q(y) - 2*p(y). Factor t(u).
4*(u - 2)**2
Let z be 21/2*(39/585 - (-2)/6). Factor z*p + 3/5*p**3 - 3*p**2 - 9/5.
3*(p - 3)*(p - 1)**2/5
Let w = 82 + -31. Let y = w + -49. Factor 0*z + 3/5*z**y + 0.
3*z**2/5
Let b(z) = -41*z**3 - 256*z**2 - 701*z - 464. Let l(y) = -22*y**3 - 128*y**2 - 350*y - 232. Let u(i) = -6*b(i) + 11*l(i). Factor u(o).
4*(o + 1)*(o + 2)*(o + 29)
Let n(j) be the first derivative of 2/3*j**3 + 9 + 0*j + 8*j**2. What is f in n(f) = 0?
-8, 0
Let m(s) = 2*s + 16. Let h be m(-10). Let t be (-3)/90*3*h. What is u in 0 + t*u - 2/5*u**2 = 0?
0, 1
Let u(k) be the second derivative of -4*k**7/21 + 11*k**6/5 - 18*k**5/5 + 7*k**4/6 - 8*k + 1. Determine y, given that u(y) = 0.
0, 1/4, 1, 7
Let i(b) be the second derivative of b**6/45 + 4*b**5/15 + 2*b**4/3 - 41*b. Factor i(h).
2*h**2*(h + 2)*(h + 6)/3
Suppose 0 = 12*c - 7*c + 4*m - 16, 5*m - 20 = 3*c. Let z(u) be the second derivative of 1/9*u**3 + 0*u**2 + 5*u + c + 1/36*u**4. Solve z(g) = 0 for g.
-2, 0
Let m(q) be the second derivative of -q**4/16 - 7*q**3/4 - 39*q**2/8 - 104*q. Find p, given that m(p) = 0.
-13, -1
Let j be 11/(165/(-12)) - 80/(-100). Solve -2/13*r**4 + 0*r - 2/13*r**3 + j*r**2 + 0 = 0.
-1, 0
Let b(o) be the third derivative of -3*o**6/10 + o**5/5 + 95*o**4/24 + 25*o**3/3 + 57*o**2 - 1. Find w such that b(w) = 0.
-5/6, 2
Let l = -12217 + 12217. Determine v so that 1/2*v**2 + v**4 + l*v + 3/2*v**3 + 0 = 0.
-1, -1/2, 0
Let j(f) = 43*f**4 - 108*f**3 - 35*f**2 + 83*f + 24. Let y(n) = -42*n**4 + 108*n**3 + 34*n**2 - 82*n - 24. Let v(u) = -6*j(u) - 7*y(u). Solve v(q) = 0 for q.
-2/3, -1/3, 1, 3
Let t be (72/120)/((-2)/(-156)*2). Suppose 72/5*x - t*x**4 - 12/5 + 27/5*x**5 + 201/5*x**3 - 171/5*x**2 = 0. What is x?
2/3, 1
Factor 10*c**2 - 58/13*c + 50/13*c**3 + 6/13.
2*(c + 3)*(5*c - 1)**2/13
Let q = 0 + 2. Let -6*d**2 + d**2 - 6*d**2 - 15*d**3 - 5*d**4 + d**q = 0. Calculate d.
-2, -1, 0
Let y(i) be the first derivative of 7*i**5/5 - 4*i**4 - 17*i**3/3 + 3*i**2 + 147. Let y(k) = 0. What is k?
-1, 0, 2/7, 3
Let z(x) = x**3 - 28*x**2 + 11*x - 305. Let y be z(28). Solve 0*j + 9*j**4 + 6*j**2 + 12/5*j**5 - 3/5 + 12*j**y = 0 for j.
-1, 1/4
Let c(n) be the second derivative of n**7/12600 + n**6/1800 + n**4 + 11*n. Let m(z) be the third derivative of c(z). Solve m(w) = 0.
-2, 0
Let z(n) be the first derivative of 0*n**2 + 3/2*n**5 - 5/12*n**4 + 4*n - 7 + 0*n**3. Let w(k) be the first derivative of z(k). Factor w(x).
5*x**2*(6*x - 1)
Let f = -236 + 7081/30. Let q(p) be the second derivative of -1/30*p**4 + 0*p**2 - 1/100*p**5 + 0 + 5*p - f*p**3. Determine g, given that q(g) = 0.
-1, 0
Let x(h) be the third derivative of -h**7/315 - h**6/36 - 7*h**5/90 - h**4/12 - 58*h**2. Suppose x(r) = 0. What is r?
-3, -1, 0
Factor -5 - 8*t**2 + 5 - 79*t**5 + 77*t**5 - 18*t**3 - 12*t**4.
