*f**3. Let d(w) = 0. What is w?
1/6, 1
Suppose 4*l + 4 = -4*h, -h - 2*l + 11 = -5*l. Factor -7*q - 2*q**4 + 12*q**h - q**4 + 7*q.
-3*q**2*(q - 2)*(q + 2)
Let b(a) be the third derivative of -a**8/560 - a**7/140 - 9*a**3/2 + 7*a**2 - 3. Let c(z) be the first derivative of b(z). Factor c(m).
-3*m**3*(m + 2)
Suppose 20405 - 20456 = -17*g. Factor 0 + 2/9*q**g + 4/9*q - 2/3*q**2.
2*q*(q - 2)*(q - 1)/9
Let a(h) be the second derivative of 8/15*h**6 + 2/21*h**7 + 18*h + 0 - 10/3*h**3 - 4*h**2 - 2/3*h**4 + 4/5*h**5. Determine m so that a(m) = 0.
-2, -1, 1
Let z(m) be the second derivative of 0*m**2 + 0*m**3 - 3/4*m**4 + 0 + 3/20*m**5 + 3*m. Let v(x) = -x**2 - x. Let k(j) = 3*v(j) - z(j). Factor k(s).
-3*s*(s - 1)**2
Suppose v + 3*v = 32. Suppose -4*c = -v - 16. Factor 3*h**2 - 1 - 5 + c - 2*h - h**3.
-h*(h - 2)*(h - 1)
Let s(i) = -5*i - 6. Let r be s(-2). Let z be (-2 + 0/6)*(-1)/r. Suppose 3*g**3 + 0 - 11/4*g**2 + z*g + 9/4*g**4 = 0. Calculate g.
-2, 0, 1/3
Let h(t) = 3*t**3 - t**2 + 4. Let r be h(2). Factor -4*x + 11*x**3 - r - x**3 + 92*x - 74*x**2.
2*(x - 6)*(x - 1)*(5*x - 2)
Let r(z) be the second derivative of 3/4*z**3 + 0 + 3/2*z**2 - 1/20*z**6 - 5*z - 1/8*z**4 - 9/40*z**5. Let r(q) = 0. Calculate q.
-2, -1, 1
Suppose -9*k**2 - 3*k**2 + 184*k + 8*k**2 - 2116 = 0. What is k?
23
Let b = 26 + -22. Suppose 1 + 7 = b*z. Solve 0 + 0*d + 27/4*d**3 - 3/2*d**z - 21/4*d**4 = 0 for d.
0, 2/7, 1
Let r(v) = -v**4 + 3*v**3 - 2*v**2 - 3*v. Let f = 75 + -79. Let t(y) = -2*y**4 + 4*y**3 - 2*y**2 - 4*y. Let k(s) = f*r(s) + 3*t(s). What is w in k(w) = 0?
-1, 0, 1
Let b(t) be the second derivative of 16/3*t**3 + 0 - 1/3*t**4 - 32*t**2 - 26*t. Factor b(u).
-4*(u - 4)**2
Let d(s) = -s**2 - 52*s - 2. Let u(x) = -x**2 - x - 1. Let l(i) = d(i) - 2*u(i). Find n, given that l(n) = 0.
0, 50
Suppose -w - 65 = -69. Determine x, given that -34 + 15*x + 9*x - w*x**2 + 2 = 0.
2, 4
Let q(o) = -14*o**2 + 8*o + 4. Suppose -x + 4*x = 0. Suppose -3*s = -3 - x. Let l(z) = z**2 - 1. Let j(b) = s*q(b) + 12*l(b). Factor j(a).
-2*(a - 2)**2
Let r(c) be the first derivative of -2*c**3/33 - 32*c**2/11 - 512*c/11 + 15. Let r(s) = 0. Calculate s.
-16
Let d be 3*(15/(-3))/(-5). Suppose d - 20*t + 27*t**2 + 3 + 47*t = 0. What is t?
-2/3, -1/3
Let l(u) be the third derivative of -5*u**8/1344 + u**7/14 - 23*u**6/48 + 5*u**5/4 - 125*u**4/96 - 18*u**2. Find n, given that l(n) = 0.
0, 1, 5
Let v = 425 + -1270/3. Let p = 15 - 44/3. Find i such that 7/3*i - 3*i**2 - 2/3 + v*i**3 - p*i**4 = 0.
1, 2
Let g(z) be the first derivative of -z**5/10 + 7*z**4/12 - z**3/3 - 3*z**2/2 + 32*z + 2. Let x(j) be the first derivative of g(j). Let x(s) = 0. What is s?
-1/2, 1, 3
Let r(w) = -135*w**4 - 671*w**3 - 994*w**2 - 576*w - 124. Let t(a) = -135*a**4 - 670*a**3 - 995*a**2 - 575*a - 125. Let f(o) = -5*r(o) + 4*t(o). Solve f(y) = 0.
