d f, given that k(f) = 0.
-1, -1/3, 0
Let x = 496 - 496. Let t(g) be the second derivative of 1/6*g**4 + x + 7*g + 10/27*g**3 + 1/3*g**2 + 1/45*g**5. Factor t(b).
2*(b + 1)*(b + 3)*(2*b + 1)/9
Let h = -67598/19 - -3558. Factor 2/19*w**2 + 2/19*w - h.
2*(w - 1)*(w + 2)/19
Suppose 0 = 4*t + 2*p - 2, 1 = 3*t + 5*p - 4*p. Let g(y) be the first derivative of -1/6*y**2 + 3 + t*y - 1/6*y**3 + 1/3*y**4 - 1/10*y**5. Solve g(v) = 0 for v.
-1/3, 0, 1, 2
Let h = 1798/2751 - -12/917. Factor 1/3*g**2 - 1/3*g**4 + 0 - 2/3*g**3 + h*g.
-g*(g - 1)*(g + 1)*(g + 2)/3
Factor 3/4*c + 1/2*c**2 + 0 - 1/4*c**3.
-c*(c - 3)*(c + 1)/4
Factor 3*y**2 + 8*y**3 - y**2 - 2*y**4 - 12*y - 2*y**2 - 2*y**2.
-2*y*(y - 3)*(y - 2)*(y + 1)
Suppose 15*y = 5*z + 11*y - 20, 3*z - 10 = 2*y. Let v(s) be the second derivative of 0*s**2 + 0 + 1/15*s**6 + z*s**3 - 4*s + 0*s**5 + 0*s**4. Factor v(q).
2*q**4
Suppose 4*y = -y + i + 28, 0 = 3*y - i - 18. Factor 0 + 9/2*t**4 + 0*t + 9/2*t**3 + 3/2*t**2 + 3/2*t**y.
3*t**2*(t + 1)**3/2
Let j = 226 - 222. Let m(g) be the third derivative of 0*g + 1/12*g**3 - 1/240*g**5 - 3*g**2 + 0 - 1/96*g**j. Factor m(d).
-(d - 1)*(d + 2)/4
Let d(k) = 217*k + 1521. Let a be d(-7). Let 3*u + 0 + 21/2*u**a - 3*u**3 - 21/2*u**4 = 0. What is u?
-1, -2/7, 0, 1
Let w(a) be the first derivative of a**4/10 + 2*a**3/3 - 56*a**2/5 - 24*a - 316. Factor w(s).
2*(s - 6)*(s + 1)*(s + 10)/5
Suppose 5*d + 4183 - 4213 = 0. Suppose -d*y - 4/3 - 14/3*y**2 = 0. What is y?
-1, -2/7
Let p(a) be the first derivative of -2*a**5/5 - 7*a**4/2 + 8*a**3 + 176*a**2 + 640*a + 131. Find q, given that p(q) = 0.
-4, 5
Let w(k) = -12*k**2 - 84*k + 285. Let m be -9 + 0*(-2)/10. Let l(q) = 7*q**2 + 42*q - 142. Let n(d) = m*l(d) - 5*w(d). Factor n(o).
-3*(o - 7)**2
Let a(f) be the first derivative of f**3/3 - 7*f**2/2 + 11*f - 26. Let m be a(6). Suppose 2/5*v**3 + 0*v - 3/5*v**4 + 0 - v**m + 0*v**2 = 0. What is v?
-1, 0, 2/5
Let k(s) = 7520*s**3 + 39468*s**2 + 11644*s + 880. Let z(c) = -1367*c**3 - 7176*c**2 - 2117*c - 160. Let w(v) = 5*k(v) + 28*z(v). Determine h so that w(h) = 0.
-5, -2/13
Let d(y) = 6*y**3 + 10*y**2. Let q(u) = -5*u**3 - 10*u**2. Let o(j) = 3*d(j) + 4*q(j). Suppose o(a) = 0. Calculate a.
-5, 0
Let q = -46/5 - -28/3. Let o be (3 - 6)/((-9)/2). Factor -q*l**3 - o*l**2 - 14/15*l - 2/5.
-2*(l + 1)**2*(l + 3)/15
Let s be 2/2 + 1 + 1. Let o = 33 + -23. Factor -3*j**2 + 13*j - 3 + s*j - o*j.
-3*(j - 1)**2
Factor 3*j**3 - 110 - 192*j - 18*j**2 - 26 - 2*j**3 + 300*j - 80.
(j - 6)**3
Let q(a) = -64*a - 17 + 78 + 72 + 3*a**2. Let f = 2 - 0. Let i(v) = 2*v**2 - 32*v + 66. Let l(x) = f*q(x) - 5*i(x). What is b in l(b) = 0?
4
Factor -45*a**2 - 5*a**4 - 10*a + 6*a**4 + 19*a**4 - 15*a**3.
