3/2*t**5. Suppose y(i) = 0. Calculate i.
-1, -2/7
Let p = 15 - 11. Let -16*o**3 + 4 + 6*o**2 - p + 7*o**3 = 0. What is o?
0, 2/3
Let k be 7/(-84) - 6/(-8). Let -2/3*f**2 + 0 + k*f**4 + 2/3*f**3 - 2/3*f = 0. What is f?
-1, 0, 1
Let a(v) be the first derivative of 2*v**5/55 - v**4/11 + 2*v**2/11 - 2*v/11 + 1. Solve a(y) = 0 for y.
-1, 1
Suppose 5*g + 7 = -3*k - 6, g + 1 = k. Let l be 0 - (-5 - (g + 1)). Factor 2*x + 2*x**5 - l*x**3 - 4*x + x + 3*x.
2*x*(x - 1)**2*(x + 1)**2
Suppose 4*s - s = -p - 5, -17 = -2*p + 3*s. Determine u so that 0*u**2 + p*u**2 + 2*u - 2*u**2 - 4 = 0.
-2, 1
What is x in 4*x**2 - 59*x + 18 + 80*x - x**2 = 0?
-6, -1
Solve 5/4*q**2 + 1/2*q**3 + 0 + 3/4*q = 0 for q.
-3/2, -1, 0
Let s be 688/120 + -5 + 1/(-3). Factor -2/5*f**2 + s*f**4 + 2/5*f**3 + 0 - 2/5*f.
2*f*(f - 1)*(f + 1)**2/5
Suppose -2*n = -7 - 11. Factor -n + 3*g**5 + 2 + 7 - 3*g**4.
3*g**4*(g - 1)
Let w(p) = -p**2 + 2*p. Let s(b) = 2*b. Let v(o) = -5*s(o) + 4*w(o). Factor v(h).
-2*h*(2*h + 1)
Let f(x) = 3*x**4 + 2*x**3 - 4*x + 1. Let k(v) = -13*v**4 - 8*v**3 + 17*v - 5. Let o(w) = 9*f(w) + 2*k(w). Let o(r) = 0. What is r?
-1, 1
Let m(x) be the first derivative of -14*x**3/9 + 86*x**2/3 - 16*x + 48. Determine z, given that m(z) = 0.
2/7, 12
Let b(q) be the third derivative of 0*q + 0 + 0*q**5 - 1/40*q**6 - 2*q**2 + q**3 + 3/8*q**4. Factor b(i).
-3*(i - 2)*(i + 1)**2
Let o(a) be the third derivative of -a**8/112 + a**7/70 + a**6/40 - a**5/20 + 10*a**2. Factor o(j).
-3*j**2*(j - 1)**2*(j + 1)
Let n(h) be the first derivative of h**4/6 + 4*h**3/3 + 3*h**2 - 12. Solve n(i) = 0 for i.
-3, 0
Factor -2*g**3 + 9*g**2 - 54*g + 0*g**3 + 54 + 9*g**2.
-2*(g - 3)**3
Let t = 6 + -1. Suppose -t*v + 52 = -v. Factor -3*a - 12*a**4 - 2 + 3*a**3 + 2*a**2 - a**2 + v*a**4.
(a - 1)*(a + 1)**2*(a + 2)
Let f be (-6)/4*(-12)/6. Factor 2*n**f + 4*n**2 + 0*n - n + n.
2*n**2*(n + 2)
Let n = 6 + -2. Let o be (-12)/42 - n/(-14). Suppose 30*u**2 - u**4 + 4 + 22*u**3 + 18*u + 7*u**4 + o*u**4 = 0. What is u?
-1, -2/3
Let h(g) be the third derivative of -g**6/1440 - g**5/160 - g**4/48 + 2*g**3/3 - g**2. Let m(c) be the first derivative of h(c). Factor m(y).
-(y + 1)*(y + 2)/4
Let y(b) = 3*b + 6. Let o be y(-2). Let d(w) be the second derivative of o*w**2 - 2/21*w**3 + 0 + 1/10*w**5 + 2*w - 5/42*w**4. What is m in d(m) = 0?
-2/7, 0, 1
Let t(y) be the third derivative of 3/160*y**5 - 1/360*y**6 + 2*y**2 - 1/6*y**3 + 0 + 0*y - 1/48*y**4. Let d(j) be the first derivative of t(j). Factor d(o).
-(o - 2)*(4*o - 1)/4
Let w(i) = -i**2 - 11*i - 7. Let v be w(-10). Let o(s) be the second derivative of 1/6*s**4 - s + 0*s**v + 1/5*s**5 + 0*s**2 + 0 + 1/15*s**6. Factor o(b).
2*b**2*(b + 1)**2
Let h(t) = 5*t**4 - 15*t**3 - 16*t**2 + 4*t - 4. Let s(m) = 30*m**4 - 90*m**3 - 95*m**2 + 25*m - 25. Let n(a) = -25*h(a) + 4*s(a). Suppose n(i) = 0. What is i?