-2*t**2*(t + 1)**2*(t + 4)
Let c(k) be the first derivative of -4*k**3/3 + 62*k**2 - 87. Factor c(d).
-4*d*(d - 31)
Let n(d) = -7*d - 37. Let i be n(-6). Factor 6*g**2 + 102*g**i + 0*g**4 + 0*g**4 - 105*g**5 + 9*g**3.
-3*g**2*(g - 2)*(g + 1)**2
Let y(t) = -5*t**2 + 35*t - 26. Let b be y(6). Let m(c) be the third derivative of c**2 - 1/12*c**3 - 2/5*c**5 + 0*c + 13/48*c**b + 3/20*c**6 + 0. Factor m(i).
(i - 1)*(6*i - 1)**2/2
Let o(r) be the third derivative of r**8/1176 - 74*r**7/735 + 114*r**6/35 + 37*r**5/105 - 1369*r**4/84 + 53*r**2 - 2*r. Find x, given that o(x) = 0.
-1, 0, 1, 37
Let y(r) be the third derivative of r**9/11340 - r**8/2520 + r**6/270 - r**5/90 + 11*r**4/12 + 4*r**2. Let m(w) be the second derivative of y(w). Factor m(u).
4*(u - 1)**3*(u + 1)/3
Let k(u) = 47*u**2 + 344*u + 14787. Let t(f) = 28*f**2 + 172*f + 7393. Let p(h) = 3*k(h) - 5*t(h). Find a such that p(a) = 0.
-86
Let j = 106 - 116. Let x be j*-2*(-2)/(-8). Solve -75/7*n**3 - 24/7*n**4 - 114/7*n**2 - 24/7 - 3/7*n**x - 12*n = 0 for n.
-2, -1
Suppose -3*f = 5*i - 8, -f + 6 = i - 0*i. Determine m, given that 5*m**2 + 4*m**3 + 11*m**4 - 14*m**3 - f*m**4 - 5*m**4 + 10*m = 0.
-2, -1, 0, 1
Let p be -3 - -3 - 1 - (-9 + 5). Suppose -p = 3*i - 4*i. Factor -3/4*g**2 + 0 + 0*g - 9/4*g**4 + i*g**3.
-3*g**2*(g - 1)*(3*g - 1)/4
Suppose -i - i - 5*t + 11 = 0, -17 = -5*i - 2*t. Find n, given that -5*n**4 - 2*n + 0*n + i + 18*n**3 - 2*n**4 - 12*n**2 = 0.
-3/7, 1
Let k be 4/(2*(-1)/(-6)). Let z(n) = -6*n**2 - 35*n - 5. Let x(d) = -15*d**2 - 87*d - 12. Let m(o) = k*z(o) - 5*x(o). Find g, given that m(g) = 0.
-5, 0
Let y be (1 + -5 + 1)*-1. Let s = -754/7 + 108. Factor -10/7*d + s*d**5 - 4/7 - 4/7*d**2 + 8/7*d**y + 8/7*d**4.
2*(d - 1)*(d + 1)**3*(d + 2)/7
Let x = 45 + -32. Determine k, given that 9*k**2 - 2*k**5 + k + 4*k**4 + k - x*k**2 = 0.
-1, 0, 1
Suppose 3*u - 7 = -22. Let c(n) = 5*n**3 - 10*n**2 - 5*n - 5. Let f(s) = s**4 + 5*s**3 - 9*s**2 - 5*s - 4. Let i(d) = u*f(d) + 4*c(d). Factor i(w).
-5*w*(w - 1)*(w + 1)**2
Let n(o) = -2*o**2 - 21*o - 40. Let v be n(-13). Let r be 6/(-10) + (-153)/v. Solve r + 8/7*g + 2/7*g**2 = 0 for g.
-3, -1
Let i = 9679/5 + -1935. Factor -i*c**4 + 0*c**3 + 4/5*c**2 + 2/5*c**5 - 2/5*c + 0.
2*c*(c - 1)**3*(c + 1)/5
Let w(z) be the third derivative of -z**5/300 - 3*z**4/10 - 54*z**3/5 + z**2 + 49. Factor w(l).
-(l + 18)**2/5
Suppose 0*m - 3*k = -2*m - 3, k + 6 = 3*m. Let 2/3*s - 2/3*s**m + 2/9*s**2 - 2/9 = 0. What is s?
-1, 1/3, 1
Suppose -17*h + 24 = -22*h + 17*h. Let 3/2*t - 5 + 1/2*t**h = 0. What is t?
-5, 2
Let j = -201 - -186. Let r be ((j - -6) + 8)*(0 + -5). Determine w so that -4/19*w - 8/19*w**r + 6/19*w**3 - 10/19*w**2 + 0 + 16/19*w**4 = 0.
