e x(p) = 0 for p.
-2, -1, 0, 2
Let d(y) = 16*y**2 - 55*y - 7. Let s(i) = -7*i**2 + 26*i + 3. Let c(l) = -3*d(l) - 7*s(l). Determine k so that c(k) = 0.
0, 17
Let k(s) be the third derivative of -2*s**7/135 + 23*s**6/270 - 2*s**5/45 - 14*s**4/27 + 16*s**3/27 - 724*s**2. Suppose k(t) = 0. Calculate t.
-1, 2/7, 2
Let f(a) be the second derivative of a**8/67200 + a**7/25200 - a**6/7200 - a**5/1200 + 3*a**4/2 + 17*a. Let t(l) be the third derivative of f(l). Factor t(b).
(b - 1)*(b + 1)**2/10
Let -368*c + 5*c**3 + 368*c - 4*c**2 - c**4 = 0. What is c?
0, 1, 4
Let y = -12 + 16. Suppose -y = -2*r + 2. Factor -3*d**r - 8*d**2 + 2*d**3 + d**5 + 8*d**2.
d**3*(d - 1)*(d + 1)
Let f be 2/1*4360/(-64). Let z = 137 + f. Factor z*l**2 + 0 + 7/4*l**4 - 3*l**3 + 1/2*l.
l*(l - 1)**2*(7*l + 2)/4
Let o(f) = -8*f**4 + 64*f**3 + 127*f**2 + 60*f + 5. Let r(u) = 3*u**4 - 32*u**3 - 63*u**2 - 30*u - 2. Let w(c) = -2*o(c) - 5*r(c). Suppose w(i) = 0. What is i?
-30, -1, 0
Let k = 529/916 + -75/229. Factor -k*u**4 + 3/4*u**2 + u - 1/2*u**3 - 1.
-(u - 1)**2*(u + 2)**2/4
Let y(a) be the third derivative of 1/144*a**8 + 0*a + 0 - 1/72*a**4 + 17/180*a**6 - 13/315*a**7 - 15*a**2 + 1/9*a**3 - 4/45*a**5. Factor y(k).
(k - 1)**4*(7*k + 2)/3
Let j(c) be the first derivative of -1 + 0*c**2 + 1/30*c**3 - 1/60*c**4 - c. Let w(f) be the first derivative of j(f). Factor w(n).
-n*(n - 1)/5
Let p(a) be the second derivative of a**4/6 - a**3/2 - a**2 + 3*a. Let b be p(-1). Factor -b - 3*c**3 - c**3 + c**3 + 3*c + 3*c**2.
-3*(c - 1)**2*(c + 1)
What is r in 6/11*r**3 + 14/11*r**4 - 8/11*r + 2/11*r**5 - 38/11*r**2 + 24/11 = 0?
-6, -2, -1, 1
Suppose 23 = -5*n - 17. Let j be -1*n/4*2. Suppose -16 - 41*i - 28*i**3 - 4*i**5 - j*i**2 + 6*i**4 + 73*i + 14*i**4 = 0. What is i?
-1, 1, 2
Let r = -15724 - -78812/5. Factor -54/5*l - 3/5 - 432/5*l**3 - 291/5*l**2 - r*l**4.
-3*(l + 1)**2*(8*l + 1)**2/5
Let g be 567/252*(-20)/(-15). Solve -1/4*q**4 + 3*q - 9/4 - q**g + 1/2*q**2 = 0 for q.
-3, 1
Let f(u) be the third derivative of -u**7/42 - 7*u**6/12 - 8*u**5/3 + 80*u**4/3 - 140*u**2. Let f(t) = 0. Calculate t.
-8, 0, 2
Let q(w) be the second derivative of w**4/78 + 46*w**3/39 + 529*w**2/13 - 351*w. Solve q(t) = 0.
-23
Let g(a) = -3*a**2 - 88*a - 483. Let s be 3 + 6/15 + (-88)/20. Let q(y) = -y**2 - 1. Let u(t) = s*q(t) - g(t). Factor u(m).
4*(m + 11)**2
Let i(t) be the second derivative of 0*t**3 - 2*t**2 + 0 + 37*t + 1/12*t**4. Solve i(z) = 0.
-2, 2
Let s(o) be the first derivative of -2*o**5/5 + 17*o**4 + 24*o**3 - 34*o**2 - 70*o - 390. Determine i, given that s(i) = 0.
-1, 1, 35
Let u(j) be the third derivative of 0*j + 1/672*j**8 + 0*j**3 + 0*j**6 + 7*j**2 - 1/60*j**5 + 0 - 1/48*j**4 + 1/210*j**7. What is y in u(y) = 0?
-1, 0, 1
Let z be ((-9)/6)/((-12)/40). Determine a so that -4*a**z + 24*a**4 - a**4 - 15*a**4 - 4*a**3 = 0.
