g - g**3 + g**2.
-g*(g + 1)**2
Let s be (8/(-20))/(1/(-50)). Suppose b - s = 3*f, 3*f + 6 = -b - 4. Factor -14/3*t**2 + 7/3*t**b - 4/3*t**3 + 2/3 + 4*t**4 - t.
(t - 1)*(t + 1)**3*(7*t - 2)/3
Let j be ((-2)/(-3))/((-400)/(-240)). Suppose -5 = -5*s + 5. Factor -2/5*y**s + 0 - 4/5*y**3 + j*y.
-2*y*(y + 1)*(2*y - 1)/5
Suppose -16*c + 13 = -51. Let m be (-2)/4 - (-18)/20. Suppose -2/5*p**c + 0*p - m*p**3 + 0 + 0*p**2 = 0. What is p?
-1, 0
Let a be -1*5*2/2. Let y be (-3)/6*1*a. Factor -y*i**2 + i + 0.
-i*(5*i - 2)/2
Let -3/2*h**3 + h**2 - 1/2*h**4 + 6*h + 4 = 0. What is h?
-2, -1, 2
Let x(i) be the third derivative of i**8/112 - i**7/70 - i**6/40 + i**5/20 + 6*i**2. Factor x(h).
3*h**2*(h - 1)**2*(h + 1)
Let l(j) be the third derivative of j**8/448 + j**7/105 + j**6/120 - j**5/40 - 7*j**4/96 - j**3/12 - j**2. Factor l(q).
(q - 1)*(q + 1)**3*(3*q + 2)/4
Find d such that -10*d**3 - 2*d**3 - d**4 - d**4 - 2*d**4 = 0.
-3, 0
Let p = 347/176 + -21/11. Let h(i) be the second derivative of -i + 0 + 1/40*i**6 + 1/8*i**3 - 3/80*i**5 - p*i**4 + 0*i**2. Factor h(x).
3*x*(x - 1)**2*(x + 1)/4
Let o be (-182102)/198 + 6/(-33). Let g = o + 921. Factor 14/9*c**2 - g*c**3 + 0 - 4/9*c.
-2*c*(c - 1)*(5*c - 2)/9
Let n(o) = -o**2 + 7*o + 4. Let x be n(7). Suppose 3*i**2 + 0*i**4 - 2*i**5 + 2*i**x + i**4 - 4*i**2 = 0. What is i?
-1/2, 0, 1
What is z in -2/3*z**5 + 0 + 0*z**4 - 2/3*z + 4/3*z**3 + 0*z**2 = 0?
-1, 0, 1
Let l(x) = -x**2 + 9*x - 3. Let o be l(8). Let h be 2 - (3/(-1) + o). Factor 0 + 1/3*j + h*j**4 + 1/3*j**5 - 2/3*j**3 + 0*j**2.
j*(j - 1)**2*(j + 1)**2/3
Let x(w) be the third derivative of -1/20*w**4 + 8*w**2 + 1/840*w**8 + 0 - 1/15*w**3 - 1/75*w**5 + 1/150*w**6 + 1/175*w**7 + 0*w. Factor x(g).
2*(g - 1)*(g + 1)**4/5
Suppose 3*x - 2*x = 0. Let o be (-4 - -8)/(x + 1). Factor 0*r**2 - r**2 - r**o + 0*r**3 - 2*r**3.
-r**2*(r + 1)**2
Let n be 1*-2 - (3 + (1 - 9)). Factor -2/9*i**n - 2/9*i**2 + 2/9 + 2/9*i.
-2*(i - 1)*(i + 1)**2/9
Let d(n) = 2*n - 5. Let j be d(4). Let p(x) be the second derivative of 2*x - 1/8*x**2 + 0 - 1/6*x**j - 1/16*x**4. Find g such that p(g) = 0.
-1, -1/3
Find x, given that 0 + 12/5*x**3 - 196/5*x**5 - 16/5*x - 16*x**2 + 56*x**4 = 0.
-2/7, 0, 1
Let c(k) be the third derivative of 2*k**7/105 - 2*k**6/15 + 2*k**5/15 + 2*k**4/3 - 2*k**3 + 2*k**2. Factor c(n).
4*(n - 3)*(n - 1)**2*(n + 1)
Let f be 0/(-3 - (4 + -4)). Let n(s) be the second derivative of 0*s**2 + 1/42*s**4 + f*s**3 - 2*s + 0. Solve n(v) = 0.
0
Suppose 2*y + i - 22 = 0, 5*y + 7 = 4*y - 5*i. Let o be (-4)/10 - (-17)/5. Factor 7*p**5 - 3*p**2 - 8*p**4 + y*p**2 - p - 2 - 4*p**o - 2*p**5.
