en that r(n) = 0.
-1
Let p be (-3)/3 - (-7 - -3). Suppose 3*f = p + 6. Determine i, given that 12/7*i**f + 8/7*i**4 - 4/7 - 12/7*i - 4/7*i**2 = 0.
-1, -1/2, 1
Let m(u) be the second derivative of -u**5/60 + 2*u**4/9 + 23*u**3/18 - 5*u**2 - 21*u - 5. Factor m(v).
-(v - 10)*(v - 1)*(v + 3)/3
Factor -270*r**2 + 565*r**2 + 154 + 23 - 275*r**2 - 52 + 125*r.
5*(r + 5)*(4*r + 5)
Let v(w) be the second derivative of -w**4/36 + 14*w**3/3 - w + 183. Find p, given that v(p) = 0.
0, 84
Let h(q) be the first derivative of 3*q**7/140 - q**6/60 - q**5/12 - q**4/12 + q**3/3 - 5. Let r(f) be the third derivative of h(f). Factor r(d).
2*(d - 1)*(3*d + 1)**2
Let n(b) = b**3 - 6*b**2 + 5*b + 3. Let o be n(5). Let t(y) = y**3 - 1. Let w(j) = -j**3 + j**2 + 2. Let q(v) = o*w(v) + 6*t(v). Suppose q(p) = 0. Calculate p.
-1, 0
Let f be 54/84*(-14)/(-12). Suppose 2*w - 10 = -0, 0 = -2*m + 4*w - 20. Suppose -1/4*y**3 - f*y**2 + 1 + m*y = 0. What is y?
-2, 1
Let k(b) be the first derivative of b**4/3 - 44*b**3/9 - 28*b**2/3 + 32*b + 700. Determine n so that k(n) = 0.
-2, 1, 12
Factor -2 + 16/7*v - 2/7*v**2.
-2*(v - 7)*(v - 1)/7
Let f(x) = -x**3 - 4*x**2 + 4*x - 5. Let n be f(-5). Suppose n = 4*w - 10 - 6. Let -3*i**w - 4*i**3 + 6*i**4 + i**4 = 0. What is i?
0, 1
Let n(l) = -5*l**5 + 2*l**4 + 3*l**3 + 6*l**2 - 12. Let h(y) = 9*y**5 - 3*y**4 - 6*y**3 - 11*y**2 + 22. Let c(s) = 6*h(s) + 11*n(s). Factor c(p).
-p**3*(p - 3)*(p - 1)
Suppose -4*r + 6 = -0*r - o, -2 = 3*r - 4*o. Let b(y) = 2*y**3 + 3*y**2 + 2*y + 1. Let l(h) = -h**3 - h**2 + h + 1. Let a(k) = r*l(k) - 2*b(k). Factor a(j).
-2*j*(j + 1)*(3*j + 1)
Let h(b) be the third derivative of -b**5/420 + 5*b**4/84 - 3*b**3/14 - 158*b**2. Determine g, given that h(g) = 0.
1, 9
Suppose 3 = 3*p - 3. Suppose p*o + 6 = -4*w, 2*o + 4 = -2. Solve 3/7*l**2 + w*l - 1/7 + 2/7*l**3 = 0 for l.
-1, 1/2
Let d = -36991/6 + 6166. Factor 5/3*o + 5/2 - d*o**2.
-5*(o - 3)*(o + 1)/6
Let a = 202 - 198. Let c be ((-3010)/(-260))/7 - a/26. Factor -3/2 - c*i + 9/8*i**2 + 3/8*i**4 + 3/2*i**3.
3*(i - 1)*(i + 1)*(i + 2)**2/8
Suppose 51 = -7*o + 10*o. Factor 12 - b + 2*b**2 + o*b + 2*b**2.
4*(b + 1)*(b + 3)
Solve 32/7*i**2 + 2/7*i**4 - 2*i**3 - 24/7*i + 0 = 0.
0, 2, 3
Let q(c) be the second derivative of 27/14*c**2 + 1/28*c**4 - 3/7*c**3 + 0 - 7*c. Factor q(d).
3*(d - 3)**2/7
Let n = -43 - -45. Find w such that -26 + 30*w + 18*w**n - 21*w**2 - 40 - 9 = 0.
5
Let q(x) be the first derivative of -2/33*x**3 - 200/11*x - 20/11*x**2 - 27. Factor q(j).
-2*(j + 10)**2/11
Let h(u) be the third derivative of 2*u**8/63 + 8*u**7/315 - 7*u**6/180 + u**5/90 + 241*u**2. Suppose h(c) = 0. Calculate c.
-1, 0, 1/4
Let j(u) be the third derivative of -u**6/900 + u**5/50 - 2*u**4/15 + 16*u**3/45 - 101*u**2. Factor j(t).