0, 1
Let x(z) be the first derivative of 2/39*z**3 - 2/13*z + 0*z**2 + 34. What is w in x(w) = 0?
-1, 1
Let u be (4 + -4)/(-1) - -2. Suppose -2*d**2 - 2*d**2 + u*d**2 - 12*d - 5 - 11 = 0. What is d?
-4, -2
Factor 0*u**2 - 27*u**4 + 45*u**3 + 0*u**2 + 3*u**5 - 21*u**3 + 9*u**4.
3*u**3*(u - 4)*(u - 2)
Let s(r) be the first derivative of -3/5*r**4 + 2 - 2/25*r**5 + 0*r - 6/5*r**3 + 0*r**2. Factor s(h).
-2*h**2*(h + 3)**2/5
Let w(l) = -l**3 + l**2 - 1. Let r(y) = 2*y - 1. Let f be r(-1). Let u(d) = -2*d**4 - 7*d**3 + 9*d**2 - 3. Let i(v) = f*w(v) + u(v). Factor i(t).
-2*t**2*(t - 1)*(t + 3)
Factor -6*b + 23*b + 3*b**3 + 3*b**4 - 9*b - 11*b + 6 - 9*b**2.
3*(b - 1)**2*(b + 1)*(b + 2)
Let l(q) = -2*q**2 - 10*q - 14. Let o = -14 - -9. Let r(m) = -m**2 - 11*m - 15. Let y(s) = o*l(s) + 6*r(s). Factor y(t).
4*(t - 5)*(t + 1)
What is l in -117 - 196*l**3 + 45*l**2 - 69*l + 396*l**3 - 203*l**3 = 0?
-1, 3, 13
Suppose -229 = -8*x - 821. Let s = x - -76. Let 1/5*a**s + 4/5 - 4/5*a = 0. What is a?
2
Let b(r) be the third derivative of r**6/300 - r**5/30 - r**4/5 + 12*r**3/5 - 88*r**2 + r. Factor b(u).
2*(u - 6)*(u - 2)*(u + 3)/5
Factor -1260*z**2 - 3640*z**4 + 7269*z**4 - 1782*z - 2*z**5 - 864 - 3681*z**4 - 392*z**3.
-2*(z + 1)*(z + 3)**3*(z + 16)
Let t be 6/39 + (-212)/26. Let i be (-27)/(-18)*t/(-6). Factor 9*m + 6 - 5*m**i + 2*m**2 + 3*m**2 + 3*m**2.
3*(m + 1)*(m + 2)
Let u(t) = -t**3 + 5*t**2 + 9*t + 14. Let v be u(5). Let h = v - 57. Factor 0*d**h + 0*d + 1/2*d**3 + 0 + 1/4*d**4.
d**3*(d + 2)/4
Let u(w) be the third derivative of 0 + 1/660*w**5 + 0*w**4 - 1/660*w**6 + 1/2310*w**7 + 11*w**2 + 0*w**3 + 0*w. Factor u(z).
z**2*(z - 1)**2/11
Suppose 8*g - 18/5*g**2 - 8/5 = 0. What is g?
2/9, 2
Let -162000 - 97200*o - 276*o**3 - 3788*o**2 - 6081*o**2 - 3*o**4 + 1229*o**2 = 0. What is o?
-30, -2
Let c(n) = n**3 - n**2 - n. Let a(v) = -2*v**4 + 26*v**3 - 22*v**2 - 22*v. Let s(j) = 2*a(j) - 44*c(j). Solve s(b) = 0.
0, 2
Let g be (2/(-6))/(6/(-54)). Find h such that -35*h - 5*h**4 - 7 - 1 - 2 - 25*h**g - 45*h**2 = 0.
-2, -1
Find c, given that 4*c**4 + 1373*c**3 - 2*c**4 + 62 - 853*c**3 + 374*c + 756*c**2 + 14*c**4 = 0.
-31, -1/2
Let p(d) be the third derivative of d**6/600 + d**5/300 - d**4/20 - d**2 - 8*d. Solve p(j) = 0.
-3, 0, 2
Let a be ((-12)/10 + 1)*(-86 - -71). Let s(j) be the second derivative of -3*j + 0 + 1/5*j**4 + 0*j**2 - 1/10*j**a. Suppose s(l) = 0. Calculate l.
0, 1/4
Let y(s) be the first derivative of -4*s**6/3 - 14*s**5 + 93*s**4/2 - 130*s**3/3 + 11*s**2 + 471. What is t in y(t) = 0?
-11, 0, 1/4, 1
Let l(f) = -f**3 - 5*f**2 - 2*f - 8. Let d be l(-5). Let r be 8/6 + (-1 - (d + -2)). Solve -1/6*b**2 + 0*b + 0 + r*b**3 - 1/6*b**4 = 0.