5*a*(a - 2)*(a + 1)*(4*a + 1)
Let h = 5/53 - 127/1908. Let l(y) be the second derivative of -h*y**4 - 3/2*y**2 + 4*y + 0 - 1/3*y**3. Factor l(d).
-(d + 3)**2/3
Suppose n + 1 + 5 = 2*h, -3*h = -3*n - 6. Let j(u) be the first derivative of -4/3*u**3 + 0*u + n*u**2 + 1. Factor j(a).
-4*a*(a - 1)
Let n(b) = 3*b**2 - 4*b - 16. Let j(d) = 21*d**2 - 27*d - 111. Let i(t) = -4*j(t) + 27*n(t). Factor i(w).
-3*(w - 2)*(w + 2)
Suppose 12*d**4 - 1182*d**3 + 12 - 1189*d**3 - 3*d**5 + 2377*d**3 - 24*d**2 - 3*d = 0. What is d?
-1, 1, 4
Let p = 5 - 2. Suppose p*r + 55 = 7*z - 3*z, -95 = -5*z - 5*r. Factor v**3 + 6*v + 12*v**2 + z + 23*v - 5*v + v**3.
2*(v + 2)**3
Let g = -1548 + 222913/144. Let t(c) be the third derivative of -1/720*c**6 + 0 + 0*c + 3*c**2 + 0*c**3 + g*c**4 + 0*c**5. Let t(b) = 0. Calculate b.
-1, 0, 1
Let v(q) = -2*q**3 + 2*q**2 + q - 20. Let o be v(4). Let x = o - -114. Factor 0 + 3/5*m**x - 3/5*m.
3*m*(m - 1)/5
Factor -1268*l + 1258*l - 4*l**4 + 15*l**2 - l**4.
-5*l*(l - 1)**2*(l + 2)
Let s(n) be the first derivative of -n**6/6 + 9*n**5/10 + 5*n**4/2 - 2*n**3 + 105. Let s(f) = 0. What is f?
-2, 0, 1/2, 6
Factor 2/5 + 4*n**3 + 2*n**4 + 2/5*n**5 + 4*n**2 + 2*n.
2*(n + 1)**5/5
Let n = -6767 - -40603/6. Factor -1/6*s**4 + n*s**2 + 1/3*s + 0 - 1/3*s**3.
-s*(s - 1)*(s + 1)*(s + 2)/6
Factor 24/5*n + 0 - 2/5*n**2.
-2*n*(n - 12)/5
Let x = 2481 + -2481. Factor 0*v + x + 1/4*v**3 - 1/2*v**2.
v**2*(v - 2)/4
Let p be (0 + -4 + 2)*(46 + -48). Let s(w) be the first derivative of -3/5*w**4 + 11/15*w**3 - 1/25*w**5 + 0*w + 2/15*w**6 - 1/5*w**2 - p. Solve s(y) = 0 for y.
-2, 0, 1/4, 1
Let m(o) be the first derivative of -3*o**4/4 - 2*o**3 + 9*o**2/2 + 24. Suppose m(q) = 0. What is q?
-3, 0, 1
Suppose 3*j + 7 = -3*v + 1, -5*j + 5*v = -30. Find b such that -18*b**4 + 39*b**3 + 9*b**j + b**5 + 2*b**5 - 8*b + 20*b - 45*b**2 = 0.
0, 1, 2
Let g(n) be the third derivative of -1/156*n**4 + 0 + 0*n**3 + 1/390*n**5 + 0*n + 4*n**2. Factor g(z).
2*z*(z - 1)/13
Let l be ((-690)/(-1932))/((-41)/(-12) + -3). Factor l*a**2 + 2/7 - 8/7*a.
2*(a - 1)*(3*a - 1)/7
Suppose 4*i + 29 = -3. Let z be 46/14 + i/28. Factor -h**2 + 0 + 1/2*h**z + 0*h.
h**2*(h - 2)/2
Let l(s) be the first derivative of 0*s**3 + 0*s + 1/6*s**2 - 1/12*s**4 + 1. Factor l(i).
-i*(i - 1)*(i + 1)/3
Find i such that 202/15*i**2 - 14/5*i**4 + 8/15 + 38/15*i**5 - 32/5*i - 22/3*i**3 = 0.
-2, 2/19, 1
Let o = -568/679 + 192/97. Let 18/7*v**3 - 18/7*v + 4/7*v**2 - o*v**4 + 4/7 = 0. Calculate v.
-1, 1/4, 1, 2
Factor -24131 - 24*z + 24131 + 3*z**3 - z**3 - 8*z**2.
2*z*(z - 6)*(z + 2)
Let x(p) = 3*p**5 - 23*p**4 + 32*p**3 - 4*p**2 - 8. Let a(q) = -2*q**5 + 15*q**4 - 21*q**3 + 3*q**2 + 5. Let i(j) = 8*a(j) + 5*x(j). Factor i(d).
