t + 3/4*t**4 = 0 for t.
-1, 1
Let s(b) be the first derivative of -b**4/18 - b**3/9 - 4*b + 2. Let m(v) be the first derivative of s(v). Find w, given that m(w) = 0.
-1, 0
Let a(i) = 4*i**2 + i - 1. Let t be a(1). Let h be -1 + 0 + (-2)/(-2). Suppose -t*d**2 - 6*d**3 + 10*d**4 + 0*d + h*d = 0. What is d?
-2/5, 0, 1
Suppose 0 + 2/19*k**3 - 2/19*k + 0*k**2 = 0. Calculate k.
-1, 0, 1
Let a(u) = -3*u**5 + 2*u**4 + 3*u**3 - 2*u**2 - 2. Let k(q) = 4*q**5 - 3*q**4 - 3*q**3 + 2*q**2 + 3. Let c(z) = -3*a(z) - 2*k(z). Factor c(f).
f**2*(f - 1)**2*(f + 2)
Let l(z) be the first derivative of z**7/35 - 7*z**6/60 + z**5/6 - z**4/12 + z**2/2 + 6. Let j(t) be the second derivative of l(t). Let j(q) = 0. What is q?
0, 1/3, 1
Suppose -2 = 23*z - 71. Factor 2/13*g**4 - 2/13*g**2 + 0 + 0*g + 2/13*g**5 - 2/13*g**z.
2*g**2*(g - 1)*(g + 1)**2/13
Let j(r) be the second derivative of r**5/20 + r**4/3 - r**3 - r**2 - 8*r. Let g be j(-5). Suppose -2/3 + 1/3*x**g + 0*x**2 - x = 0. Calculate x.
-1, 2
Let m(s) be the second derivative of 7*s + 1/28*s**7 + 0*s**5 - 1/20*s**6 + 0*s**4 + 0*s**2 + 0 + 0*s**3. Factor m(z).
3*z**4*(z - 1)/2
Let r(l) be the third derivative of -l**5/2 + 65*l**4/24 - 5*l**3/3 - 33*l**2. Factor r(q).
-5*(q - 2)*(6*q - 1)
Let h(w) be the first derivative of 1/21*w**6 + 5 + 0*w**2 - 4/35*w**5 + 0*w**3 + 1/14*w**4 + 0*w. Suppose h(s) = 0. What is s?
0, 1
Let p(u) = -14*u**2 + 240*u + 1452. Let g(h) = -6*h**2 + 96*h + 581. Let v(o) = 12*g(o) - 5*p(o). Factor v(w).
-2*(w + 12)**2
Let o(a) be the second derivative of a**7/49 + 4*a**6/35 + 3*a**5/14 + a**4/7 + 9*a. Factor o(m).
6*m**2*(m + 1)**2*(m + 2)/7
Let f(q) be the first derivative of -q**3/3 - 5*q**2/2 - 2*q + 3. Let m be f(-3). Solve 2*d**2 + 4 + m*d - 3 + 1 = 0.
-1
Factor -2/19*s + 4/19*s**2 - 2/19*s**4 + 4/19*s**3 - 2/19 - 2/19*s**5.
-2*(s - 1)**2*(s + 1)**3/19
Let t = -46 + 46. Factor t + 2/3*x**4 + 0*x + 0*x**3 - 2/3*x**2.
2*x**2*(x - 1)*(x + 1)/3
Let h be 4/(-4)*1 - 84/(-70). Factor -1/5*f - 1/5*f**4 + h*f**2 + 1/5*f**3 + 0.
-f*(f - 1)**2*(f + 1)/5
What is p in -11/4*p**2 + 1/4*p**3 + 19/4*p - 9/4 = 0?
1, 9
Let d(v) be the first derivative of v**6/39 - 2*v**5/13 + 9*v**4/26 - 14*v**3/39 + 2*v**2/13 - 7. Factor d(r).
2*r*(r - 2)*(r - 1)**3/13
Let a = 21/62 + -65/558. Factor -2/9*t**4 - 2/9*t + 4/9*t**3 + 4/9*t**2 - a - 2/9*t**5.
-2*(t - 1)**2*(t + 1)**3/9
Let u(r) be the second derivative of r**7/24 + r**6/60 - 7*r**5/80 - r**4/24 + r. Determine p so that u(p) = 0.
-1, -2/7, 0, 1
Factor 1/4*h**2 - 1/4*h**4 + 3/4*h**3 + 0 - 3/4*h.
-h*(h - 3)*(h - 1)*(h + 1)/4
Let q(d) = d**5 + d**4 - 9*d**3 + 5*d**2 - 4*d - 6. Let i(f) = 3*f**5 + 3*f**4 - 26*f**3 + 14*f**2 - 11*f - 17. Let o(k) = 6*i(k) - 17*q(k). Solve o(y) = 0.
