8 + z**2/14 + 2. Factor m(i).
-i*(i - 1)*(i + 1)/7
Let c = -2/333 + 1669/666. Factor 7/2*p**4 - p**2 + 0 - c*p**3 + 0*p.
p**2*(p - 1)*(7*p + 2)/2
Let f = -20/3 - -43/6. Factor 1/2*d - 1/2*d**3 - f + 1/2*d**2.
-(d - 1)**2*(d + 1)/2
Let m(h) = -h**2 - 9*h + 3. Let c be m(-9). Suppose -c*a = -2*a - 7. Suppose 0 - u**2 + a*u**2 - 3 + 3*u = 0. What is u?
-1, 1/2
Let f(y) = -y**2 - 10*y - 6. Let k be ((-18)/12)/((-1)/(-6)). Let u be f(k). Factor -4*a + 4*a + u*a**3 - 3*a**4.
-3*a**3*(a - 1)
Suppose -2*l + 0*l = -4. Let c = l - -3. Let 3*j**4 + j**3 + 3*j**4 - j**5 - c*j**4 - j**2 = 0. What is j?
-1, 0, 1
Let -3*k**2 - 8*k**4 + 0*k**4 + 5*k**4 + 2*k**3 + 4*k**3 = 0. What is k?
0, 1
Let c be (-2 + 2 - 0)*1. Suppose -5*f + 3*f + 4 = c. Factor 13*s**3 - 38*s**3 - 4 - 2*s**f - 3*s**2 + 16*s.
-(s + 1)*(5*s - 2)**2
Let t(r) = -3*r**2 - 12*r - 1. Let x(p) = p**2 + 4*p. Let d(f) = 3*t(f) + 8*x(f). Factor d(g).
-(g + 1)*(g + 3)
Suppose 8 = -2*x + 4*x. Let s(u) be the first derivative of 0*u**x - 2/35*u**5 + 0*u + 0*u**2 + 0*u**3 + 2. Suppose s(i) = 0. What is i?
0
Let h(j) be the second derivative of 0*j**2 + 0*j**3 + 0 + 3*j + 1/54*j**4. What is v in h(v) = 0?
0
Suppose c + 6 = 4*c. Suppose 7 = 3*q - 2*q. Factor 4 - 5*v**c - q*v**3 + 2*v - 4.
-v*(v + 1)*(7*v - 2)
Let v(r) = -5*r**2 - r - 5. Let m(t) be the third derivative of t**5/30 + t**3/3 - t**2. Let f(d) = -11*m(d) - 4*v(d). Factor f(w).
-2*(w - 1)**2
Let x(l) be the second derivative of l**4/16 + l**3/8 - 9*l**2/4 + 23*l. Determine p so that x(p) = 0.
-3, 2
Let g(z) be the second derivative of z**5/100 + z**4/60 + 2*z + 1. Factor g(m).
m**2*(m + 1)/5
Let s(m) = 2*m**5 - 2*m**3 - 4*m. Let h(r) = 2*r**5 - r**4 - 3*r**3 - 5*r. Let g(i) = -4*h(i) + 5*s(i). Let g(x) = 0. What is x?
-1, 0
Let j = -1/23 - 6/391. Let k = 46/85 - j. Find p such that -k*p - 4/5*p**2 + 1/5 = 0.
-1, 1/4
Suppose -a - 4*j + 40 = 0, 40 = 2*a + 3*j - 20. Solve 5*p**3 + 2*p**3 + a*p**2 + 8*p + 11*p**3 = 0 for p.
-2/3, 0
Let x(i) be the second derivative of -i**6/40 - 3*i**5/40 + i**3/4 + 3*i**2/8 - 13*i. Solve x(l) = 0 for l.
-1, 1
Let a(u) = -u**2 + 34*u - 262. Let o be a(22). Let 1/2*k - 1/4*k**o + 0 - 1/4*k**3 = 0. Calculate k.
-2, 0, 1
Let z be ((-36)/20 - -1)*20/(-8). What is l in 4/5*l**z + 0*l**3 + 2/5*l**5 - 2/5*l - 4/5*l**4 + 0 = 0?
-1, 0, 1
Determine a, given that 18*a**3 - 9*a**3 - 5*a**2 - 8*a**3 - 3 + 7*a = 0.
1, 3
Let k(n) be the third derivative of n**7/840 + n**6/160 + n**5/120 + 6*n**2. Factor k(d).
d**2*(d + 1)*(d + 2)/4
Let v(r) be the first derivative of r**4/12 - r**3 + 5*r**2/2 + 25*r/3 + 2. Suppose v(g) = 0. What is g?
-1, 5
Let u be -14*(-4)/(-32)*-2. Let o(r) be the first derivative of -2 + 1/5*r**3 + u*r**4 - 49/25*r**5 - 4/5*r - 2*r**2. What is s in o(s) = 0?
