*5.
2*(v + 1)**3*(v + 2)**2/3
Factor 2/7*w**3 + 0*w - 6/7*w**2 + 8/7.
2*(w - 2)**2*(w + 1)/7
Let m = -2 + 6. Let h be 60/14 - m/14. Factor h*x**3 + 0*x + x + 4*x**2 + 4*x**3 - 3*x**3 + 2*x**4.
x*(x + 1)**2*(2*x + 1)
Determine m so that 0 + 4/3*m - 2/3*m**2 = 0.
0, 2
Let z be ((-2)/(-2))/((-5)/(-30)). Let a be z/(-9) - (-110)/75. Let 1/5 - a*b**2 - 3/5*b = 0. What is b?
-1, 1/4
Let b(h) = -h**2 + 4*h - 3. Suppose -2*v + 9 = f + 2, 4*v + 1 = 3*f. Let x be b(f). Find n such that -4/5*n + 56/5*n**3 + x - 2/5*n**2 = 0.
-1/4, 0, 2/7
Factor -12/5 - 3*k - 3/5*k**2.
-3*(k + 1)*(k + 4)/5
Factor 2/5*q**2 - 2/5*q + 0.
2*q*(q - 1)/5
Suppose 5*f - 13 = -3. Suppose -f*s = s. Let 3/2*l**2 - 3/2*l**3 + 0*l + s = 0. What is l?
0, 1
Let q be 1/2 + (-5)/(-2). Suppose -5*f + 12 = -f, -q*f + 13 = 2*i. Determine u so that -3*u**3 + u + 4*u**3 + 0*u**i + 2*u**2 = 0.
-1, 0
Factor -7/4*b**3 + 3/4*b**2 + 0*b + 0.
-b**2*(7*b - 3)/4
Let r be (-2 - -3)/(2/(-8)) + 4. What is y in r*y + 1/2*y**2 - 1/2 = 0?
-1, 1
Suppose -d - 3*d = j - 18, -2*j = d - 8. Factor 0*q - 1/4*q**d + 1/2*q**2 - 1/4*q**3 + 0.
-q**2*(q - 1)*(q + 2)/4
Suppose 2*v - 7 = 1. Suppose f = 2*f. Determine k so that 0*k + 1/3*k**v + f - 2/3*k**3 + 0*k**2 = 0.
0, 2
Let l(t) be the third derivative of -t**7/490 + 3*t**6/280 - 3*t**5/140 + t**4/56 - 18*t**2. Factor l(m).
-3*m*(m - 1)**3/7
Suppose -5*d + 4*c + 2 = -28, 23 = 4*d - 3*c. Let s = 4 - 4. Factor -1/2*j**d + s - j.
-j*(j + 2)/2
Let x(f) be the second derivative of -3*f**6/10 + 11*f**5/20 + 7*f**4/12 - 11*f**3/6 + f**2 + f. Solve x(h) = 0 for h.
-1, 2/9, 1
Factor 0*p + 0 - 4*p**3 + 0*p**2 + 4/3*p**5 - 8/3*p**4.
4*p**3*(p - 3)*(p + 1)/3
Let q(d) = d**2 + 2*d + 1. Let x be q(-4). Factor 5*p - 1 - x*p - 1 + 0*p - 2*p**2.
-2*(p + 1)**2
Let 3/2*d**2 + 6 - 6*d = 0. What is d?
2
Let g(u) be the first derivative of u**4/16 + u**3/12 - u**2/8 - u/4 + 24. What is y in g(y) = 0?
-1, 1
Let k be (12/9)/(2/3). Suppose -2*z - k*z = 0. Determine w, given that 0*w + z - 1/5*w**2 - 1/5*w**3 = 0.
-1, 0
Let w(i) be the third derivative of 3*i**2 + 1/60*i**5 + 0 - 1/4*i**4 + 0*i + 3/2*i**3. Determine v, given that w(v) = 0.
3
Factor -2/3*b**2 + 10/3 + 8/3*b.
-2*(b - 5)*(b + 1)/3
Let p(w) be the third derivative of w**7/105 + w**6/60 + 28*w**2. Factor p(v).
2*v**3*(v + 1)
Let u(f) be the first derivative of f**4/42 + 2*f**3/21 + f**2/7 + f + 2. Let n(s) be the first derivative of u(s). Factor n(c).
2*(c + 1)**2/7
Let u(b) be the first derivative of -4*b**3/15 - 4*b**2/5 - 4*b/5 + 15. Find p, given that u(p) = 0.
-1
Suppose -2/9*l**4 - 8/9 + 0*l + 0*l**3 + 10/9*l**2 = 0. What is l?
-2, -1, 1, 2
Suppose 5/3*a**3 + 2/3*a**4 + 4/3*a**2 + 0 + 1/3*a = 0. Calculate a.
