Let t(p) be the first derivative of 2*p**6/15 - p**5/5 + 16*p - 23. Let a(h) be the first derivative of t(h). Let a(k) = 0. What is k?
0, 1
Factor -75/2*p**2 + 39/2*p + 0 + 3/2*p**4 + 33/2*p**3.
3*p*(p - 1)**2*(p + 13)/2
Let o(v) be the third derivative of -v**8/36960 + v**7/3465 - v**6/792 + v**5/330 - v**4/2 + 2*v**2. Let w(n) be the second derivative of o(n). Factor w(m).
-2*(m - 2)*(m - 1)**2/11
Let m be (33/13 - 3)*-61. Let h = m + -28. Factor -2/13*l**2 - 2/13*l**3 + h*l + 2/13.
-2*(l - 1)*(l + 1)**2/13
Let r(q) be the first derivative of q**6/6 - 5*q**5/4 + 15*q**4/4 - 35*q**3/6 + 5*q**2 - 12*q + 4. Let h(x) be the first derivative of r(x). Factor h(t).
5*(t - 2)*(t - 1)**3
Suppose 0 = 7*r - 5*r - 6. Suppose 4*w - 9 = r. Factor 5*s**2 + 2*s**2 + 4*s - w*s**2.
4*s*(s + 1)
Let h(d) be the second derivative of -3*d**5/20 - 3*d**4 - 21*d**3/2 - 15*d**2 + 20*d. What is w in h(w) = 0?
-10, -1
Let u be 0/(3/(-8) - 65/104). Let d(h) be the third derivative of u*h - 9/8*h**3 - 1/80*h**5 + 4*h**2 + 0 - 3/16*h**4. Factor d(p).
-3*(p + 3)**2/4
Let g(j) be the first derivative of 132*j**5/5 + 399*j**4/4 + 88*j**3 - 21*j**2/2 - 18*j + 292. Suppose g(n) = 0. What is n?
-2, -1, -3/11, 1/4
Suppose -2/5*r**2 + 8/5 + 6/5*r = 0. What is r?
-1, 4
Let s(i) be the second derivative of 5*i**4/12 - 10*i**3/3 - i + 46. Determine j so that s(j) = 0.
0, 4
Let x(f) be the first derivative of -2*f**5/85 - 7*f**4/34 + 16*f**3/51 - 324. What is o in x(o) = 0?
-8, 0, 1
Let o(f) be the third derivative of -1/10*f**4 - 1/100*f**5 + 0 + 0*f + 0*f**3 + 7*f**2. Determine b so that o(b) = 0.
-4, 0
Let r = -23 + 19. Let b be (-7 - -3) + 10 + r. Factor 3*w**2 + 12*w - b - 10 - w**2 - 5*w**2.
-3*(w - 2)**2
Let j be 708/(-84) + 8 + -1 + 2. Determine k, given that 8/7*k**2 - 4/7*k**3 - 4/7 + 2/7*k**5 + 2/7*k - j*k**4 = 0.
-1, 1, 2
Let p(w) = 4*w**4 + w**3 - 32*w**2 + 43*w + 5. Let j(t) = 2*t**4 + t**3 - 16*t**2 + 21*t + 3. Let x = -34 - -40. Let b(n) = x*p(n) - 10*j(n). Factor b(y).
4*y*(y - 2)**2*(y + 3)
Let s(i) = 9*i**4 + 336*i**3 - 1440*i**2 + 1233*i + 3000. Let a(m) = m**4 + 42*m**3 - 180*m**2 + 154*m + 375. Let k(o) = 33*a(o) - 4*s(o). Factor k(g).
-3*(g - 5)**3*(g + 1)
Let a = 6728/77 - 936/11. Suppose 12/7*r - a - 2/7*r**2 = 0. What is r?
2, 4
Let k(r) be the third derivative of -r**5/30 + 5*r**4/12 - 4*r**3/3 - 121*r**2. Factor k(s).
-2*(s - 4)*(s - 1)
Let s(u) = 3 + 9 - 15 + 3*u - 6*u. Let x be s(-3). Find n such that -3/2*n**2 - x*n - 9/2 = 0.
-3, -1
Let t(h) be the second derivative of 0*h**3 + 34*h + 1/4*h**5 + 5/42*h**7 - 1/3*h**6 + 0*h**4 + 0*h**2 + 0. Let t(j) = 0. Calculate j.
0, 1
Let p(d) be the first derivative of 1/4*d**3 - 13 + 1/8*d**2 + 0*d + 3/16*d**4 + 1/20*d**5. Find g such that p(g) = 0.
-1, 0
Let o = -9 - -18. Suppose -10*b + 2 = -o*b. Suppose -c**5 + c**5 - 2*c**5 + b*c**2 - 2 - 3*c + 4*c**3 + c**5 = 0. Calculate c.