-1, 0, 4
Let c be 3/2 - (-1)/2. Let l be ((-8)/16)/(2/(-20)). Solve 3*i**4 - c*i**3 + i**5 - 2*i**l + i**2 - i**3 = 0.
0, 1
Let j(y) be the third derivative of 0*y**3 - 1/6*y**4 + 0 + 0*y + 1/30*y**5 + y**2. Factor j(f).
2*f*(f - 2)
Suppose -56/3*g + 98/3*g**2 + 8/3 = 0. Calculate g.
2/7
Let a(f) be the second derivative of 0 + 5/12*f**3 - 1/6*f**4 + 1/2*f**2 - 3/40*f**5 - 4*f. Let a(z) = 0. Calculate z.
-2, -1/3, 1
Let r(h) = 2*h**2 - 3*h - 4. Let u be r(3). Let 10*t**2 + 32*t**3 + 9*t**5 - 4*t - 4*t**2 + 3*t**u + 35*t**4 - 1 = 0. What is t?
-1, -1/4, 1/3
Let z(a) be the third derivative of 3*a**2 + 1/30*a**5 + 0 - 1/3*a**3 + 1/6*a**4 + 0*a + 1/360*a**6. Let t(o) be the first derivative of z(o). Factor t(k).
(k + 2)**2
Let s(q) = -2 - 5*q**2 + 6 + q**3 - 3*q**2 + 4*q + 3*q**2. Let w be s(4). Solve 0 - 1/2*y**w + 14*y**5 - 15*y**3 + y + 1/2*y**2 = 0 for y.
-1, -1/4, 0, 2/7, 1
Let v(t) = 5*t**3 - 80*t**2 + 320*t. Let i(n) = -n**3 + 16*n**2 - 64*n. Let r(y) = -11*i(y) - 2*v(y). Determine d, given that r(d) = 0.
0, 8
Suppose -l - 5 = -2. Let b = 8 + l. Factor -60*i**2 - 13*i + 3 + 32*i + 63*i**3 - b.
(3*i - 1)**2*(7*i - 2)
Let z be 0*-4*4/(-32). Suppose -4*y = -z*y. Factor -1/2*k**5 + y*k + 0*k**4 + 0 + 1/2*k**3 + 0*k**2.
-k**3*(k - 1)*(k + 1)/2
Let s(q) be the second derivative of -4*q + 2/27*q**3 + 0 + 0*q**4 - 1/45*q**5 - 1/135*q**6 + 1/9*q**2. Factor s(i).
-2*(i - 1)*(i + 1)**3/9
Find c, given that 0*c + 1/4 - 1/4*c**2 = 0.
-1, 1
Let q(x) be the third derivative of 1/90*x**6 + 0 + 1/45*x**5 + 0*x**3 + 0*x - 7*x**2 + 0*x**4. Solve q(t) = 0.
-1, 0
Suppose -5*y - 5 = 0, -3*l + 3*y + 2*y + 23 = 0. Let 4*b**4 - l*b**3 + 5*b**4 - 6*b**5 - b**4 + 4*b**3 = 0. Calculate b.
0, 1/3, 1
Let r(s) be the third derivative of 0*s + 1/280*s**7 + 3/160*s**6 + 1/80*s**5 + 0 - 3/32*s**4 - 1/4*s**3 - s**2. Factor r(b).
3*(b - 1)*(b + 1)**2*(b + 2)/4
Let w(z) = -z + 7. Let y be w(4). Let -1 + f**3 + 2*f**y - 3*f - 5 + 0*f**3 + 6*f**2 = 0. What is f?
-2, -1, 1
Let j(n) be the second derivative of -n**4/28 + n**3/7 - 3*n**2/14 - 15*n. Factor j(b).
-3*(b - 1)**2/7
Factor -20 + 23 + 6*n**2 - 3*n**2 - 6*n.
3*(n - 1)**2
Let b be 0 - 15/22*8/(-3). Factor 0*v**2 + 10/11*v - b*v**3 + 20/11*v**4 - 4/11 - 6/11*v**5.
-2*(v - 1)**4*(3*v + 2)/11
Let a(t) = -2 + 2*t - 4*t + 0 + 3*t. Let h be a(4). Suppose 4/3 - 4/3*v + 1/3*v**h = 0. Calculate v.
2
Factor 17*i - 21*i + 4*i**3 + 5*i**2 - 8 + 3*i**2.
4*(i - 1)*(i + 1)*(i + 2)
Suppose 0 = -2*c + y + 5, 2*y + 6 = 0. Let a(j) be the first derivative of 6/5*j**2 + 26/15*j**3 + 2/5*j + 6/5*j**4 + 8/25*j**5 + c. Find v such that a(v) = 0.