-2/7, 1
Let t be (-1)/3 + 1*(-23)/(-33). Factor -2/11 + t*r - 2/11*r**2.
-2*(r - 1)**2/11
Let b be -2 - -5 - 4 - -4. Factor 0*s**2 + 0 + 3/5*s - 3/5*s**b.
-3*s*(s - 1)*(s + 1)/5
Let s(x) be the first derivative of -x**6/3 - 2*x**5/5 - 7. Factor s(q).
-2*q**4*(q + 1)
Let o be ((-3)/(-2))/((-6)/36). Let f = o + 11. Let -2/11*s + 2/11*s**4 + 2/11*s**3 - 2/11*s**f + 0 = 0. What is s?
-1, 0, 1
Suppose q + 4 = 3*q. Suppose 2/11*m**3 + 0 - 2/11*m + 0*m**q = 0. What is m?
-1, 0, 1
Let f be 161/138*(-4)/(-21). Suppose 2/9*w - 4/9 + f*w**2 = 0. Calculate w.
-2, 1
Let b be 40/12 - 2*1. Suppose k = -k. Factor -4/3*j**3 - b*j + 10/3*j**2 + k.
-2*j*(j - 2)*(2*j - 1)/3
Factor 1 - 1/3*k**4 - 2/3*k**2 + 4/3*k**3 - 4/3*k.
-(k - 3)*(k - 1)**2*(k + 1)/3
Suppose 5*q - 24 = -q. Let z(k) be the first derivative of 2/21*k**3 + 0*k + 1/7*k**q - 2/7*k**2 + 1 - 2/35*k**5. Factor z(n).
-2*n*(n - 2)*(n - 1)*(n + 1)/7
Let t(l) be the first derivative of -4*l**3/15 + 2*l**2/5 + 8*l/5 - 13. Determine r, given that t(r) = 0.
-1, 2
Let c(y) be the third derivative of -y**7/735 + y**6/105 - y**5/42 + y**4/42 - 46*y**2. Determine z, given that c(z) = 0.
0, 1, 2
Let y(l) = -8*l**4 - 4*l**3 + 8*l**2 + 4*l - 6. Let t(k) = 9*k**4 + 5*k**3 - 9*k**2 - 5*k + 7. Let d(o) = -6*t(o) - 7*y(o). Find u such that d(u) = 0.
-1, 0, 1
Let p(q) = 21*q**4 - 6*q**3 - 15*q**2 - 5*q + 5. Let f(s) = 4*s**4 - s**3 - 3*s**2 - s + 1. Let o(a) = 11*f(a) - 2*p(a). Find n such that o(n) = 0.
-1, 1/2, 1
Let m(n) be the first derivative of 2*n**3/3 - 8*n + 5. Factor m(z).
2*(z - 2)*(z + 2)
What is i in 77*i**3 - 6*i**5 - 89*i**3 - 73*i**3 + i**5 + 50*i**4 + 40*i**2 = 0?
0, 1, 8
Let l = 7 - 4. Let z be (1*3/(-42))/((-4)/16). Solve z*t - 2/7*t**2 + 2/7 - 2/7*t**l = 0.
-1, 1
Let w(a) be the first derivative of 4*a**3/3 - 8*a**2 + 12*a - 47. Factor w(h).
4*(h - 3)*(h - 1)
Let v be (-26)/(-162) - (-2)/(-12). Let m = v + 3893/810. Factor 12/5*o**2 + m*o + 16/5 + 2/5*o**3.
2*(o + 2)**3/5
Let c = -156 - -781/5. Factor c*k**2 + 2/5*k + 0.
k*(k + 2)/5
Let m = -89 + 179/2. Factor 0 - 1/2*n**4 - m*n**3 + 0*n + 0*n**2.
-n**3*(n + 1)/2
Factor 15*w**2 + 5/2*w**3 + 10 + 45/2*w.
5*(w + 1)**2*(w + 4)/2
Let -18/7*q**2 + 24/7*q + 72/7 - 6/7*q**3 = 0. What is q?
-3, -2, 2
Factor 4/3 + 7*c**2 + 8*c - 49/3*c**3.
-(c - 1)*(7*c + 2)**2/3
Suppose 13*f + 80 = 9*f. Let y = f - -41/2. Factor 1/2*z**4 + 3/2*z**3 + 3/2*z**2 + y*z + 0.
z*(z + 1)**3/2
Suppose 0*p = -3*p - 27. Let k = -1 - p. Factor -10*s**4 + 2*s**4 - k*s + 8*s**2 + 2*s**5 - 4*s**3 + 10*s**3.
2*s*(s - 2)**2*(s - 1)*(s + 1)
Let p = -13 + 16. Let c(h) be the first derivative of 0*h**p + 1/11*h**2 + 1 - 1/22*h**4 + 0*h. Solve c(t) = 0 for t.