-3, -2/3
Let y = 93 + -89. Suppose 2*o + 2 = y*g, 0*o - 15 = -3*o. Factor -3/5*x**g + 12/5 + 12/5*x - 3/5*x**2.
-3*(x - 2)*(x + 1)*(x + 2)/5
Let l(y) be the third derivative of -y**8/1848 + y**7/1155 + y**6/66 + 4*y**5/165 + 2*y**2 - 54*y. Find p, given that l(p) = 0.
-2, -1, 0, 4
Let l(d) be the first derivative of 2*d**3/21 - 50*d/7 + 106. Factor l(s).
2*(s - 5)*(s + 5)/7
Factor 14*n**2 - 2*n**3 - 18*n**2 - 2*n**3 + 27*n**2 - 21*n**2 + 2*n**4.
2*n**2*(n - 1)**2
Let g(j) be the first derivative of j**5/20 + j**4/60 - j**3/6 - j**2/10 + 8*j - 4. Let n(w) be the first derivative of g(w). Factor n(v).
(v - 1)*(v + 1)*(5*v + 1)/5
Determine w so that -7/3*w**3 + 0 - 12*w**2 + w**4 - 20/3*w = 0.
-2, -2/3, 0, 5
Let c(d) be the second derivative of d**7/273 - 3*d**5/130 + d**4/39 + 81*d. Factor c(h).
2*h**2*(h - 1)**2*(h + 2)/13
Determine a so that 5/6*a**4 - 15/2*a + 0 - 7/2*a**2 + 31/6*a**3 - 1/3*a**5 = 0.
-3, -1, 0, 3/2, 5
Let z(y) = -y**3 - 3*y**2 - 2*y - 16. Let p(q) = -2*q**3 - 6*q**2 - 4*q - 28. Let n(r) = -4*p(r) + 7*z(r). Let n(f) = 0. Calculate f.
-2, -1, 0
Let u be (-2 + -2)/(20/(-2) - -7). Let q = 1552/465 - 2/465. Suppose u*c**2 + 16/3*c**3 - q*c + 2/3 = 0. Calculate c.
-1, 1/4, 1/2
Let r(y) = 3*y**3 - 334*y**2 + 107*y + 446. Let f be r(111). Factor 1/2*u**f - u - 3/2.
(u - 3)*(u + 1)/2
Factor 0 + 3/2*s**4 - 48*s**3 + 93/2*s**2 + 0*s.
3*s**2*(s - 31)*(s - 1)/2
What is u in 6*u**3 + 165*u**2 + 144*u**2 - 6*u**3 - 3*u**3 - 8109*u + 7803 = 0?
1, 51
Let w(h) be the first derivative of 4*h**3/39 - 5*h**2/13 - 6*h/13 + 79. Suppose w(v) = 0. Calculate v.
-1/2, 3
Let r(n) be the second derivative of 1/195*n**6 - 10*n + 0 + 1/39*n**3 - 1/130*n**5 - 1/78*n**4 + 0*n**2. Factor r(j).
2*j*(j - 1)**2*(j + 1)/13
Solve -h**4 - 241*h + 207*h - 366*h - 28*h**3 + 47*h**2 - 287*h**2 + 2000 = 0 for h.
-10, 2
Let r(p) be the first derivative of 2*p**6/3 + 52*p**5/5 + 9*p**4 - 148*p**3/3 - 20*p**2 + 96*p - 513. Suppose r(i) = 0. What is i?
-12, -2, -1, 1
Let p(l) be the second derivative of 3*l**5/80 - 3*l**3/8 - 3*l**2/4 + 20*l + 3. Suppose p(v) = 0. Calculate v.
-1, 2
Let s(q) be the first derivative of 12*q**5/7 - q**4/7 - 136*q**3/7 + 200*q**2/7 - 96*q/7 + 307. Solve s(o) = 0.
-3, 2/5, 2/3, 2
Let j(v) = -v - 2. Let q be j(9). Let c = q + 14. Let 0*g + 0 + 8/19*g**2 - 16/19*g**c - 2/19*g**5 + 10/19*g**4 = 0. What is g?
0, 1, 2
Let u = 565 + -563. Let q(c) be the first derivative of 0*c**u - 5 + 0*c**3 + 1/2*c**4 + 2/5*c**5 + 0*c. Let q(x) = 0. Calculate x.
-1, 0
Let u(m) = -m + 117. Let c be u(8). Suppose 111*q = c*q. Factor q + 3/4*n**3 - 3/8*n**4 + 0*n + 0*n**2.
-3*n**3*(n - 2)/8
Let n be (4 + -6)*3/(-42). Let r(g) be the second derivative of n*g**2 - 2*g + 0 - 1/3*g**3 + 2/7*g**4. Factor r(k).