(p - 1)**3*(p + 1)*(5*p + 2)
Let v(k) = 3*k**3 + 4*k**2 + 4. Let p(t) be the third derivative of t**6/40 + t**5/20 + t**3/2 - 3*t**2. Let m(d) = -4*p(d) + 3*v(d). Find q such that m(q) = 0.
0
Suppose 5*d - 2*d = 0. Suppose -2 = -2*x - 5*y + 3, d = -5*y + 5. Factor -2*v + x*v - 2*v**2 + v + 1.
-(v + 1)*(2*v - 1)
Let d(t) = -t**4 + 6*t**3 + 3*t**2 + 4. Let i(p) = -2*p**4 + 6*p**3 + 3*p**2 + 5. Let b(u) = 5*d(u) - 4*i(u). Factor b(n).
3*n**2*(n + 1)**2
Suppose -20 = -2*g + 7*g, -3*y + 16 = -4*g. Let 0*l**3 + y - 1/4*l**4 + 0*l + 1/4*l**2 = 0. What is l?
-1, 0, 1
Let x(k) = -3*k**2 + 11*k + 8. Let j(h) = h**2 - 4*h - 3. Let f(b) = -8*j(b) - 3*x(b). Factor f(y).
y*(y - 1)
Let p be 53/17 - (-32)/(-272). Determine u, given that 0*u + 0 + 0*u**2 - 2/3*u**p = 0.
0
Let i(s) be the second derivative of -s**8/1344 - s**7/840 + s**6/480 + s**5/240 - s**2/2 + s. Let o(f) be the first derivative of i(f). Solve o(y) = 0 for y.
-1, 0, 1
Let m(g) be the second derivative of -g**6/480 - g**5/80 - g**4/32 + 4*g**3/3 + 8*g. Let q(k) be the second derivative of m(k). Solve q(l) = 0 for l.
-1
Let n be 1 + 2*(-3)/6. Let j(q) be the third derivative of 2*q**2 + 0 + 0*q**4 + 0*q + 1/60*q**5 - 1/420*q**7 - 1/12*q**3 + n*q**6. Factor j(o).
-(o - 1)**2*(o + 1)**2/2
Let q(z) be the third derivative of z**10/15120 + z**9/7560 + z**4/24 + 2*z**2. Let p(l) be the second derivative of q(l). Find h such that p(h) = 0.
-1, 0
Let f = 444643/2520 - 1588/9. Let c(m) be the third derivative of 1/24*m**4 - 1/40*m**5 + 2*m**2 + 0 + 1/120*m**6 - f*m**7 + 0*m - 1/24*m**3. Factor c(y).
-(y - 1)**4/4
Let d(q) be the first derivative of -q**6/60 - q**5/30 - 9*q**2/2 - 8. Let b(r) be the second derivative of d(r). Factor b(z).
-2*z**2*(z + 1)
Factor -30 - 5*v**2 - 19*v + 53 + 32 - 31*v.
-5*(v - 1)*(v + 11)
Let s(o) be the second derivative of 1/18*o**6 + 3/20*o**5 + 1/126*o**7 + 7/36*o**4 + 5*o + 0 + 0*o**2 + 1/9*o**3. Factor s(r).
r*(r + 1)**3*(r + 2)/3
Let b be 1/(20/24*8). Let g(a) be the third derivative of 3*a**2 + 0*a**3 + 1/6*a**4 + 0 + 0*a - 1/10*a**5 - b*a**6. Determine p so that g(p) = 0.
-2/3, 0, 1/3
Let y(a) be the first derivative of -a**6/39 + a**4/26 + 8. Factor y(x).
-2*x**3*(x - 1)*(x + 1)/13
Let y(x) = -5*x**3 + 23*x**2 - 12*x. Let a(t) = 5*t**3 - 22*t**2 + 13*t. Let w(r) = -3*a(r) - 2*y(r). Factor w(b).
-5*b*(b - 3)*(b - 1)
Suppose 0 = 5*t, -4*a - 4*t = -5*t + 40. Let s(k) = -k**3 - 11*k**2 - 9*k + 12. Let u be s(a). Factor -r**3 - 10*r**4 + 0*r**u + 2*r**2 + 9*r**4.
-r**2*(r - 1)*(r + 2)
Let o(n) be the third derivative of -n**6/240 + 3*n**5/40 - 5*n**4/16 + 7*n**3/12 + 32*n**2. Determine m so that o(m) = 0.
1, 7
Let o be (-6)/(-60)*-9 - 15/(-6). Let r = 3/16 + 17/80. Let r + 8/5*t + 12/5*t**2 + 2/5*t**4 + o*t**3 = 0. What is t?
-1
Let q(k) be the first derivative of -k**4/18 - 2*k**3/9 - 4*k + 2. Let t(x) be the first derivative of q(x). Factor t(c).