-2*(t - 4)**2*(t - 1)/15
Let m = 321/11 + -29. Let m*j**2 - 4/11 - 2/11*j = 0. What is j?
-1, 2
Let t be (-1380)/210 + 4/2 - (-6)/1. Factor 20/7*o**3 + t*o**4 + 10/7*o + 2/7*o**5 + 20/7*o**2 + 2/7.
2*(o + 1)**5/7
Factor 0 - 4/3*x**3 + 1/3*x - 1/6*x**2 - 5/6*x**4.
-x*(x + 1)**2*(5*x - 2)/6
Let p be 28/(-6) + (-2562)/(-441). Factor -4/7*g - 4/7*g**2 + p.
-4*(g - 1)*(g + 2)/7
Factor 35*i - 83*i - 117 - 459 - i**2.
-(i + 24)**2
Let u be -4 + (2 - -2 - -76). Let y = -72 + u. Find k, given that 0*k**2 - 1/2*k**5 - 2*k**3 + 0*k - 2*k**y + 0 = 0.
-2, 0
Let s(w) = w**2 - 24*w + 144. Let z be s(14). Suppose -4/7*i**z - 8/7*i**2 - 2/7*i - 10/7*i**3 + 0 = 0. Calculate i.
-1, -1/2, 0
Let q = -3980 + 3983. Factor -3/5*i**q + 2/5 - 1/5*i**2 - 1/5*i**4 + 3/5*i.
-(i - 1)*(i + 1)**2*(i + 2)/5
Suppose 0 = -4*h - j - 4, -28 + 20 = 2*j. What is a in 3/5*a**2 + 0*a + h = 0?
0
Suppose -3*i - 18 = -6*i - 4*u, -3*i + 12 = 2*u. Suppose 0 = 3*v - 2*v - 4*y - 25, -4*v - i*y + 10 = 0. Suppose -w**v + 3*w**4 + 1 - 1 - 4*w**4 = 0. What is w?
-1, 0
Let v(l) = 8*l**2 + 7*l - 3. Let k be v(1). Let d(z) = -z**2 + 10*z + 27. Let y be d(k). Factor 2/7*u**y - 2/7*u**2 + 0 - 2/7*u + 2/7*u**4.
2*u*(u - 1)*(u + 1)**2/7
Suppose 0 = -3*u + 4*u, -105 = -5*o - u. Let h = o + -8. Factor -24*z**2 + 3*z**3 + h*z - 7*z + 5*z**3 - 4 + 12*z.
2*(z - 2)*(2*z - 1)**2
Let s = 19 + -21. Let k be 4/(-7)*7/s. Solve x**k + 369*x - 1 - 369*x = 0 for x.
-1, 1
Let t(z) be the third derivative of -z**6/420 + 4*z**5/105 - z**4/4 + 6*z**3/7 - 14*z**2 - 8. Factor t(q).
-2*(q - 3)**2*(q - 2)/7
Let o = 23 - 20. Suppose 0*a - 6 = -o*a. Factor 14*v + a*v - 7*v + 3*v**2.
3*v*(v + 3)
Let y = 53293/7 - 7613. Determine v, given that 6/7*v**2 + 2/7*v - y*v**3 - 6/7 = 0.
-1, 1, 3
Let u(r) be the third derivative of -r**7/105 + r**6/60 + r**5/30 - r**4/12 + 80*r**2. Suppose u(f) = 0. What is f?
-1, 0, 1
Let n(c) be the third derivative of -c**7/420 + c**6/60 - c**4/3 - 25*c**3/6 - 51*c**2. Let j(v) be the first derivative of n(v). Factor j(w).
-2*(w - 2)**2*(w + 1)
Let w be (2 - (-9)/(-5))*(-105)/(-42). Let g(s) be the first derivative of -6 - s**2 + 1/2*s**3 + w*s. Suppose g(y) = 0. What is y?
1/3, 1
Let w(k) = -k**2 - k - 1. Let a(v) = -3*v**4 - 12*v**2 - 12*v - 12. Suppose -5*p - 43 - 17 = 0. Let c(s) = p*w(s) + a(s). Factor c(f).
-3*f**4
Let o(z) be the first derivative of z**4/12 - 17*z**3/9 - z**2/6 + 17*z/3 + 539. Factor o(r).
(r - 17)*(r - 1)*(r + 1)/3
Let j(v) be the first derivative of 2*v**3/15 + 18*v**2/5 + 162*v/5 + 86. Solve j(w) = 0.
-9
Let n = 32509 - 226271/7. Let h = n + -184. Factor 0 + h*l - 2/7*l**2.
-2*l*(l - 2)/7
Suppose -5*i = -5*t + 404 - 434, -5*t = -2*i + 6. Factor -2/5 + 1/5*g**t - 1/5*g.
(g - 2)*(g + 1)/5
Let a(p) be the second derivative of p**4/18 - p**2/3 + 16*p. Suppose a(i) = 0. What is i?