-1, 1, 2
What is k in -326*k**2 + 19*k**3 + 990*k - 58*k**2 - 94 - 6 + 19*k**3 = 0?
2/19, 5
Let d(n) be the second derivative of n**4/6 - 12*n**3 + 128*n**2 + 2*n - 145. Factor d(j).
2*(j - 32)*(j - 4)
Let i(n) be the third derivative of -3*n**5/100 + 43*n**4/120 + n**3/3 + 17*n**2. Find w such that i(w) = 0.
-2/9, 5
Suppose 3*d + 2*g = 33, -6*g = -5*d - g + 30. Factor -d*r**2 + 8*r**4 - 3*r**4 - 6*r**2 - 90*r + 20*r**3.
5*r*(r - 2)*(r + 3)**2
Let d(x) be the third derivative of -x**8/112 + 6*x**7/35 + x**6/20 - 6*x**5/5 - x**4/8 + 6*x**3 - 2*x**2 - 107. Determine i, given that d(i) = 0.
-1, 1, 12
Suppose 0 = -5*t + 10*t - 10. Factor -7 + 2*l + 2 - 1 + 2*l + t*l**2.
2*(l - 1)*(l + 3)
Factor -2/11*q**3 + 40/11*q**2 + 86/11*q + 4.
-2*(q - 22)*(q + 1)**2/11
Let d be 0 + 9 - 15/3. Let h(f) be the second derivative of 0 + 1/27*f**3 + 0*f**2 - 2*f + 0*f**d - 1/90*f**5. Suppose h(s) = 0. What is s?
-1, 0, 1
Let n(r) be the second derivative of 0*r**3 + 0*r**5 + 0 + 0*r**2 - 2/15*r**6 + 1/3*r**4 - 6*r. Let n(u) = 0. What is u?
-1, 0, 1
Suppose -3*f - 4*b = -22, f = -0*b + 2*b - 6. Factor -15*s**f + 10*s**2 - 8*s + 8*s - 10*s - 5.
-5*(s + 1)**2
Suppose 28*h - 104 = 15*h. Let z = h + -5. Factor 0 + 5*w**z + 0*w - 5/2*w**2 - 5/2*w**4.
-5*w**2*(w - 1)**2/2
Suppose -1/9*z**2 - 2/3 - 7/9*z = 0. What is z?
-6, -1
Let f(x) be the second derivative of -x**5/210 + 4*x**3/21 - 21*x**2/2 - 15*x. Let w(i) be the first derivative of f(i). Find h, given that w(h) = 0.
-2, 2
Let j(x) be the first derivative of -x**3/12 + 27*x**2/8 + 158. Factor j(k).
-k*(k - 27)/4
Suppose 4*b - 15 - 1 = 0. Suppose 0 = -b*a + 8 + 40. Let -86*c**2 - 10*c**2 + 36*c + a*c**3 + 27*c**4 + 33*c**3 = 0. What is c?
-3, 0, 2/3
Suppose -5*h - 1 = -16. Suppose 142 - 448 = -153*g. Factor 3/7 - 6/7*a**g + 3/7*a**4 + 0*a**h + 0*a.
3*(a - 1)**2*(a + 1)**2/7
Let i = -1275 - -3841/3. Find a such that -128/9*a + 32/9 + 8/3*a**5 + 160/9*a**3 - i*a**2 + 122/9*a**4 = 0.
-2, 1/4, 2/3
Let s(n) = 10*n**2 + 8*n - 6. Let l(a) = a - 7. Let b be l(-5). Let f(t) = t**2. Let z(p) = b*f(p) + s(p). Suppose z(q) = 0. What is q?
1, 3
Let v(g) = 2*g**3 + 4*g**2 - 9*g - 15. Let s be v(-2). Factor -2/5*f**2 + 0 + 0*f - 1/5*f**s.
-f**2*(f + 2)/5
Let q = -28 - -59. Factor 3*y**2 + 16*y - q*y + 14*y + 7*y.
3*y*(y + 2)
Suppose -p + 1 = 2*c, 2*c + 5*p = -c - 2. Factor -c - k**2 - 30*k - 2 + 0*k**2 + 34*k.
-(k - 3)*(k - 1)
Let k(f) be the third derivative of f**6/60 + 3*f**5/10 + 9*f**4/4 + 9*f**3 + 3*f**2 - 22. Let k(x) = 0. Calculate x.
-3
Let p be 15/(-18)*25/(-10)*72/450. Factor -2/3 + p*b**2 - 1/3*b.
(b - 2)*(b + 1)/3
Let u = -12682 + 12685. Factor 4/15*s**u + 2/15*s**4 + 0*s - 2/5*s**2 + 0.