-1, -1/2, 0
Let c(d) be the third derivative of d**6/180 - d**4/36 + 11*d**2. Factor c(b).
2*b*(b - 1)*(b + 1)/3
Let g(r) = 4*r**3 - 19*r**2 - 5*r. Let m(t) = -t**3 + 6*t**2 + 2*t. Let q(v) = 2*g(v) + 7*m(v). Find z such that q(z) = 0.
-2, 0
Factor 12*j**3 - 4*j - 3*j**3 + j**3 - 6*j**2 + 0*j**3.
2*j*(j - 1)*(5*j + 2)
Let a(j) be the second derivative of j**7/1260 + j**6/90 + j**5/15 + j**4/6 + j. Let t(d) be the third derivative of a(d). Let t(f) = 0. Calculate f.
-2
Let n(s) = -s**2 + 9*s - 5. Let a be n(8). Factor 12*y**3 - y - 4*y**4 - a*y**2 + y**2 - 5*y**3.
-y*(y - 1)**2*(4*y + 1)
Suppose 3*w - 36 = 7*w + 4*p, 15 = -3*p. Let j be 60/(-216) - 2/w. Determine v so that -4/9 - 2/3*v - j*v**2 = 0.
-2, -1
Suppose 2*x - 6 = 4*x + 3*n, 5*x + 5 = -5*n. Suppose 3*k + 14 = -r + 6*r, 0 = 4*r - x*k - 10. Let -3*w**3 - 2*w + r*w**3 - w**2 + 0*w**2 = 0. Calculate w.
-1, 0, 2
Factor 5*f - f**3 + 3*f**3 + f + 8*f**2.
2*f*(f + 1)*(f + 3)
Solve 3/2 + 15/2*h + 63/8*h**4 - 75/4*h**3 + 15/8*h**2 = 0 for h.
-1/3, -2/7, 1, 2
Let n be 2/7 - (-47)/7. Suppose 4*w - 5 = n. Factor 2*d - 3*d**w - d + 2*d**2 + 4*d**3.
d*(d + 1)**2
Let i be (-18)/84 + (-3)/(-6). Let o = 17 + -117/7. What is a in -i*a**4 - o*a**3 + 0*a + 0*a**2 + 0 = 0?
-1, 0
Suppose -3*k = 4*v - 4, 2*k - 5*v + 6 = 6*k. Suppose 12 = -5*g + 4*l - 8*l, g = -k*l - 12. Factor 0*f**2 - 2/9*f**3 + g + 0*f.
-2*f**3/9
Factor 5/2*x + 1/4*x**2 + 25/4.
(x + 5)**2/4
Let x(l) be the second derivative of 0*l**2 - 1/10*l**5 + 0 + 1/6*l**4 + 0*l**3 - 3*l. Factor x(g).
-2*g**2*(g - 1)
Let i(p) be the second derivative of 28/5*p**4 + 0 + 16/5*p**2 - 6*p - 36/5*p**3 + 49/50*p**5. Factor i(l).
2*(l + 4)*(7*l - 2)**2/5
Let l(z) be the third derivative of z**7/1050 + 7*z**6/600 + z**5/20 + 13*z**4/120 + 2*z**3/15 + 5*z**2 + 6*z. Factor l(q).
(q + 1)**3*(q + 4)/5
Let y(p) be the first derivative of 1/4*p**2 + 3 + 3/8*p**4 - 1/10*p**5 + 0*p - 1/2*p**3. What is x in y(x) = 0?
0, 1
Let d(a) be the second derivative of -a**7/98 + 3*a**6/70 - 9*a**5/140 + a**4/28 + 4*a. Factor d(y).
-3*y**2*(y - 1)**3/7
Let j(z) be the third derivative of -1/180*z**6 - 1/90*z**5 + 0 + 0*z**3 + 1/18*z**4 + 4*z**2 + 0*z. Factor j(y).
-2*y*(y - 1)*(y + 2)/3
Let k be 3/6*(-2)/(-4). Let i(t) = -t**3 - 6*t**2 - 5*t + 3. Let h be i(-5). Find x such that 0 + 0*x - k*x**2 + 1/4*x**h = 0.
0, 1
Let v be -1 + 1 - (-477)/(-18). Let o = 269/10 + v. Factor o*j**2 - j**3 + 0*j + 3/5*j**4 + 0.
j**2*(j - 1)*(3*j - 2)/5
Let q(r) be the first derivative of r**2 + 1/360*r**6 + 1/6*r**4 - 1/30*r**5 + 0*r - 4/9*r**3 - 2. Let z(p) be the second derivative of q(p). Factor z(h).
(h - 2)**3/3
What is u in u**2 + 1/3*u**4 - 5/3*u + 5/3*u**3 - 4/3 = 0?
-4, -1, 1
Let w**2 + 1/2*w**3 + 0 + 1/2*w = 0. Calculate w.
