3 + n**4 + 0*n**3 - 136*n**2.
-2*n**2*(n - 7)*(n - 2)
Let u(o) be the first derivative of 2*o**3/3 - 114*o**2 + 6498*o - 32. Factor u(q).
2*(q - 57)**2
Factor -71*s + 39*s**2 - 4*s + 36 - 3*s**4 + 22*s**3 - 19*s**3.
-3*(s - 3)*(s - 1)**2*(s + 4)
Let t(r) be the third derivative of r**5/300 - 5*r**4/12 + 125*r**3/6 - 2*r**2 + 14. Determine m so that t(m) = 0.
25
Let c(w) be the second derivative of 4/3*w**2 + 0 + 17/27*w**4 + 2/135*w**6 - 7/45*w**5 + 32*w - 34/27*w**3. Factor c(r).
4*(r - 3)*(r - 2)*(r - 1)**2/9
Let b(d) be the second derivative of -4*d + 0*d**3 - 1/16*d**4 + 0*d**2 + 0. Factor b(l).
-3*l**2/4
Let c(g) = -g**3 - 1. Let h(f) = f**3 + 5*f**2 - 5*f - 9. Let s = 51 + -52. Let k(v) = s*h(v) + 4*c(v). Factor k(n).
-5*(n - 1)*(n + 1)**2
Suppose -4*c + o = -4, -4 = -o - 0*o. Solve -3*l**3 - 33*l**2 + 20*l**2 + 15*l**c + 7*l**3 = 0 for l.
-1/2, 0
Let f = 281/54 - 280/27. Let t = f - -35/6. Solve -t - 4/9*p + 2/9*p**2 = 0 for p.
-1, 3
Let g(n) be the first derivative of -36*n + 33/5*n**5 - 97/3*n**3 + 3/2*n**6 - 29/4*n**4 + 9 + 60*n**2. Solve g(w) = 0 for w.
-3, 2/3, 1
Let f be (-4)/(6/(-9) + 0). Let g be 18/f + 1 + 0. Factor 5*l**4 - 1 - g*l**4 + 1 + l**2 - 2*l**3.
l**2*(l - 1)**2
Let o = 28 - 24. Factor -6*p**3 + 4*p**o - 9*p + 6*p**2 + 7*p - 2*p**4.
2*p*(p - 1)**3
Let c(m) be the second derivative of m**4/54 - 16*m**3/27 - 4*m**2 + 119*m + 1. Let c(d) = 0. What is d?
-2, 18
Suppose w - 9 = -2*h, 0*h - 5*w - 33 = -3*h. Suppose m = 5*x + 2, m - 8 - h = -x. Factor 2*f**2 - 9*f**2 - 12*f**2 - m*f**3 - 3*f + 4*f**2.
-3*f*(f + 1)*(4*f + 1)
Let v(f) be the first derivative of 20 - 4/3*f**3 + f**4 - 10*f**2 - 12*f. Solve v(t) = 0.
-1, 3
Solve 96/13 - 2/13*m**4 - 8*m + 24/13*m**2 + 6/13*m**3 = 0.
-4, 2, 3
Let h(l) be the first derivative of 0*l + 4/15*l**5 + 44/9*l**3 - 3 + 2*l**4 + 4*l**2. Factor h(t).
4*t*(t + 1)*(t + 2)*(t + 3)/3
Suppose -7*k**3 + 25*k**2 + 25*k - 2*k**3 + 4*k**3 - 45*k**2 = 0. What is k?
-5, 0, 1
Factor c**2 + 2/3 - 5/3*c - 1/3*c**4 + 1/3*c**3.
-(c - 1)**3*(c + 2)/3
Let h(q) be the second derivative of -q**4/48 - 16*q**3/3 - 512*q**2 + 131*q - 1. What is y in h(y) = 0?
-64
Let i(n) be the third derivative of 49*n**6/1620 + 7*n**5/135 + n**4/27 - 7*n**3/3 + 17*n**2. Let z(y) be the first derivative of i(y). Factor z(c).
2*(7*c + 2)**2/9
Let o(y) be the third derivative of y**8/672 + y**7/84 + 7*y**6/240 - y**5/120 - y**4/6 - y**3/3 + 38*y**2. Find m such that o(m) = 0.
-2, -1, 1
Let x(h) be the third derivative of 11/210*h**7 + 1/60*h**5 + 10*h**2 + 3/40*h**6 + 0 - 1/24*h**4 + 1/84*h**8 + 0*h + 0*h**3. Find v, given that x(v) = 0.
-1, 0, 1/4
Suppose 0 = 6*o - o - 20. Suppose -3*d = 2*g + 11, 2 = -o*d - 18. Solve 2*s**g + 0 + 4/5*s = 0.