-2*c*(c + 2)/3
Let x(i) be the first derivative of i**6/12 - 3*i**4/8 + i**3/3 - 8. Factor x(a).
a**2*(a - 1)**2*(a + 2)/2
Suppose 4*c = 2*c + 4. Determine m, given that 3*m**4 - 2*m**2 + 5*m**c - 2*m**3 - 4*m**3 = 0.
0, 1
Let w = -56 + 225/4. Suppose 0*u + 0 + w*u**5 + 3/4*u**4 + 3/4*u**3 + 1/4*u**2 = 0. Calculate u.
-1, 0
Let a be 4/4*(-4)/(-2). Let q = a + 2. Factor c**4 - c + c**3 + q*c**4 + c**2 - 6*c**4.
-c*(c - 1)**2*(c + 1)
Let i(n) be the second derivative of 1/15*n**6 + 0 + 0*n**2 - 1/6*n**4 + 1/21*n**7 + 0*n**3 - 1/10*n**5 + 2*n. Factor i(o).
2*o**2*(o - 1)*(o + 1)**2
Let h(z) be the third derivative of -z**8/1680 + z**6/360 - 2*z**3/3 - 4*z**2. Let a(w) be the first derivative of h(w). What is r in a(r) = 0?
-1, 0, 1
Let n(u) be the third derivative of u**7/840 - u**6/240 - u**4/24 - 3*u**2. Let p(l) be the second derivative of n(l). Solve p(g) = 0 for g.
0, 1
Suppose -3*m + 3*y = -0*y - 24, 2*m + 3*y = 31. Let u = m + -9. Determine l, given that -4/3*l + 2/3*l**u + 2/3 = 0.
1
Let s(b) be the first derivative of b**5/15 + 7*b**4/36 - 13*b**3/27 - 23*b**2/18 - 2*b/3 + 23. Let s(d) = 0. Calculate d.
-3, -1, -1/3, 2
Let k(x) = -x**4 - x**3 - x + 1. Let p(v) = v**4 - 16*v**3 + 23*v**2 - 18*v + 6. Let g(t) = -6*k(t) + 3*p(t). Factor g(o).
3*(o - 2)*(o - 1)**2*(3*o - 2)
Let k(x) be the first derivative of -x**6/4 - 6*x**5/5 - 3*x**4/2 - 6. Suppose k(a) = 0. What is a?
-2, 0
Let s(f) be the first derivative of 2/3*f**2 + 5/2*f**4 + 1/3*f**6 + 0*f + 3 - 2*f**3 - 22/15*f**5. Factor s(d).
2*d*(d - 1)**3*(3*d - 2)/3
Let u be (-26)/52*(4 + -4). Factor 0 + u*k + 2/13*k**2.
2*k**2/13
Factor -w**2 - 7*w**3 + 5*w**3 + w**4 + 0*w**2 + 2*w**2.
w**2*(w - 1)**2
Let g(x) be the first derivative of 7 + 2*x**2 + 1/6*x**3 + 8*x. Solve g(r) = 0 for r.
-4
Factor 5*q**4 - 10*q + 25*q**2 - 17*q + 28*q - 11*q - 20*q**3.
5*q*(q - 2)*(q - 1)**2
Let x(b) be the third derivative of -b**8/336 + b**7/105 + b**6/120 - b**5/30 - 13*b**2. Factor x(n).
-n**2*(n - 2)*(n - 1)*(n + 1)
Let f(k) = 5*k - 1. Let w be f(1). Factor d**4 - 16*d**2 - 5*d**w + 2*d**4 + 8*d + 10*d**3.
-2*d*(d - 2)**2*(d - 1)
Let l = 9 + 1. Suppose -l = 2*q - 7*q. What is r in r**4 + q*r**4 - r**4 = 0?
0
Let j(q) be the third derivative of q**8/80640 - q**7/6720 + q**6/1440 + q**5/60 - 4*q**2. Let v(h) be the third derivative of j(h). Factor v(f).
(f - 2)*(f - 1)/4
Let y be 1 - ((-7)/(-8) - (-2)/16). Let x(z) be the first derivative of 1/3*z**4 - 2 + y*z + 1/6*z**2 + 5/9*z**3. Factor x(j).
j*(j + 1)*(4*j + 1)/3
Suppose 12 = 5*i - 2*i. Let 24*z**5 - 3*z**2 + 16*z**3 + 2*z**2 - 36*z**4 - z**2 - 2*z**i = 0. Calculate z.
0, 1/4, 1/3, 1
Find n such that -4*n**3 + 4*n**3 - 4*n**2 - 3*n**3 - n**5 + 4*n**4 + 4*n + 0*n**4 = 0.
-1, 0, 1, 2
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