-2, -1, 0, 1
Factor -10/3*m + 10/3*m**3 + 4/3 - 4/3*m**2.
2*(m - 1)*(m + 1)*(5*m - 2)/3
Let q be 1*(-1 - -2) + 1. Let i be 6/21 + 12/7. Factor -67 - 160*g**q + 3 - 80*g**3 + 22*g - 20*g**4 - 182*g - i*g**5.
-2*(g + 2)**5
Let i(m) be the third derivative of m**11/1164240 + m**10/264600 + m**9/211680 - m**5/30 - 4*m**2. Let s(f) be the third derivative of i(f). Factor s(w).
2*w**3*(w + 1)**2/7
Factor p - 2/5*p**2 - p**3 + 2/5.
-(p - 1)*(p + 1)*(5*p + 2)/5
Let m(t) be the third derivative of -t**7/840 + 2*t**3/3 + 4*t**2. Let c(z) be the first derivative of m(z). Let c(a) = 0. What is a?
0
Let r(b) be the third derivative of -b**5/210 + b**3/21 + 11*b**2. Solve r(m) = 0.
-1, 1
Let t(y) = -3*y**2 + y. Let d be t(-2). Let f be 3/(-9) + d/(-6). Determine k so that 0 - 3/2*k**f - k**3 - 1/2*k = 0.
-1, -1/2, 0
Let q = -118 + -7. Let o = q + 257/2. Find w such that 0 + o*w**2 + w - 9/2*w**3 = 0.
-2/9, 0, 1
Factor -w + 7*w**3 - 11*w + 2*w**3 + 3*w**4.
3*w*(w - 1)*(w + 2)**2
Let i(g) be the first derivative of 2*g**5/65 - 14*g**4/13 + 10*g**3 + 28*g**2/13 - 392*g/13 - 12. Determine q, given that i(q) = 0.
-1, 1, 14
What is o in -3/8*o**2 + 0 - 3/8*o**3 + 3/4*o = 0?
-2, 0, 1
Let u(z) be the first derivative of -z**7/4200 - z**6/1800 + 2*z**3/3 + 1. Let d(v) be the third derivative of u(v). Factor d(l).
-l**2*(l + 1)/5
Suppose 0 = 4*h - h - 6. Suppose 0 = -2*c - 0*c + 8. Factor -6*p + 1 + 0*p**4 + 4*p - p**c + h*p**3.
-(p - 1)**3*(p + 1)
Let l(o) be the first derivative of 1/6*o**2 + 1 + 1/18*o**3 + 0*o. Factor l(q).
q*(q + 2)/6
Let r(t) be the second derivative of t**6/60 + 3*t**5/40 + t**4/8 + t**3/12 - 37*t. Factor r(i).
i*(i + 1)**3/2
Let p(s) be the second derivative of -27/8*s**2 + 1/80*s**5 - s + 9/8*s**3 + 0 - 3/16*s**4. Suppose p(b) = 0. What is b?
3
Let r(i) be the first derivative of -4*i**3/3 + 12*i**2 - 36*i + 3. Factor r(l).
-4*(l - 3)**2
Suppose -4*z + 88 = -4*j + 24, 0 = -3*z - 2*j + 28. Factor -3/4 - 3/4*a**2 + 18*a**3 - z*a**4 - 9/2*a.
-3*(a - 1)**2*(4*a + 1)**2/4
Factor 2/11*q**2 + 8/11 - 8/11*q.
2*(q - 2)**2/11
Let p = 80 - 80. Let m be (-3 - -1) + 22/8. Let m*n**3 + 1/4*n**5 + p*n + 0 - 3/4*n**4 - 1/4*n**2 = 0. What is n?
0, 1
Let n = -3 - 0. Let c be (-1)/n*(-12)/(-14). Factor c*t + 0 - 2/7*t**2.
-2*t*(t - 1)/7
Let b = 17 + -16. Let m be 1/b + 1 + -2. Factor 4/3*y - 2/3*y**2 + m.
-2*y*(y - 2)/3
Let g(t) be the third derivative of -t**5/180 + t**4/72 - 27*t**2. Find u such that g(u) = 0.
0, 1
Let c(s) be the first derivative of 0*s**4 + 0*s + 0*s**2 - 1/270*s**5 - 1/1620*s**6 - 1 - 1/3*s**3. Let t(n) be the third derivative of c(n). Factor t(h).
-2*h*(h + 2)/9
Let 63*l - 55*l - 245 - 78*l - 5*l**2 = 0. Calculate l.
-7
Let w be -1 - (1/(-2) + (-2)/4). Factor 6*m + w*m**2 + 0 - 3/2*m**4 - 9/2*m**3.
