Calculate w.
-3, -2, -1
Let j(u) be the first derivative of 49*u**3/3 + 63*u**2 + 81*u + 204. Factor j(i).
(7*i + 9)**2
Suppose -11*p = -10*p - 2. Let u(s) be the first derivative of -1 - 3*s + 3/8*s**4 + 0*s**3 - 9/4*s**p. Factor u(m).
3*(m - 2)*(m + 1)**2/2
Let n(s) be the second derivative of s**7/11340 - s**6/405 + 4*s**5/135 + 5*s**4/6 + 8*s. Let z(c) be the third derivative of n(c). Let z(i) = 0. What is i?
4
Solve 3*m**3 + 3/4*m**4 - 27/4*m**2 - 12*m + 15 = 0 for m.
-5, -2, 1, 2
Let c be (2/(-3))/((-50)/75). Let m(q) = q**3 - q**2 - q. Let x(w) = 5*w**3 - 3*w**3 - w**2 + 2*w**2. Let f(t) = c*m(t) - x(t). Factor f(g).
-g*(g + 1)**2
Let s(a) be the second derivative of 5*a**4/12 - 55*a**3/6 - 30*a**2 + 103*a + 1. Factor s(r).
5*(r - 12)*(r + 1)
What is b in -1/2*b**2 + b + 3/2 = 0?
-1, 3
Let b(y) be the second derivative of -y**5/5 + 33*y**4/7 - 34*y**3 + 14*y**2 + 15*y - 4. Determine o, given that b(o) = 0.
1/7, 7
Let h(t) = -t**3 - 83*t**2 + 140*t + 60. Let f(b) = -28*b**2 + 46*b + 20. Let g(y) = -8*f(y) + 3*h(y). Factor g(i).
-(i - 2)*(i + 10)*(3*i + 1)
Let w = -517 + 5691/11. Let a = -2017 - -2019. Factor -4/11*v**a - w + 10/11*v.
-2*(v - 2)*(2*v - 1)/11
Let n(w) be the second derivative of w**7/168 - w**6/8 + w**5 - 10*w**4/3 - 7*w**3/3 + 18*w. Let f(b) be the second derivative of n(b). Factor f(v).
5*(v - 4)**2*(v - 1)
What is j in 3/2*j - 2/3 + 1/6*j**3 - j**2 = 0?
1, 4
Let d(v) = -19*v**2 + 11*v - 1. Let j(a) = -7*a**2 + 4*a. Let t(n) = -4*d(n) + 11*j(n). Factor t(l).
-(l - 2)*(l + 2)
Determine q, given that 20/3 - 25/3*q + 5/3*q**2 = 0.
1, 4
Let k(g) = g**2 - 74*g + 16. Let q(f) = f**2 - 50*f + 10. Let n(m) = 5*k(m) - 8*q(m). Factor n(a).
-3*a*(a - 10)
Let a = 465 - 462. Let l(m) be the second derivative of -2/3*m**a + 0 + 5*m - 3*m**2 + 1/6*m**4. Find v such that l(v) = 0.
-1, 3
Let v be (-18)/3*(4 - 52/12). Let t(s) be the second derivative of 5*s + 0 + 5/12*s**4 + v*s**2 + 2*s**3. Factor t(m).
(m + 2)*(5*m + 2)
Let a(n) = 3*n**2 + 5*n + 2. Let b(f) = -7*f**2 - 11*f - 4. Let l(p) = -7*p**2 - 11*p - 4. Let w(t) = 5*b(t) - 4*l(t). Let r(h) = 5*a(h) + 2*w(h). Factor r(v).
(v + 1)*(v + 2)
Let o(z) be the second derivative of -z**5/8 + 9*z**4/8 - 5*z**3/2 + 2*z**2 + 55*z. Let o(m) = 0. What is m?
2/5, 1, 4
Let t(j) be the third derivative of 0*j + 1/735*j**7 - 11*j**2 + 0*j**4 + 1/210*j**6 + 0*j**5 + 0 - 1/1176*j**8 + 0*j**3. Suppose t(m) = 0. Calculate m.
-1, 0, 2
Suppose -4*c = 88 - 120. Suppose 7 = 2*t + 3*r - 9, -r = 2*t - c. Find n such that -1/8*n**t + 1/8*n + 0 = 0.
0, 1
Let p(v) = 2*v**3 + 13*v**2 - 5*v. Let g(b) = 2*b**3 + 12*b**2 - 6*b. Let z(t) = 5*g(t) - 6*p(t). Determine x, given that z(x) = 0.
-9, 0
Let j = 42 - 6. Let p be -1 - -3 - j/22. Find q, given that 6/11*q - p + 0*q**2 - 2/11*q**3 = 0.
-2, 1
Let p(l) be the first derivative of -5*l**6/6 - l**5 + 5*l**4/4 + 5*l**3/3 + 175. Let p(o) = 0. Calculate o.
-1, 0, 1
Let y(q) be the first derivative of -3/4*q**3 + 7/16*q**4 + 1/4*q**2 - 13 + 0*q. Suppose y(n) = 0. What is n?
0, 2/7, 1
Factor 3 - 1/2*i**3 + 0*i**2 + 7/2*i.
-(i - 3)*(i + 1)*(i + 2)/2
Let n(j) be the third derivative of -j**7/1680 - j**6/192 - j**5/160 + 3*j**4/64 + 17*j**2 + 2. Let n(c) = 0. What is c?
-3, 0, 1
Let k = -18334 + 128356/7. What is z in 0 + k*z**2 - 8/7*z**3 - 4/7*z = 0?