-1/2, 0, 1, 2
Let d(l) be the second derivative of l**6/420 + l**5/210 + 3*l**2 - 5*l. Let f(v) be the first derivative of d(v). Factor f(p).
2*p**2*(p + 1)/7
Let y(d) = d**2 - 7*d + 12. Let h be y(5). Find p such that 4*p**h - 25*p - 6 + 22*p + 6 - p**3 = 0.
0, 1, 3
Let z(f) be the third derivative of 11*f**5/390 + 9*f**4/52 - 6*f**3/13 - 179*f**2. What is i in z(i) = 0?
-3, 6/11
Let i(w) = -w**2 - w + 2. Let t be i(3). Let f be (t - -8)*(-10)/4. Let -f*a**3 - 3*a**2 - 6*a + 6*a**3 + 5*a**3 + 3*a**4 = 0. Calculate a.
-2, -1, 0, 1
Suppose -10 = -3*v - 1. Determine j so that 4*j**3 - v*j**4 + 5*j**5 + 11*j**4 - j**5 = 0.
-1, 0
Let o be -10*(288/45 + -7). Factor -5/2*m**2 - o*m + 3*m**3 - 2.
(m - 2)*(2*m + 1)*(3*m + 2)/2
Factor -18*s + 3/7*s**2 + 189.
3*(s - 21)**2/7
Let q(m) be the first derivative of -2*m**5 + 0*m + 18 - 5/6*m**6 + 0*m**2 + 5/4*m**4 + 10/3*m**3. Find z such that q(z) = 0.
-2, -1, 0, 1
Let w(d) = 5*d**2 - 140*d + 485. Let z(m) = m**2. Let f(y) = -10*y**2 + 210*y - 728. Let n(p) = -f(p) - 2*z(p). Let l(b) = 5*n(b) - 7*w(b). Factor l(c).
5*(c - 7)**2
Let z(g) be the third derivative of g**6/240 - g**5 - 81*g**4/16 - 61*g**3/6 + 733*g**2. Find k such that z(k) = 0.
-1, 122
Let x(f) be the third derivative of -f**5/30 + 3*f**4/4 - 8*f**3/3 - 56*f**2. Determine u so that x(u) = 0.
1, 8
Suppose -5*o + 0*o = 4*k + 21, -4*o = 3*k + 17. Let x = 0 + 3. Determine h, given that 32*h**2 + 9 - 9*h**3 - 6 - 22*h - 5*h**x + k = 0.
2/7, 1
Factor -39/2*f + 3/4*f**2 + 507/4.
3*(f - 13)**2/4
Let g(f) be the first derivative of -3*f**5/35 + 3*f**3/7 + 3*f**2/7 - 180. Find k such that g(k) = 0.
-1, 0, 2
Let q(z) be the first derivative of -10*z**5/11 - 30*z**4/11 - 92*z**3/33 - 12*z**2/11 - 2*z/11 + 221. Factor q(g).
-2*(g + 1)**2*(5*g + 1)**2/11
Suppose -8*r + 180 = 7*r. Suppose 0 = -3*b + 24 - r. Factor 2/3 - 2*x**2 - 4/3*x**b - 10/3*x**3 + 2/3*x.
-2*(x + 1)**3*(2*x - 1)/3
Let x(m) = 13*m**3 + 77*m**2 + 216*m + 221. Let s(o) = -7*o**3 - 39*o**2 - 108*o - 111. Let y(j) = 5*s(j) + 3*x(j). Factor y(t).
4*(t + 3)**3
Let n(j) be the third derivative of j**7/6 - 4*j**6 + 35*j**5/3 + 10*j**4 - 9*j**2. Factor n(u).
5*u*(u - 12)*(u - 2)*(7*u + 2)
Let z = 3920 - 3918. Solve -18/7*r**z + 3/7*r**3 - 24/7 + 36/7*r = 0 for r.
2
Factor -h**2 - 52*h - h**2 - 43*h - 15*h + 0*h**2 + 112.
-2*(h - 1)*(h + 56)
Let p = 589/2041 - -3/157. Let r be (3 + (1 - 5))/((-7)/21). Find b such that 4/13*b**2 - 8/13*b**r - 8/13*b**4 - 2/13*b**5 + 10/13*b + p = 0.
-2, -1, 1
Factor 34*r**4 + 42*r**4 + 324*r**2 - 72*r**3 - 72*r**4.
4*r**2*(r - 9)**2
Let 9*g + 80*g**4 + 23*g**5 + 175*g**3 - 81*g**3 + 2*g**5 + 48*g**2 = 0. Calculate g.
-1, -3/5, 0
Let p(n) be the third derivative of 1/6*n**4 + 0 + 1/3*n**5 + 4*n**2 + 0*n +