-3*m*(m - 1)*(m + 2)**2/2
Let y(w) be the third derivative of -w**5/540 - w**4/108 - w**3/54 + 3*w**2. Solve y(i) = 0 for i.
-1
Let k = -104 - -262. Let g = -1102/7 + k. Factor 0 + 0*p + 0*p**2 + 2/7*p**4 - 2/7*p**5 + g*p**3.
-2*p**3*(p - 2)*(p + 1)/7
Let c = 212/3 - 70. Let o(t) be the first derivative of 4/3*t**2 + 1 + c*t**3 + 2/3*t. Suppose o(j) = 0. Calculate j.
-1, -1/3
Let u(o) be the third derivative of 5*o**2 - 1/6*o**4 + 0 + 1/10*o**5 + 1/420*o**7 + 0*o + 0*o**3 - 1/40*o**6. Find a, given that u(a) = 0.
0, 2
Suppose -2*s - s = 5*v - 9, s - 3*v = 3. Let g be (2/s)/(1/3). Factor -7/4*a - 3/4*a**3 + 1/2 + g*a**2.
-(a - 1)**2*(3*a - 2)/4
Factor -c - 3*c**3 + c**3 - 4*c**2 - c.
-2*c*(c + 1)**2
Factor -5*a**4 + 0 - 5*a + 380*a**2 + 5*a**3 - 375*a**2 + 0.
-5*a*(a - 1)**2*(a + 1)
Let f(y) = y + 9. Let m be f(-7). Let 0*z**m - 3*z - 3*z**2 + 3*z = 0. Calculate z.
0
Let l(h) = -2*h**2 + 1 + 6*h**5 + h**2 + h + 4*h**3 - 4*h**4 - 3*h**5. Let q(x) = x**5 + x**4 + x + 1. Let c(u) = -2*l(u) + 2*q(u). Solve c(n) = 0 for n.
0, 1/2, 1
Suppose 6*c - 6 = 3*c. Factor -3/4*g**c - 1/4*g + 1/2.
-(g + 1)*(3*g - 2)/4
Factor 8*w**3 + 10*w**2 + 6*w**4 + 28*w - 24*w - 4*w**4.
2*w*(w + 1)**2*(w + 2)
Factor -21/5*v**3 + 33/5*v**2 + 3/5*v**4 - 3*v + 0.
3*v*(v - 5)*(v - 1)**2/5
Let i(d) be the third derivative of d**5/20 - d**4/8 - 4*d**2. Factor i(f).
3*f*(f - 1)
Let w be ((-21)/(-6) - 6)*8/(-10). Suppose -1/6*c**w + 1/6*c + 0 = 0. Calculate c.
0, 1
Let y(t) be the second derivative of 3*t**7/14 + 7*t**6/10 - t**4 - 4*t. Find a, given that y(a) = 0.
-2, -1, 0, 2/3
Let p(f) = 4*f - 30. Let a be p(8). Let v(h) be the second derivative of 0 - 1/4*h**4 + 1/2*h**3 + 0*h**a + 3*h. Factor v(r).
-3*r*(r - 1)
Suppose -2*m**3 + 0*m**3 - 15*m**2 - 11*m**2 = 0. What is m?
-13, 0
Suppose -3*l + 3 = -18. Let z be 2 - 1 - (-6 + l). Factor z - 2/3*j**3 + 0*j**2 + 2/3*j.
-2*j*(j - 1)*(j + 1)/3
Suppose -4*j + 23 = 5*c, -3*c + 23 = 5*j + 4. Factor 4*g + j*g**3 - 14*g**2 + 4*g + 6*g**2.
2*g*(g - 2)**2
Let h = 6 + -12. Let m be 8/(-6) - 8/h. Factor m - 1/3*q**2 + 1/3*q.
-q*(q - 1)/3
Let f be (0 - -3)/(3/3). Factor 3*l**3 + l**4 + 4*l**2 + 5*l**4 - 13*l**f + 0*l**2.
2*l**2*(l - 1)*(3*l - 2)
Let o(x) be the first derivative of x**7/42 + x**6/10 - x**4/3 - 3*x + 4. Let p(c) be the first derivative of o(c). Solve p(f) = 0.
-2, 0, 1
Let u(o) = -o**2. Let f(h) = -2*h - 10. Let b be f(-6). Let k(d) = 10*d**2 - d. Let q(w) = b*k(w) + 22*u(w). Solve q(z) = 0 for z.
-1, 0
Suppose -683*a + 674*a = -18. Factor 7/5*j - 3/5 - 4/5*j**a.
-(j - 1)*(4*j - 3)/5
Let n(p) = -p**3 - 2*p**2 + p - 4. Let f be n(-3). Let v(u) be the first derivative of 0*u - 1/14*u**4 - 2 + 0*u**f + 2/21*u**3. Factor v(k).
-2*k**2*(k - 1)/7
Let d(n) be the second 