0, 1/4, 2
Let c(s) be the second derivative of 1/12*s**4 - 3*s**2 + 5/6*s**3 + 0 - 3*s. Let g(u) = 2*u**2 + 16*u - 18. Let k(x) = -7*c(x) + 2*g(x). Solve k(o) = 0.
-2, 1
Let u be (-3)/9*(-2)/20. Let m(w) be the third derivative of u*w**4 + 1/150*w**5 + 0 + 3*w**2 + 1/15*w**3 + 0*w. Let m(c) = 0. Calculate c.
-1
Let q = -15921187/99 + 160815. Let p = -44/9 - q. Factor -2/11*k + 4/11*k**2 + p*k**3 - 4/11.
2*(k - 1)*(k + 1)*(k + 2)/11
Solve 45/2 - 15/2*v + 25/2*v**4 - 35*v**2 + 5/2*v**5 + 5*v**3 = 0.
-3, -1, 1
Let -75/4*k**3 - 51 - 1215/4*k**2 + 252*k = 0. Calculate k.
-17, 2/5
Let q(p) be the second derivative of 24*p + 0*p**2 + 0 + 1/60*p**5 + 1/36*p**4 - 1/9*p**3. Find o, given that q(o) = 0.
-2, 0, 1
Suppose 5*b - 2 = -a + 2, 0 = -4*b + 2*a + 20. Suppose 0 - 2/3*z**b + 2/3*z**5 + 2/3*z**4 - 2/3*z**3 + 0*z = 0. Calculate z.
-1, 0, 1
Let z = -48/29 - -1613/957. Let n(a) be the first derivative of z*a**6 + 0*a**2 + 1/22*a**4 + 0*a - 9 + 0*a**3 - 4/55*a**5. Suppose n(l) = 0. What is l?
0, 1
Let t(m) = -4*m - 4. Let c be t(-2). Let v(a) = a**2 - 5*a + 8. Let b be v(c). Let o + o**4 + 3*o**2 - b*o**2 + o**3 - 2*o = 0. Calculate o.
-1, 0, 1
Let a(c) = c**2 - c. Let z(x) = -30*x**2 + 36*x - 6. Let m(q) = -2*a(q) - z(q). Factor m(n).
2*(n - 1)*(14*n - 3)
Let p = -52 + 55. Factor -6*o**5 + 2*o**5 + 8*o**p + 4*o**3 - 70*o**2 + 62*o**2.
-4*o**2*(o - 1)**2*(o + 2)
Let s be (-16)/(-2) - (1 - 1). Let q(u) be the first derivative of 6*u**2 + 6 - u**4 + 11 - s + 8*u. Suppose q(w) = 0. What is w?
-1, 2
Let f(a) = 2*a**3 - 13*a**2 + a - 54. Let t be f(7). Factor z - 1/3*z**t + 0.
-z*(z - 3)/3
Factor 0*x**4 + 42*x**3 + 57*x**3 - 116*x**3 + 380*x + 400 - x**4 - 36*x**2.
-(x - 4)*(x + 1)*(x + 10)**2
Factor 0*o - 3/8*o**3 + 0 - 3/2*o**2.
-3*o**2*(o + 4)/8
Factor -36/5*a - 24/5*a**2 + 0 - 3/5*a**3.
-3*a*(a + 2)*(a + 6)/5
Let y(j) be the first derivative of -5*j**6/72 + 7*j**5/24 - 5*j**4/12 - j**3/3 - 21. Let k(f) be the third derivative of y(f). Find r such that k(r) = 0.
2/5, 1
Let w(d) = 20*d**2 + 9028*d + 1021544. Let y(j) = 8*j**2 + 3611*j + 408618. Let v(h) = -5*w(h) + 12*y(h). Factor v(o).
-4*(o + 226)**2
Suppose 131 = -3*k + 143. Let j(r) be the first derivative of 1/6*r**2 + k + 1/9*r**3 - 2/3*r. Factor j(b).
(b - 1)*(b + 2)/3
Let h = 13 + -17. Let x(c) = c**4 + 24*c**3 - 9*c**2 - 9*c. Let t(f) = -6*f**3 + 2*f**2 + 2*f. Let n(q) = h*x(q) - 18*t(q). What is k in n(k) = 0?
0, 3
Let 208/3*h**4 + 4754/3*h**3 + 70840/3*h - 33676/3*h**2 + 2/3*h**5 - 48400/3 = 0. What is h?
-55, 2
Let i(s) = s - 3. Let l be i(8). Factor -5 - l*k**2 - 40*k + 30*k + 0*k**2.
-5*(k + 1)**2
Suppose -3*s + 5*f = 2*s - 20, f = -2*s + 20. Let w be -6*((-10)/4 + 2). Factor -d**2 + d + 0*d**4 - 4*d - s*d**2 + 9*d**4 + w*d**3.
3*d*(d - 1)*(d + 1)*(3*d + 1)
Let k(q) be the third derivative of -1/140*q**5 + 0 - 29*q**2 + 0*q - 14*q**3 + 1/2*q**4. Factor k(x).
-3*(x - 14)**2/7
Let q(z) be the third derivative of z**6/150 - 4*z**5/75 - z**4/6 - 101*z**2 - 3. Suppose q(i) = 0. Calculate i.
-1, 0, 5
Let w(t) = -t**3 - 10*t**2 - 15*t + 8. Let b be w(-8). Suppose 4*p - 3 - 13 = b. Suppose -6*g**3 + p*g**2 - 2*g + 0*g + 4*g**3 = 0