-1, -1/2
Suppose -d - 65 = -67. Let -n + 1/5*n**d + n**3 - 3/5*n**4 + 2/5 = 0. Calculate n.
-1, 2/3, 1
Let l(c) = -5*c**3 - c**2 + 5*c + 19. Let f(i) = -24*i**3 - 6*i**2 + 26*i + 94. Let v(h) = -3*f(h) + 14*l(h). Suppose v(b) = 0. Calculate b.
-2, 2
Factor 1/7*h**2 + 1/7 + 2/7*h.
(h + 1)**2/7
Suppose 0 = 3*s + 3*n + 2*n - 29, 4*s = 2*n + 4. Factor 0*c + 2/3*c**s + 0 + 0*c**2.
2*c**3/3
Let v(o) be the third derivative of o**5/150 + o**4/60 + 24*o**2. Factor v(b).
2*b*(b + 1)/5
Let j = -5 + 11. Suppose 5*i + 10 = 0, v - 8 = j*i - 2*i. Suppose v*f - 2/7*f**4 - 4/7*f**3 + 0 + 2/7*f**5 + 0*f**2 = 0. What is f?
-1, 0, 2
Let d(z) = -5*z - 4. Let n be d(-3). Let l = n + -6. Factor 1/2*v**4 - 1/2*v**2 + 0 + 0*v**3 + 1/4*v**l - 1/4*v.
v*(v - 1)*(v + 1)**3/4
Let d = -7 - -11. Let r(h) = 3*h**2 - 8*h - 3. Let g(p) = 6*p**2 - 17*p - 7. Let n(k) = d*g(k) - 9*r(k). Factor n(l).
-(l - 1)*(3*l - 1)
Let r(l) = l**3 - l**2 - l - 1. Let h(c) = -18*c**3 + 13*c**2 - 11*c - 7. Let d(b) = 5*h(b) - 35*r(b). Factor d(u).
-5*u*(5*u - 2)**2
Suppose -d = -5*d - 24. Let u be (d/2)/(-3) - -1. Determine l, given that u*l**4 - 4*l**2 + l**3 + 2*l**2 + l**3 - 2*l = 0.
-1, 0, 1
Let y(a) be the second derivative of -a**6/120 + 3*a**5/80 - a**4/48 - a**3/8 + a**2/4 + 6*a. Factor y(r).
-(r - 2)*(r - 1)**2*(r + 1)/4
Let h(o) be the second derivative of o**6/180 - o**5/120 - o**4/36 - 33*o. Determine k, given that h(k) = 0.
-1, 0, 2
Let p be (-4)/(((-18)/15)/(-3)). Let d be 6/(-48) - p/16. Factor -1/4 - 1/4*z**2 + d*z.
-(z - 1)**2/4
Factor 6 + 33/2*y**2 + 9/2*y**3 + 18*y.
3*(y + 1)*(y + 2)*(3*y + 2)/2
Let t(n) be the third derivative of n**6/35 - 2*n**5/105 - 5*n**4/84 + 2*n**3/21 + 14*n**2. Suppose t(o) = 0. Calculate o.
-2/3, 1/2
Let p(b) = -4*b**3 - b**2 + 1. Let t be p(1). Let s be (-12)/27*2/t. Factor -s*u**2 + 0*u + 2/9.
-2*(u - 1)*(u + 1)/9
Let g(l) be the third derivative of -l**8/336 + l**7/70 - l**6/40 + l**5/60 - 4*l**2. Factor g(k).
-k**2*(k - 1)**3
Let l(a) = a - 11. Let f be l(6). Let c(h) = -3*h**2 - 3*h + 1. Let w(k) = k**2 - k - 1. Let y(n) = f*w(n) + c(n). Solve y(j) = 0.
-3/4, 1
Let p = -43/45 + 7/5. Let k(t) be the first derivative of -p*t - 2 - 1/9*t**2 + 2/27*t**3. Factor k(q).
2*(q - 2)*(q + 1)/9
Let g(k) = -k - 4. Let m be g(-4). Let l = m + 0. Factor l*q**3 - q**3 + 2*q**2 - 3*q**3 + 2*q**4.
2*q**2*(q - 1)**2
Let l(n) be the first derivative of 2*n + 1/20*n**5 - 1/10*n**6 + 0*n**3 - 2 + 0*n**4 + 0*n**2. Let y(c) be the first derivative of l(c). Factor y(g).
-g**3*(3*g - 1)
Let m(i) be the first derivative of -i**6/12 - 3*i**5/10 - 3*i**4/8 - i**3/6 - 5. Determine q, given that m(q) = 0.
-1, 0
Let l be ((-65)/10 + 6)*(-7)/2. Solve 1/2 + 4*z**2 + 11/4*z + l*z**3 = 0 for z.
-1, -2/7
Let v = 25 + -16. Suppose 2*l = -l + v. Let l*h**5 - 3*h - 