0, 1
Let k = -1 + 7. Find d such that -k*d**2 - 2*d**2 - 3*d**3 + d**4 + 16*d + d**4 - d**3 = 0.
-2, 0, 2
Let k(w) = w**3 + 7*w**2 + 13*w + 6. Let m be k(-2). Find n, given that m - 12/5*n + 3/5*n**2 = 0.
0, 4
Suppose 4*x + 0*x = 64. Let t = -10 + x. Factor -17*k**2 + 15*k**2 + t*k - 2*k.
-2*k*(k - 2)
Let w(t) = -4*t - 9 + 2*t + t. Let u be w(-11). Find l, given that -3*l**4 - 10*l**3 - u*l**4 - 4*l**2 - l**2 = 0.
-1, 0
Let s = -17842 - -17842. Determine m, given that 1/2*m - 1/2*m**2 + s = 0.
0, 1
Let p be 10/(-1)*(-4 + 6). Let h = 22 + p. What is k in 8*k**2 + 0*k**h - 14*k + 2*k + 4 = 0?
1/2, 1
Let c(o) = 27*o + 21. Let j(i) = -i**2 - 55*i - 44. Let x(f) = -5*c(f) - 3*j(f). Factor x(g).
3*(g + 1)*(g + 9)
Let q(d) be the third derivative of d**8/84 - 4*d**7/35 + d**6/6 + 8*d**5/5 - 6*d**4 + 6*d**2 - 7*d. Factor q(z).
4*z*(z - 3)**2*(z - 2)*(z + 2)
Let s be 4*(-2 + (-65)/(-20)). Suppose s*z**4 + 12*z**5 - 3*z**3 - 3*z**2 - 9*z**3 - 2*z**4 = 0. What is z?
-1, -1/4, 0, 1
Let -4*o**2 + 2*o**4 - 36*o**3 + 36*o + 157 + 2*o**4 - 157 = 0. Calculate o.
-1, 0, 1, 9
Let q(o) = -4*o + 15. Let t be q(7). Let h = 15 + t. Factor 828*k**2 - 828*k**h + 2*k - 2*k**3.
-2*k*(k - 1)*(k + 1)
Let m(c) = -35*c**2 + 4*c + 4. Let t(h) be the first derivative of -2 + 3*h**3 - h - 1/2*h**2. Let v(w) = 6*m(w) + 26*t(w). Find z, given that v(z) = 0.
-1/4, 1/3
Suppose -6 = -2*h - 2. Determine c, given that 2*c + 30*c**h - 3 - 16*c**2 - 13*c**2 = 0.
-3, 1
Let s be (0 - 1)*-1*3. Suppose -5*b = -25 + 10. What is p in b + p**2 + 0*p**2 + 3*p - s*p**3 - 2*p**2 - 2*p**2 = 0?
-1, 1
Determine r so that -246*r**4 + 24/5 + 802/5*r**3 + 1206/5*r**2 - 90*r**5 - 352/5*r = 0.
-3, -1, 2/15, 1
Let f(y) be the third derivative of y**8/84 + 8*y**7/21 + 5*y**6/6 - 142*y**5/3 + 910*y**4/3 - 2704*y**3/3 + 19*y**2 - 2*y. Solve f(g) = 0 for g.
-13, 2
Factor -4*w**4 + 46*w**2 - 7*w**2 - 23*w**2.
-4*w**2*(w - 2)*(w + 2)
Let l be 8 - 2/1 - 8671/1450. Let q(g) be the second derivative of 9*g + l*g**5 - 4/15*g**3 - 8/5*g**2 + 0 + 1/15*g**4. Factor q(d).
2*(d - 2)*(d + 2)**2/5
Suppose -13*d + 175 = -18*d. Let w be ((24/d)/1)/((-30)/105). Factor 12/5 - w*n + 3/5*n**2.
3*(n - 2)**2/5
Let w = 6621/5 + -46337/35. Factor 16/7*i - w*i**2 - 32/7.
-2*(i - 4)**2/7
Suppose 0 = 5*a + 46 - 56. Let v be 3 - -6*-1*a/4. Factor 0 + 2/3*u**2 + u**3 - 2/3*u**4 + v*u.
-u**2*(u - 2)*(2*u + 1)/3
Let b = 136 + -133. Suppose -3*x = 5*d - 8*x - 45, b*d + 8 = -4*x. Determine m so that 11/3*m - 6*m**d + 2/3 - 3*m**5 - 2/3*m**3 + 16/3*m**2 = 0.
-1, -2/3, -1/3, 1
Let o = -15411 + 77059/5. Factor -4/5*x**4 + 0*x - 1/5*x**2 + 0 - o*x**3.
-x**2*(2*x + 1)**2/5
Determine d so that 4*d - 85*d**4 + 4*d**3 - 19*d**2 - 2*d**3 + 12 + 89*d**4 - 3