-1, 1
Factor 10 + 35/3*z + 5/3*z**4 - 5*z**3 - 5*z**2.
5*(z - 3)*(z - 2)*(z + 1)**2/3
Factor 6/17*z**4 + 128/17*z**2 + 0 - 64/17*z - 52/17*z**3.
2*z*(z - 4)**2*(3*z - 2)/17
Let m(l) = 5*l**3 - 8*l**2 + l. Let i be 4 - 5 - 1*-3. Let a(z) = 6*z**3 - 9*z**2. Suppose 13 = -3*r + 4. Let x(d) = i*a(d) + r*m(d). Factor x(k).
-3*k*(k - 1)**2
Factor 23/4*v**5 + 0*v**2 + 0*v**3 + 0*v + 0 - 1/2*v**4.
v**4*(23*v - 2)/4
Let i = 70819/4 + -17689. Solve 47/4*c**2 - 1 + 0*c + 5*c**4 - i*c**3 = 0 for c.
-1/4, 2/5, 1, 2
Let s(x) be the first derivative of -x**5/15 - x**4/3 + 2*x**3 - 5*x**2 + 13. Let h(u) be the second derivative of s(u). Factor h(t).
-4*(t - 1)*(t + 3)
Let o(c) = 2*c**2 - 10*c + 10. Let l(k) = 4*k**2 - 20*k + 19. Let f(q) = 2*l(q) - 5*o(q). Determine r so that f(r) = 0.
2, 3
Determine p so that 1/4*p**3 - 63/4*p**2 - 9261/4 + 1323/4*p = 0.
21
Let d = 37297/3 - 12432. Find p, given that 2/3*p + d*p**2 - 1 = 0.
-3, 1
Suppose -1/3*h**3 + h**2 + 1/3 - h = 0. Calculate h.
1
Suppose -4*r + 30 = 3*u, 36 = -3*r + 8*r + 3*u. Factor -3*w**4 + 2*w**2 - 2*w**2 + 9*w + r - 3*w**2 - 9*w**3 + 0*w**2.
-3*(w - 1)*(w + 1)**2*(w + 2)
Let v(o) be the first derivative of -4/21*o**3 + 4/7*o + 1/7*o**2 + 22 - 1/14*o**4. What is y in v(y) = 0?
-2, -1, 1
Let h(q) be the third derivative of 0 + 5/2*q**3 + 0*q + 5/12*q**4 + 3*q**2 - 1/12*q**5. Factor h(o).
-5*(o - 3)*(o + 1)
What is m in 4 - 11/3*m + 1/3*m**3 - 2/3*m**2 = 0?
-3, 1, 4
Suppose 0 = -50*s + 2*s + 288. Let c(a) be the third derivative of a**2 + 1/720*a**s + 0*a**5 + 0*a + 0 + 0*a**4 + 0*a**3. Factor c(z).
z**3/6
Let u(g) be the second derivative of 0*g**6 - 1/90*g**5 - 8*g + 0*g**2 + 0*g**3 + 0*g**4 + 0 + 1/189*g**7. Factor u(b).
2*b**3*(b - 1)*(b + 1)/9
Let h(z) be the second derivative of 0 + 3/91*z**7 + 11/39*z**4 - 3*z - 28/39*z**3 + 19/130*z**5 + 8/13*z**2 - 2/13*z**6. Find v, given that h(v) = 0.
-1, 2/3, 1, 2
Find s, given that -4/5 - 1/5*s**2 + s = 0.
1, 4
Let a(h) = 26*h**2 + 5*h + 4. Let r(k) = -62*k**2 - 12*k - 10. Let x(q) = 12*a(q) + 5*r(q). Factor x(b).
2*(b - 1)*(b + 1)
Determine o so that 522/5*o**2 + 40 - 162/5*o**3 - 112*o = 0.
1, 10/9
Let p(z) be the first derivative of -2*z**5/5 - 3*z**4 - 2*z**3/3 + 24*z**2 - 32*z + 311. Determine l so that p(l) = 0.
-4, 1
Find h such that 5/2*h**3 - 1/2*h**4 + 0 - 5/6*h**5 - h - 1/6*h**2 = 0.
-2, -3/5, 0, 1
Let w(c) be the first derivative of -5*c**6/36 - 5*c**5/3 - 25*c**4/4 - 50*c**3/9 + 155*c**2/12 + 25*c - 437. Let w(a) = 0. What is a?
-5, -3, -2, -1, 1
Let t(h) be the first derivative of 5/2*h**4 + 0*h**3 + 0*h + 5 + 0*h**2 + 5/6*h**6 - 3*h**5. Factor t(u).
5*u**3*(u - 2)*(u - 1)
Let n = 4 + -1. Suppose 0 = 17*p 