-2/5, 0
Let y(a) = 8*a**4 + 18*a**3 + 45*a**2 - 81*a - 5. Let g(b) = -3*b**4 - 9*b**3 - 23*b**2 + 39*b + 2. Let q(m) = -5*g(m) - 2*y(m). Factor q(j).
-j*(j - 11)*(j - 1)*(j + 3)
Let x be (-3)/63*1*30/(-10). Let n(z) be the first derivative of 6 - x*z**3 - 9/14*z**2 - 6/7*z. Factor n(t).
-3*(t + 1)*(t + 2)/7
Suppose 5 = -5*l + 5. Suppose l = y + 6*y - 8*y. Solve -2/5*i**3 + 2/5*i**2 + y - 2/5*i**4 + 0*i + 2/5*i**5 = 0.
-1, 0, 1
Let s(a) be the first derivative of -a**6/840 + a**5/420 + a**4/168 + a**3 - 10. Let d(w) be the third derivative of s(w). Suppose d(o) = 0. What is o?
-1/3, 1
Let k(s) be the second derivative of -s**7/210 - s**6/120 + s**5/20 + 5*s**4/24 + s**3/3 - s**2 - 4*s. Let u(d) be the first derivative of k(d). Factor u(a).
-(a - 2)*(a + 1)**3
Let b = -4941/10 - -989/2. Solve 0*u + 0*u**4 + 6/5*u**3 + 4/5*u**2 - b*u**5 + 0 = 0.
-1, 0, 2
Let v be ((-5)/((-50)/(-5)))/(4/(-54)). Let r(m) be the first derivative of 5 + 9/4*m**2 + 1/4*m**3 + v*m. Factor r(j).
3*(j + 3)**2/4
Let v(r) = -3*r**2 - 5. Let s = 11 - 8. Let b(l) = 2*l**2 + 4. Let y(o) = s*v(o) + 4*b(o). Factor y(q).
-(q - 1)*(q + 1)
Suppose 5*p = y + 5, -3*p + 0*p = -5*y - 3. Let b(f) be the third derivative of 0*f - 1/540*f**6 - 1/27*f**3 + f**2 + 1/108*f**4 + y + 1/270*f**5. Factor b(w).
-2*(w - 1)**2*(w + 1)/9
Let q(a) = -a**2 - 9*a - 11. Let n be q(-7). Let w(y) be the third derivative of 0*y**4 + 4/27*y**n + 0*y + 0 - 1/90*y**5 - y**2 + 1/540*y**6. Factor w(h).
2*(h - 2)**2*(h + 1)/9
Let a be (-112)/63 - 6/(-3). Let l(y) be the third derivative of 7*y**2 + 1/45*y**5 + 1/36*y**4 - 1/180*y**6 - a*y**3 + 0 + 0*y. Solve l(p) = 0 for p.
-1, 1, 2
Let a(g) = 4*g**4 - 9*g**3 + 5*g**2 - 7*g - 7. Let o(v) = 2*v**4 - 4*v**3 + 2*v**2 - 4*v - 4. Let x(f) = 4*a(f) - 7*o(f). Suppose x(k) = 0. What is k?
0, 1, 3
Suppose -3*x + 4*x = 7*x. Let d(u) be the first derivative of 1/3*u**3 + 1/15*u**5 + 7 + 1/4*u**4 + x*u + 1/6*u**2. Solve d(a) = 0.
-1, 0
Factor 578/15 + 34*s - 22/5*s**2 + 2/15*s**3.
2*(s - 17)**2*(s + 1)/15
Let l(p) be the third derivative of 19*p**6/240 + p**5/40 - 19*p**4/48 - p**3/4 + 243*p**2. Factor l(y).
(y - 1)*(y + 1)*(19*y + 3)/2
Let l(f) be the second derivative of f**7/112 - f**6/60 - f**5/40 + f**4/16 + f**3/48 - f**2/8 - 14*f - 2. Let l(v) = 0. What is v?
-1, -2/3, 1
Factor 20*j - 75*j**3 - 240 + 100*j**2 - 121*j**2 + 5*j**4 + 201*j**2.
5*(j - 12)*(j - 2)**2*(j + 1)
Let m be (52/(-54) + 1)/(10/30). Let a(t) be the second derivative of -m*t**3 + 0 + 1/9*t**2 + 1/18*t**4 - 7*t - 1/90*t**5. Factor a(d).
-2*(d - 1)**3/9
Let l(g) = g**2 - 1. Let x(s) = -5*s**2 + 10*s - 5. Let m(q) = -4*l(q) - x(q). Suppose m(h) = 0. Calculate h.