-1, 0, 1
Let f(y) = 2*y**5 + 2*y**4 - 6*y**3 + y**2 + 7*y - 3. Let z(c) = -4*c**5 - 4*c**4 + 12*c**3 - 3*c**2 - 15*c + 7. Let k(q) = 7*f(q) + 3*z(q). Factor k(u).
2*u*(u - 1)**2*(u + 1)*(u + 2)
Let i(y) = 3*y**5 - 6*y**4 - 15*y**3 + 6*y**2 + 12*y. Let u(j) be the second derivative of j**5/20 - j**3/6 - 3*j. Let o(n) = -i(n) - 15*u(n). Factor o(f).
-3*f*(f - 1)**3*(f + 1)
Let f(m) = -m**3 - m - 25. Let o be f(0). Let d = -223/9 - o. Factor d*a**4 + 2/9*a + 4/9 - 2/3*a**2 - 2/9*a**3.
2*(a - 2)*(a - 1)*(a + 1)**2/9
Let h be (-5)/((-4)/(-2) + -3). Suppose -u + 2*c = 4, 5*u - h*c + 4 + 1 = 0. Factor 2*n**5 + 0*n**4 - 3*n**5 - n**3 - u*n**4.
-n**3*(n + 1)**2
Let j(r) be the second derivative of -r**7/21 - 13*r**6/60 - 3*r**5/8 - 7*r**4/24 - r**3/12 + 4*r + 1. What is f in j(f) = 0?
-1, -1/4, 0
Let v(b) be the second derivative of b**7/630 - b**5/90 + b**3/18 - b**2 - 3*b. Let g(l) be the first derivative of v(l). Find o, given that g(o) = 0.
-1, 1
Let t(a) be the second derivative of -a**7/126 + 2*a**6/45 - a**5/10 + a**4/9 - a**3/18 + 4*a. Suppose t(q) = 0. What is q?
0, 1
Let q(l) = -2*l. Let k be q(8). Let r be (-8)/(-20) + k/(-10). What is z in 6*z**2 + 4 - 4*z**r + 2*z - 4 = 0?
-1, 0
Let k(t) be the first derivative of t**4/2 - 2*t**3/3 - t**2 + 10*t + 3. Let a(v) = -v**2 - v + 1. Let s(z) = -8*a(z) + k(z). Factor s(u).
2*(u + 1)**3
Factor -3*s**2 - 7*s**5 + 12*s**3 - 6*s**4 - 9*s**4 + 13*s**5.
3*s**2*(s - 1)**2*(2*s - 1)
Let o be (-28)/(-1617)*6 + (-2)/(-11). Factor -8/7*k**2 + 0 + 10/7*k**3 + o*k - 4/7*k**4.
-2*k*(k - 1)**2*(2*k - 1)/7
Factor 0 - 2/3*w + 1/3*w**5 - w**3 - 1/3*w**4 + 5/3*w**2.
w*(w - 1)**3*(w + 2)/3
Let u(d) be the second derivative of 9*d**5 + 5*d**4 + 5*d**3/6 - 8*d. Let u(w) = 0. Calculate w.
-1/6, 0
Let k(i) = i**3 - 25*i**2 + 2*i + 17. Let a(g) = -2*g**3 + 24*g**2 - 2*g - 16. Let f(d) = 5*a(d) + 4*k(d). Solve f(p) = 0.
-2/3, 1, 3
Let i(z) be the second derivative of z**9/7560 - z**8/1120 + z**7/420 - z**6/360 + z**4/12 + z. Let a(g) be the third derivative of i(g). Factor a(o).
2*o*(o - 1)**3
Let y = 22 + -17. Let i(n) be the first derivative of n**6 - 44/35*n**y - 4/7*n - 11/7*n**4 + 16/7*n**3 + 1 + 1/7*n**2. Solve i(v) = 0 for v.
-1, -2/7, 1/3, 1
Let t(j) be the second derivative of j**8/1344 + j**7/840 - 2*j**2 - 4*j. Let n(a) be the first derivative of t(a). Let n(z) = 0. Calculate z.
-1, 0
Let m be (0 - -3)*(-25)/(-15). Suppose -2*a + 1 = n - 7, -m*n + 16 = 4*a. Suppose 0*h**3 - 2/3*h**5 + 0*h + 2/3*h**4 + 0*h**2 + n = 0. Calculate h.
0, 1
Let y be (-1 - 2)/(2 + -1). Let m(u) = -u**2 - 2*u + 3. Let w be m(y). Determine p, given that w + 0*p**2 - 1/2*p**3 + 0*p + 1/2*p**4 = 0.
0, 1
Let w(v) = 3*v**3 - 6*v**2 - 6*v - 6. Let p(c) = c**2 + c + 1. Suppose 3*s - 1 = -4. Let x(y) = s*w(y) - 6*p(y). Factor x(l).
-3*l**3
Suppose