-d**2*(d - 2)**2*(d - 1)
Let j(y) = 4*y**2 - 61*y + 324. Let b(m) = -m**2 + 15*m - 81. Suppose -77 - 11 = 4*s. Let v(r) = s*b(r) - 6*j(r). Determine i so that v(i) = 0.
9
Let r(v) be the first derivative of -2*v**6/3 + 12*v**5/5 - 5*v**4/4 - 4*v**3 + 9*v**2/2 + 127. Solve r(a) = 0.
-1, 0, 1, 3/2
Factor 0*f + 0 - 3/8*f**2 - 3/4*f**3 - 3/8*f**4.
-3*f**2*(f + 1)**2/8
Factor -7*y**3 + 2*y**3 - 60 + 2*y**3 - 15*y**2 - 80*y + 5*y**3 + 3*y**3.
5*(y - 6)*(y + 1)*(y + 2)
Let g be (8/(-3))/((-10)/15 - 0). Find r such that -4*r + 3*r**3 - 33*r**2 + g*r**4 + r**3 + 29*r**2 = 0.
-1, 0, 1
Let q be (3 - 7) + (9 - 2). Factor -19*x**q + 11*x**3 + 0*x**4 + 4*x**4 + 4*x**2.
4*x**2*(x - 1)**2
Let w(p) be the third derivative of -p**7/4620 - p**6/1980 + p**5/330 + 7*p**3/3 + 5*p**2. Let d(i) be the first derivative of w(i). Factor d(a).
-2*a*(a - 1)*(a + 2)/11
Let d(s) be the third derivative of -s**7/525 + s**6/20 + s**5/150 - s**4/4 + 40*s**2 - s. Find n, given that d(n) = 0.
-1, 0, 1, 15
Let w(d) be the first derivative of d**4/14 + 4*d**3/21 - 13*d**2/7 + 20*d/7 - 412. Factor w(f).
2*(f - 2)*(f - 1)*(f + 5)/7
Suppose 6/5 + 5*d - 2/5*d**4 + 18/5*d**3 + 36/5*d**2 - 3/5*d**5 = 0. What is d?
-1, -2/3, 3
Let v(r) be the third derivative of -r**9/52920 + r**8/5880 - r**7/2205 + r**4/3 - 9*r**2. Let b(f) be the second derivative of v(f). Factor b(o).
-2*o**2*(o - 2)**2/7
Let o = 74 - 71. Factor -26*w**o + 7*w**2 + 31*w**3 + 12*w - 4*w**3.
w*(w + 3)*(w + 4)
Suppose -4*w**2 - 144*w**3 - w**5 - 3*w**5 + 10*w**4 + 142*w**3 = 0. What is w?
-1/2, 0, 1, 2
Suppose 0 = 3*p - 2*r + 65, p + 0*p + 33 = -5*r. Let a = 28 + p. Find h, given that -2*h**2 - 3*h**2 + 3*h**2 + a*h**2 + 9*h = 0.
-3, 0
Let y(v) be the first derivative of 1/45*v**6 - 5 - 4/15*v**2 + 0*v - 8/75*v**5 + 8/45*v**3 + 1/10*v**4. Solve y(r) = 0.
-1, 0, 1, 2
Let o = -33 + 31. Let m be 66/42 - (-2)/o. Factor -2/7*n**2 + m*n - 2/7.
-2*(n - 1)**2/7
Let w(x) be the first derivative of 4*x**5/25 + 3*x**4/5 - 8*x**3/15 - 24*x**2/5 - 32*x/5 - 627. Factor w(j).
4*(j - 2)*(j + 1)*(j + 2)**2/5
Let w(d) be the third derivative of d**6/160 - 19*d**5/80 - 11*d**4/4 - 23*d**3/2 + 316*d**2. Factor w(n).
3*(n - 23)*(n + 2)**2/4
Let i(r) be the third derivative of -1/1365*r**7 + r**2 - 1/390*r**6 + 0*r + 1/78*r**4 + 0 + 1/39*r**3 + 0*r**5. Solve i(k) = 0.
-1, 1
Let k be (-9)/(-60)*5/234. Let f = k - -6857/2184. Let -24/7*n + f*n**2 - 6/7*n**3 + 8/7 = 0. Calculate n.
2/3, 1, 2
Let 0 + 0*d + 14*d**5 + 16/15*d**2 + 332/15*d**4 - 56/5*d**3 = 0. Calculate d.
-2, 0, 2/15, 2/7
Solve -2/3 - 1/6*d**2 + 2/3*d = 0 for d.
2
Let f(m) be the third derivative of m**7/42 + 7*m**6/30 - 16*m**5/25 + 2*m**4/3 + 7*m**3/2 - 7*m**2. Let z(w) be the first derivative of f(w). Factor z(n).
4*(n + 5)*(5*n - 2)**2/5
Suppose 6*b - 4 = 4*b. Let v = b + -2. Find d such that -