2*s**2*(s - 1)*(s + 3)/15
Let a = -19 - -21. Factor a*k**5 + 6*k**2 - 42*k**3 + 36*k**3 - 2*k**2.
2*k**2*(k - 1)**2*(k + 2)
Factor 410*o**3 - 414*o**3 - 6248*o - 2216*o + 368*o**2.
-4*o*(o - 46)**2
Let n = -2556 - -2558. Solve 4/3 - 2/3*y**n + 2/3*y = 0 for y.
-1, 2
Let w = -26305/9 - -2923. Suppose 2/9 + 2/9*s - 2/9*s**2 - w*s**3 = 0. What is s?
-1, 1
Let j be -11 + 30 - 1352/78. Factor -j + 5*q**4 - 10/3*q**3 - 5/3*q**5 - 10/3*q**2 + 5*q.
-5*(q - 1)**4*(q + 1)/3
Let b = -118 + 118. Suppose -8*i + 10*i = b. Suppose -1/4 + 1/4*m**2 + i*m = 0. Calculate m.
-1, 1
Let z(l) = 3*l**2 + l + 8. Let g(p) be the first derivative of p**3/3 + 4*p - 18. Let m(n) = -9*g(n) + 4*z(n). Factor m(q).
(q + 2)*(3*q - 2)
Let p be (((-220)/36)/5)/((-2)/3). Let l = p - 4/3. Factor -l*a**2 + 1 + 1/2*a.
-(a - 2)*(a + 1)/2
Let a = 36/61 + -587/1098. Let g(l) be the first derivative of -2/9*l**3 + 1/4*l**4 - 6 + 0*l**5 + 0*l + 0*l**2 - a*l**6. Suppose g(z) = 0. Calculate z.
-2, 0, 1
Suppose 3*i + h = 47, -5*i + 2*h = 7*h - 85. Factor 2*a**2 - i*a**4 - 7*a**2 + 6*a**5 - a**5 + 15*a**3.
5*a**2*(a - 1)**3
Let y(u) = -2*u - 4*u**2 + 2*u**4 + 10*u**3 + 2*u**2 + 4*u**4. Let k(p) = -13*p**4 - 21*p**3 + 5*p**2 + 5*p. Let d(w) = 2*k(w) + 5*y(w). What is g in d(g) = 0?
-2, 0
Let b(z) be the second derivative of -z**5/60 + z**4/9 + z**3/18 - 2*z**2/3 + 18*z. Factor b(u).
-(u - 4)*(u - 1)*(u + 1)/3
Factor -15/8*f + 7/8*f**2 + 9/8 - 1/8*f**3.
-(f - 3)**2*(f - 1)/8
Let d(m) = -4*m**3 - 2*m**2. Let w(s) = -s**2 - 11*s - 16. Let o be w(-9). Let u(i) = i**3. Let y(h) = o*d(h) + 12*u(h). Let y(x) = 0. What is x?
0, 1
Let z(t) be the third derivative of 1/10*t**5 - 1/60*t**6 + 0*t**4 - 27*t**2 + 0*t - 4/3*t**3 + 0. What is b in z(b) = 0?
-1, 2
Let k(h) be the first derivative of 8/9*h - 4/9*h**2 - 3 + 2/27*h**3. Find l such that k(l) = 0.
2
Let g be ((-16)/(-10))/(-1)*18/(-7 - 137). Let -1/5*l**2 - g*l + 2/5 = 0. What is l?
-2, 1
Let c(u) = 67*u + 8044. Let n be c(-120). Factor -4/3*y**3 + 0*y - 4/3*y**5 + 0 - 8/3*y**n + 0*y**2.
-4*y**3*(y + 1)**2/3
Let b be ((-12)/15)/((-2)/5). Let c be 2/4 - (25/14)/5. Factor -2/7 + c*j + 1/7*j**b.
(j - 1)*(j + 2)/7
Let d(p) = -13*p**3 - 11*p**2 + 29*p + 11. Let u(w) = -7*w**3 - 6*w**2 + 15*w + 6. Let q(c) = 6*d(c) - 11*u(c). Factor q(j).
-j*(j - 3)*(j + 3)
Factor 3*u + 10 - 26*u**2 - 36*u**2 + 56*u**2 + u**3.
(u - 5)*(u - 2)*(u + 1)
Let u(x) be the second derivative of -33*x + 0 + 0*x**2 + 1/12*x**4 - 1/40*x**5 + 0*x**3. Factor u(h).
-h**2*(h - 2)/2
Let d(n) be the third derivative of -n**8/336 + n**7/56 - n**5/6 - 17*n**3/6 - 14*n**2. Let a(y) be the first derivative of d(y). Factor a(w).
-5*w*(w - 2)**2*(w + 1)
Let c(m) = -m**2 + 1