1, 9
Suppose -2*y - 2 = 2*g, -4*y + 17*g - 12*g + 23 = 0. Factor 2*x**3 + 3/2*x**y + 0*x + 1/2*x**4 + 0.
x**2*(x + 1)*(x + 3)/2
Let l(f) be the first derivative of 11 - f**2 + 2*f**3 + 0*f - 3/2*f**4 + 2/5*f**5. Factor l(h).
2*h*(h - 1)**3
Let h(z) be the second derivative of 5*z**4/12 - 230*z**3/3 - 470*z**2 - 108*z - 3. Factor h(g).
5*(g - 94)*(g + 2)
Let s(u) be the first derivative of 5*u**3/6 - 4*u**2 + 3*u/2 - 164. Factor s(h).
(h - 3)*(5*h - 1)/2
Let b(u) be the third derivative of -u**6/540 + u**5/135 + 7*u**4/36 + 2*u**3/3 - 350*u**2. Solve b(y) = 0 for y.
-3, -1, 6
Let u be (-5 + 4)/(-2)*4. Factor 2/3 + 2/3*a**u - 4/3*a.
2*(a - 1)**2/3
Let v(r) = r**5 + r**4 + r**2 - r. Let p(y) = -y**5 - 11*y**4 - 10*y**3 + 4*y**2 + 11*y - 5. Let g(f) = p(f) + 6*v(f). Find x, given that g(x) = 0.
-1, 1
Let s(v) be the second derivative of -v**7/735 + v**6/140 - v**5/70 + v**4/84 - 4*v**3 + 21*v. Let z(o) be the second derivative of s(o). Factor z(u).
-2*(u - 1)**2*(4*u - 1)/7
Suppose -2*m = 5 - 83. Find a, given that 30*a**4 - 39*a**4 - 12*a**2 - 3*a**3 + m*a**3 - 15*a**5 = 0.
-2, 0, 2/5, 1
Suppose -39*l + 43*l - 264 = 0. Let r be 3 - l/21 - (-154)/49. Solve -2/5*v + 2/5*v**r + 6/5*v**2 - 6/5 = 0 for v.
-3, -1, 1
Factor -1/2*l**2 - 2 - 2*l.
-(l + 2)**2/2
Suppose 172*u - 183*u + 46 = -3*i, 3*u = -5*i - 34. Suppose -16/7 - 2/7*d**u + 12/7*d = 0. Calculate d.
2, 4
Factor -525*k**5 + 527*k**5 + 12*k**4 - 6*k - 6*k + 2*k - 12*k**2 + 8*k**3.
2*k*(k - 1)*(k + 1)**2*(k + 5)
Let n(c) = c**3 - c**2 + 1. Let d be n(2). Let v(u) = 4*u**2 - 13*u + 9. Let k(h) = -3*h**2 + 9*h - 6. Let r(j) = d*v(j) + 7*k(j). Let r(m) = 0. What is m?
-3, 1
Let g(z) be the third derivative of z**6/630 + 11*z**5/630 + 5*z**4/126 - 8*z**3/63 + 290*z**2. Factor g(j).
2*(j + 2)*(j + 4)*(2*j - 1)/21
Let c(i) = -8*i**2 - 2*i - 7. Let a(v) = -v**2 - v - 1. Suppose 5*k - 280 = -5*k. Let u(b) = k*a(b) - 4*c(b). Find w, given that u(w) = 0.
0, 5
Let x(r) be the second derivative of r**8/40320 - r**7/5040 + r**6/2160 - r**4/6 - 16*r. Let d(l) be the third derivative of x(l). Determine b so that d(b) = 0.
0, 1, 2
What is n in -56*n**2 - 36*n - 85*n**2 - 8*n - 5*n**3 - 56*n + 36*n**2 = 0?
-20, -1, 0
Suppose -4*g = -8*g + 20. Suppose 4*x - i + 2*i = 13, -3*x + 14 = g*i. What is a in 5*a**3 + 2*a**2 - 2*a**x + a**3 - a**3 + a**4 = 0?
-2, -1, 0
Let o(c) be the second derivative of 2*c**7/7 - 16*c**6/5 + 143*c**5/15 + 8*c**4/9 - 32*c**3/9 - 411*c. Suppose o(j) = 0. Calculate j.
-1/3, 0, 1/3, 4
Let p(d) = -10*d**3 + 210*d**2 - 190*d - 5. Let s(y) = 15*y**3 - 315*y**2 + 286*y + 7. Let g(x) = 7*p(x) + 5*s(x). Find z such that g(z) = 0.
0, 1, 20
Let l(x) be the first derivative of 5*x**4 + 184*x**3 + 1848*x**2 - 1568*x - 455. Determine a, given that l(a) = 0.
-14, 2/5
Let r(k) be the second derivative of -2/3*k**2 + 1/54*k**4 + 6*k + 0 + 5/27*k*