-1, 0
Let c be 2/(-40)*(4 - 63). Let u = c + -11/5. Factor 9/4*x**2 + 9/4*x + u*x**3 + 3/4.
3*(x + 1)**3/4
Let h be (-33)/(-27) - (0 + 1). Let f = 1/6 - -1/18. Suppose 0 + f*w**2 + h*w = 0. Calculate w.
-1, 0
Let k be 54/9 + (1 - -1). Suppose 0*r - k = -4*r. Factor -t**5 + 1 - t + 3*t**3 - 2*t**r + 3*t**3 + t**4 - 4*t**3 + 0*t**3.
-(t - 1)**3*(t + 1)**2
Let b(l) be the first derivative of -l**4/42 + 2*l**3/21 + 6*l - 2. Let j(y) be the first derivative of b(y). What is f in j(f) = 0?
0, 2
Suppose 11*k = -13*k + 19*k. Suppose 5*p - 11 = -1. Suppose k*l**p + 2/3*l**3 + 0 - 2/3*l = 0. Calculate l.
-1, 0, 1
Let t(v) be the first derivative of 3*v**5/10 + v**4 + 11*v**3/9 + 2*v**2/3 + v/6 + 2. Factor t(f).
(f + 1)**2*(3*f + 1)**2/6
Let l(b) = -b**3 - 15*b**2 - 15*b - 11. Let q be l(-14). Factor -4/11 + 0*j**2 - 2/11*j**q + 6/11*j.
-2*(j - 1)**2*(j + 2)/11
Let 0*k**2 + 0 + 0*k**4 + 2/3*k**5 + 0*k + 0*k**3 = 0. Calculate k.
0
Let w(t) be the third derivative of -t**6/540 + t**5/270 + t**4/108 - t**3/27 + t**2. Factor w(x).
-2*(x - 1)**2*(x + 1)/9
Let y be 7 + ((-20)/4 - -4). Suppose 0*l + 12 = y*l. Determine o so that -2/5*o**l - 4/5*o**3 + 0 - 2/5*o**4 + 0*o = 0.
-1, 0
Solve 5/4*j + 1/4*j**2 - 7/2 = 0 for j.
-7, 2
Factor 20/11*x**2 - 8/11 - 2/11*x + 14/11*x**3.
2*(x + 1)**2*(7*x - 4)/11
Let f be (-170)/(4 - 2) + 1. Let t be (1/3)/((-4)/f). Let -19*w**2 + 2 - 16*w**2 + t*w**2 + w = 0. What is w?
-1/4, 2/7
Let p(f) = -4*f**3 - 2*f**2 + 2*f + 4. Let c be p(-1). What is a in c*a - 8 - 1/2*a**2 = 0?
4
Let u = -2/151 - -622/1359. Let j = 78/43 - 100/387. Determine i, given that -j*i**4 + 0 + 0*i**2 + 0*i + u*i**3 = 0.
0, 2/7
Let t(h) = h**2 + h + 1. Let q(p) = -6*p**2 - 15*p + 9. Let c(u) = -2*q(u) - 14*t(u). Factor c(l).
-2*(l - 4)**2
Suppose -3*g + 4*a = 1, 7*a = 4*g + 2*a. Let r(y) be the second derivative of y + 0 + 0*y**2 + 1/3*y**3 - 1/10*y**g + 0*y**4. Factor r(f).
-2*f*(f - 1)*(f + 1)
Let f(m) be the first derivative of m**8/112 - m**7/70 - m**6/40 + m**5/20 + 3*m**2/2 - 3. Let y(z) be the second derivative of f(z). What is d in y(d) = 0?
-1, 0, 1
Let m(c) be the first derivative of -1/9*c**3 + 1/9*c**6 + 1/15*c**5 - 1/4*c**4 + 1/6*c**2 + 0*c + 4. Suppose m(a) = 0. Calculate a.
-1, 0, 1/2, 1
Let r(g) be the first derivative of -8*g**5/65 + 9*g**4/26 - 4*g**3/39 + 15. Factor r(o).
-2*o**2*(o - 2)*(4*o - 1)/13
Solve -2*x**5 - 3 - 6*x**3 + 21*x**4 - 7*x**5 + 15*x - 18*x**2 + 0*x**4 = 0 for x.
-1, 1/3, 1
Let z(d) be the first derivative of 4*d**3/3 + 16*d**2 + 64*d - 3. Suppose z(j) = 0. What is j?
-4
Let n(u) be the second derivative of -u**4/30 - 2*u**3/15 - 4*u. Factor n(b).
-2*b*(b + 2)/5
Let m(w) be the second derivative of w**5/110 + 2*w**4/33 + 5*w**3/33 + 2*w**2/11 - w. Determine d so that m(d) = 0.
-2, -1
Let b be ((-3)/(-6))/((-1)/100). L