2*(3*k - 1)*(4*k - 1)/7
Let m = 58772/5 - 11754. Solve -6/5*n - m*n**2 + 8/5 = 0 for n.
-4, 1
Suppose -96 + 16 = -5*y. Suppose 11*f + 10 = y*f. Let -2/9 + 2/9*z**f + 2/9*z - 2/9*z**3 = 0. Calculate z.
-1, 1
Suppose -1 = -4*p - 2*n + 3, 0 = -3*p - 4*n - 7. Let x(r) be the first derivative of 0*r**p - 2/5*r**5 + 0*r**2 + 3 + 1/2*r**4 + 0*r. Factor x(l).
-2*l**3*(l - 1)
Suppose -204 = i - 7*i. Let g be 3/(60/i) - (-6)/(-12). Suppose -6/5*v + g*v**2 - 2/5*v**3 + 2/5 = 0. What is v?
1
Let f(n) be the second derivative of -n**6/30 - n**5/5 + n**4/6 + 2*n**3 - 9*n**2/2 - 109*n. Suppose f(o) = 0. What is o?
-3, 1
Let w(k) = 2*k + 2. Let g be w(-2). Let n be g*(-8)/4 - 2. Solve 4 + 16*m + 10*m**2 + 2*m**n + 4*m**2 = 0.
-1/2
Let r(p) be the first derivative of -5*p**4/4 + 35*p**3/3 - 10*p**2 - 60*p - 67. Factor r(s).
-5*(s - 6)*(s - 2)*(s + 1)
Let w be (-11 + (-644)/(-60))*-10. Factor 4/3*y - 8/3*y**2 + w*y**4 + 0*y**3 + 0 - 4/3*y**5.
-4*y*(y - 1)**3*(y + 1)/3
Let g(z) = 2*z**3 + 4*z**2 - 4*z + 31. Let w(l) = -l**3 + l + 1. Let i(d) = -g(d) - 4*w(d). Let b(u) be the first derivative of i(u). What is h in b(h) = 0?
0, 4/3
Let t(a) be the second derivative of a**4/3 + 62*a**3/3 + 116*a**2 - 66*a + 2. Factor t(l).
4*(l + 2)*(l + 29)
Let b = -6 + 10. Let l = b + -2. Suppose -33 - z + 6 - 3*z**l - 7*z - 10*z = 0. What is z?
-3
Solve -190*c**3 - 20 + 149*c**3 - 3*c**5 - 3*c**2 + 23*c**4 + 5*c + 39*c = 0.
-1, 2/3, 1, 2, 5
Let s(d) = 13*d + 1032. Let q be s(0). Suppose 2*f - q*f**2 - 4*f**3 + 2*f**5 + 1032*f**2 = 0. What is f?
-1, 0, 1
Let x(f) be the first derivative of 2*f**5/135 + 17*f**4/108 + 4*f**3/27 + 15*f**2/2 + 10. Let o(w) be the second derivative of x(w). What is a in o(a) = 0?
-4, -1/4
Let p be 0 + ((-1814)/454 + 4)/1. Let g = p + 899/2043. Let 0 - 2/9*u**4 + g*u**3 - 4/9*u + 2/9*u**2 = 0. Calculate u.
-1, 0, 1, 2
Let h(z) be the first derivative of -z**4/16 - z**3/2 - 3*z**2/8 + 5*z/2 - 327. Factor h(f).
-(f - 1)*(f + 2)*(f + 5)/4
Suppose 30*i + 90 = 83*i - 16. Factor 7/2*h**i + 5/2*h**4 + 0 + h + 1/2*h**5 + 9/2*h**3.
h*(h + 1)**3*(h + 2)/2
Determine i so that 22*i + 22*i - 38*i + 3*i**2 + 0*i**2 - 45 = 0.
-5, 3
Let j(n) = n**5 + n**3 - 1. Let f(o) = 5*o**5 + 20*o**3 - 5*o - 10. Let g(c) = f(c) - 10*j(c). Factor g(x).
-5*x*(x - 1)**2*(x + 1)**2
Let s be 3 + ((-1)/60)/((-48)/(-8440)). Let n(v) be the third derivative of -s*v**4 + 1/180*v**6 + 1/9*v**3 + 0 + 0*v + 6*v**2 + 1/180*v**5. Factor n(o).
(o - 1)*(o + 2)*(2*o - 1)/3
Find i such that 0*i - 4/3*i**5 - 20/3*i**4 - 4*i**3 + 0 + 12*i**2 = 0.
-3, 0, 1
Solve 1/2*m**2 - 9/2*m + 7 = 0 for m.
2, 7
Let p(v) be the third derivative of v**7/840 - v**6/480 - 3*v